TSTP Solution File: SWV338-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV338-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 21:12:03 EDT 2022
% Result : Timeout 300.01s 300.02s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV338-1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 15 01:38:35 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.76/2.03 ============================== Prover9 ===============================
% 1.76/2.03 Prover9 (32) version 2009-11A, November 2009.
% 1.76/2.03 Process 3220 was started by sandbox on n011.cluster.edu,
% 1.76/2.03 Wed Jun 15 01:38:36 2022
% 1.76/2.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3050_n011.cluster.edu".
% 1.76/2.03 ============================== end of head ===========================
% 1.76/2.03
% 1.76/2.03 ============================== INPUT =================================
% 1.76/2.03
% 1.76/2.03 % Reading from file /tmp/Prover9_3050_n011.cluster.edu
% 1.76/2.03
% 1.76/2.03 set(prolog_style_variables).
% 1.76/2.03 set(auto2).
% 1.76/2.03 % set(auto2) -> set(auto).
% 1.76/2.03 % set(auto) -> set(auto_inference).
% 1.76/2.03 % set(auto) -> set(auto_setup).
% 1.76/2.03 % set(auto_setup) -> set(predicate_elim).
% 1.76/2.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.76/2.03 % set(auto) -> set(auto_limits).
% 1.76/2.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.76/2.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.76/2.03 % set(auto) -> set(auto_denials).
% 1.76/2.03 % set(auto) -> set(auto_process).
% 1.76/2.03 % set(auto2) -> assign(new_constants, 1).
% 1.76/2.03 % set(auto2) -> assign(fold_denial_max, 3).
% 1.76/2.03 % set(auto2) -> assign(max_weight, "200.000").
% 1.76/2.03 % set(auto2) -> assign(max_hours, 1).
% 1.76/2.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.76/2.03 % set(auto2) -> assign(max_seconds, 0).
% 1.76/2.03 % set(auto2) -> assign(max_minutes, 5).
% 1.76/2.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.76/2.03 % set(auto2) -> set(sort_initial_sos).
% 1.76/2.03 % set(auto2) -> assign(sos_limit, -1).
% 1.76/2.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.76/2.03 % set(auto2) -> assign(max_megs, 400).
% 1.76/2.03 % set(auto2) -> assign(stats, some).
% 1.76/2.03 % set(auto2) -> clear(echo_input).
% 1.76/2.03 % set(auto2) -> set(quiet).
% 1.76/2.03 % set(auto2) -> clear(print_initial_clauses).
% 1.76/2.03 % set(auto2) -> clear(print_given).
% 1.76/2.03 assign(lrs_ticks,-1).
% 1.76/2.03 assign(sos_limit,10000).
% 1.76/2.03 assign(order,kbo).
% 1.76/2.03 set(lex_order_vars).
% 1.76/2.03 clear(print_given).
% 1.76/2.03
% 1.76/2.03 % formulas(sos). % not echoed (2948 formulas)
% 1.76/2.03
% 1.76/2.03 ============================== end of input ==========================
% 1.76/2.03
% 1.76/2.03 % From the command line: assign(max_seconds, 300).
% 1.76/2.03
% 1.76/2.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.76/2.03
% 1.76/2.03 % Formulas that are not ordinary clauses:
% 1.76/2.03
% 1.76/2.03 ============================== end of process non-clausal formulas ===
% 1.76/2.03
% 1.76/2.03 ============================== PROCESS INITIAL CLAUSES ===============
% 1.76/2.03
% 1.76/2.03 ============================== PREDICATE ELIMINATION =================
% 1.76/2.03 1 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom). [assumption].
% 1.76/2.03 2 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom). [assumption].
% 1.76/2.03 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1,a,2,a)].
% 1.76/2.03 3 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom). [assumption].
% 1.76/2.03 Derived: c_lessequals(A,A,tc_nat). [resolve(3,a,2,a)].
% 1.76/2.03 4 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom). [assumption].
% 1.76/2.03 Derived: c_lessequals(A,A,tc_set(B)). [resolve(4,a,2,a)].
% 1.76/2.03 5 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 1.76/2.03 Derived: -class_LOrder_Ojoin__semilorder(A) | c_lessequals(B,B,A). [resolve(5,b,2,a)].
% 1.76/2.03 6 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom). [assumption].
% 1.76/2.03 Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(6,b,2,a)].
% 1.76/2.03 7 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom). [assumption].
% 1.76/2.03 Derived: -class_LOrder_Omeet__semilorder(A) | c_lessequals(B,B,A). [resolve(7,b,2,a)].
% 1.76/2.03 8 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom). [assumption].
% 1.76/2.03 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(B,B,A). [resolve(8,b,2,a)].
% 1.76/2.03 9 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom). [assumption].
% 1.76/2.03 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(B,B,A). [resolve(9,b,2,a)].
% 1.76/2.04 10 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(10,b,2,a)].
% 1.76/2.04 11 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(11,b,2,a)].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(12,b,2,a)].
% 1.76/2.04 13 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A). [resolve(13,b,2,a)].
% 1.76/2.04 14 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(14,b,2,a)].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,B,A). [resolve(15,b,2,a)].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(16,b,2,a)].
% 1.76/2.04 17 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_Orderings_Olinorder(A) | c_lessequals(B,B,A). [resolve(17,b,2,a)].
% 1.76/2.04 18 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom). [assumption].
% 1.76/2.04 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(18,a,1,a)].
% 1.76/2.04 Derived: class_Orderings_Oord(tc_nat). [resolve(18,a,3,a)].
% 1.76/2.04 Derived: class_Orderings_Oord(tc_set(A)). [resolve(18,a,4,a)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_LOrder_Ojoin__semilorder(A). [resolve(18,a,5,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(18,a,6,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_LOrder_Omeet__semilorder(A). [resolve(18,a,7,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(18,a,8,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(18,a,9,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(18,a,10,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(18,a,11,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(18,a,12,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(18,a,13,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(18,a,14,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(18,a,15,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(18,a,16,b)].
% 1.76/2.04 Derived: class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(18,a,17,b)].
% 1.76/2.04 19 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom). [assumption].
% 1.87/2.10 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(19,b,2,a)].
% 1.87/2.10 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].
% 1.87/2.10 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(20,b,2,a)].
% 1.87/2.10 21 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom). [assumption].
% 1.87/2.10 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A). [resolve(21,b,2,a)].
% 1.87/2.10 22 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom). [assumption].
% 1.87/2.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(22,b,2,a)].
% 1.87/2.10 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].
% 1.87/2.10 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,B,A). [resolve(23,b,2,a)].
% 1.87/2.10 24 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom). [assumption].
% 1.87/2.10 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,B,A). [resolve(24,b,2,a)].
% 1.87/2.10 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].
% 1.87/2.10 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(25,b,2,a)].
% 1.87/2.10 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].
% 1.87/2.10 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(26,b,2,a)].
% 1.87/2.10 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].
% 1.87/2.10 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(27,b,2,a)].
% 1.87/2.10 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].
% 1.87/2.10 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A). [resolve(28,b,2,a)].
% 1.87/2.10 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].
% 1.87/2.10 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(29,b,2,a)].
% 1.87/2.10 30 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom). [assumption].
% 1.87/2.10 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(30,b,2,a)].
% 1.87/2.10 31 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom). [assumption].
% 1.87/2.10 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(31,b,2,a)].
% 1.87/2.10 32 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom). [assumption].
% 1.87/2.10 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(32,b,2,a)].
% 1.87/2.10 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(32,b,18,a)].
% 1.87/2.10 33 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl_0) # label(axiom). [assumption].
% 1.87/2.10 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(33,a,1,a)].
% 1.87/2.10 Derived: -c_less(A,A,tc_nat). [resolve(33,a,3,a)].
% 1.87/2.10 Derived: -c_less(A,A,tc_set(B)). [resolve(33,a,4,a)].
% 1.87/2.10 Derived: -c_less(A,A,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(33,a,5,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(33,a,6,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_LOrder_Omeet__semilorder(B). [resolve(33,a,7,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(33,a,8,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(33,a,9,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(33,a,10,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(33,a,11,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(33,a,12,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(33,a,13,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(33,a,14,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(33,a,15,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(33,a,16,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(33,a,17,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(33,a,19,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(33,a,20,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(33,a,21,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(33,a,22,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(33,a,23,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(33,a,24,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(33,a,25,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(33,a,26,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(33,a,27,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(33,a,28,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(33,a,29,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(33,a,30,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(33,a,31,b)].
% 1.89/2.12 Derived: -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(33,a,32,b)].
% 1.89/2.12 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].
% 1.89/2.12 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(34,a,1,a)].
% 1.89/2.12 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(34,a,3,a)].
% 1.89/2.12 Derived: -c_less(A,B,tc_set(C)) | c_SetInterval_OatLeastAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(34,a,4,a)].
% 1.89/2.12 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(34,a,5,b)].
% 1.89/2.12 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(34,a,6,b)].
% 1.89/2.12 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(34,a,7,b)].
% 1.89/2.12 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)].
% 1.89/2.12 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)].
% 1.89/2.12 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)].
% 1.89/2.12 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(34,a,17,b)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(34,a,32,b)].
% 1.89/2.13 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].
% 1.89/2.13 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(35,a,1,a)].
% 1.89/2.13 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(35,a,3,a)].
% 1.89/2.13 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_set(B)) = c_insert(A,c_emptyset,tc_set(B)). [resolve(35,a,4,a)].
% 1.89/2.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(35,a,5,b)].
% 1.89/2.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(35,a,6,b)].
% 1.89/2.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Omeet__semilorder(B). [resolve(35,a,7,b)].
% 1.89/2.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(35,a,8,b)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(35,a,17,b)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(35,a,32,b)].
% 1.89/2.13 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].
% 1.89/2.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(36,a,1,a)].
% 1.89/2.13 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(36,a,3,a)].
% 1.89/2.13 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OatLeastLessThan(B,A,tc_set(C)) = c_emptyset. [resolve(36,a,4,a)].
% 1.89/2.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(36,a,5,b)].
% 1.89/2.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(36,a,6,b)].
% 1.89/2.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(36,a,7,b)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(36,a,17,b)].
% 1.89/2.13 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)].
% 1.89/2.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(36,a,20,b)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(36,a,32,b)].
% 1.89/2.13 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].
% 1.89/2.13 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(37,a,1,a)].
% 1.89/2.13 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(37,a,3,a)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 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)].
% 1.89/2.13 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(37,a,19,b)].
% 1.89/2.13 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(37,a,20,b)].
% 1.89/2.13 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(37,a,21,b)].
% 1.89/2.13 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(37,a,22,b)].
% 1.89/2.13 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(37,a,23,b)].
% 1.89/2.13 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(37,a,24,b)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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].
% 1.89/2.14 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(38,a,1,a)].
% 1.89/2.14 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(38,a,3,a)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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].
% 1.89/2.14 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(39,a,1,a)].
% 1.89/2.14 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(39,a,3,a)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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].
% 1.89/2.14 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(40,a,1,a)].
% 1.89/2.14 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(40,a,3,a)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.14 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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].
% 1.89/2.15 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(41,a,1,a)].
% 1.89/2.15 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(41,a,3,a)].
% 1.89/2.15 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OgreaterThanAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(41,a,4,a)].
% 1.89/2.15 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(41,a,5,b)].
% 1.89/2.15 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(41,a,6,b)].
% 1.89/2.15 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(41,a,7,b)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(41,a,17,b)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(41,a,32,b)].
% 1.89/2.15 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].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 1.89/2.15 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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].
% 2.27/2.51 44 class_HOL_Oone(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_1) # label(axiom). [assumption].
% 2.27/2.51 45 class_HOL_Oone(tc_nat) # label(clsarity_nat_0) # label(axiom). [assumption].
% 2.27/2.51 46 -class_Numeral_Onumber__ring(A) | class_HOL_Oone(A) # label(clsrel_Numeral_Onumber__ring_20) # label(axiom). [assumption].
% 2.27/2.51 47 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_0) # label(axiom). [assumption].
% 2.27/2.51 48 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Omonoid__mult_0) # label(axiom). [assumption].
% 2.27/2.51 49 -class_Power_Orecpower(A) | class_HOL_Oone(A) # label(clsrel_Power_Orecpower_2) # label(axiom). [assumption].
% 2.27/2.51 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].
% 2.27/2.51 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].
% 2.27/2.51 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].
% 2.27/2.51 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].
% 2.27/2.51 54 -class_Ring__and__Field_Ofield(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ofield_13) # label(axiom). [assumption].
% 2.27/2.51 55 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oidom_13) # label(axiom). [assumption].
% 2.27/2.51 56 -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__field_16) # label(axiom). [assumption].
% 2.27/2.51 57 -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__idom_13) # label(axiom). [assumption].
% 2.27/2.51 58 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__semidom_7) # label(axiom). [assumption].
% 2.27/2.51 59 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oring__1_18) # label(axiom). [assumption].
% 2.27/2.51 60 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1_2) # label(axiom). [assumption].
% 2.27/2.51 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].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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].
% 2.27/2.51 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].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.51 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.52 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.53 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)].
% 2.27/2.54 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].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.27/2.54 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 71 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_0) # label(axiom). [assumption].
% 2.47/2.73 72 class_Ring__and__Field_Osemiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_10) # label(axiom). [assumption].
% 2.47/2.73 73 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat_18) # label(axiom). [assumption].
% 2.47/2.73 74 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom). [assumption].
% 2.47/2.73 75 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Power_Orecpower_10) # label(axiom). [assumption].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 83 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ofield_20) # label(axiom). [assumption].
% 2.47/2.73 84 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom). [assumption].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 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].
% 2.47/2.73 98 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring_0) # label(axiom). [assumption].
% 2.47/2.73 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].
% 2.47/2.73 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(71,a,72,a)].
% 2.47/2.73 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(71,a,73,a)].
% 2.47/2.73 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(71,a,74,b)].
% 2.47/2.73 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(71,a,75,b)].
% 2.47/2.73 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(71,a,76,b)].
% 2.47/2.73 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(71,a,77,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(71,a,78,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(71,a,79,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(71,a,80,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(71,a,81,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(71,a,82,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(71,a,83,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(71,a,84,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(71,a,85,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(71,a,86,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(71,a,87,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(71,a,88,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(71,a,89,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(71,a,90,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(71,a,91,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(71,a,92,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(71,a,93,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(71,a,94,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(71,a,95,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(71,a,96,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(71,a,97,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(71,a,98,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(71,a,99,b)].
% 2.47/2.74 100 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_1) # label(axiom). [assumption].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(100,a,72,a)].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(100,a,73,a)].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(100,a,74,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(100,a,75,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(100,a,76,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(100,a,77,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(100,a,78,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(100,a,79,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(100,a,80,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(100,a,81,b)].
% 2.47/2.74 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(100,a,82,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(100,a,83,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(100,a,84,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(100,a,85,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(100,a,86,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(100,a,87,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(100,a,88,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(100,a,89,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(100,a,90,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(100,a,91,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(100,a,92,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(100,a,93,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(100,a,94,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(100,a,95,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(100,a,96,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(100,a,97,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(100,a,98,b)].
% 2.47/2.75 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(100,a,99,b)].
% 2.47/2.75 101 -class_Ring__and__Field_Osemiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring_2) # label(axiom). [assumption].
% 2.47/2.75 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(101,a,72,a)].
% 2.47/2.75 Derived: class_HOL_Oplus(tc_nat). [resolve(101,a,73,a)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(101,a,74,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(101,a,75,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(101,a,76,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(101,a,77,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(101,a,78,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(101,a,79,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(101,a,80,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(101,a,81,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(101,a,82,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(101,a,83,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(101,a,84,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(101,a,85,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(101,a,86,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(101,a,87,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(101,a,88,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(101,a,89,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(101,a,90,b)].
% 2.47/2.75 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(101,a,91,b)].
% 2.47/2.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(101,a,92,b)].
% 2.47/2.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(101,a,93,b)].
% 2.47/2.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(101,a,94,b)].
% 2.47/2.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(101,a,95,b)].
% 2.47/2.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(101,a,96,b)].
% 2.47/2.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(101,a,97,b)].
% 2.47/2.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(101,a,98,b)].
% 2.47/2.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(101,a,99,b)].
% 2.47/2.77 102 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring_3) # label(axiom). [assumption].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(102,a,72,a)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(102,a,73,a)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(102,a,74,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(102,a,75,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(102,a,76,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(102,a,77,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(102,a,78,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(102,a,79,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(102,a,80,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(102,a,81,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(102,a,82,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(102,a,83,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(102,a,84,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(102,a,85,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(102,a,86,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(102,a,87,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(102,a,88,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(102,a,89,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(102,a,90,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(102,a,91,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(102,a,92,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(102,a,93,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(102,a,94,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(102,a,95,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(102,a,96,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(102,a,97,b)].
% 2.47/2.77 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(102,a,98,b)].
% 2.47/2.81 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(102,a,99,b)].
% 2.47/2.81 103 -class_Ring__and__Field_Osemiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring_4) # label(axiom). [assumption].
% 2.47/2.81 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(103,a,72,a)].
% 2.47/2.81 Derived: class_HOL_Otimes(tc_nat). [resolve(103,a,73,a)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(103,a,74,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(103,a,75,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(103,a,76,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(103,a,77,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(103,a,78,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(103,a,79,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(103,a,80,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(103,a,81,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(103,a,82,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(103,a,83,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(103,a,84,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(103,a,85,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(103,a,86,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(103,a,87,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(103,a,88,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(103,a,89,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(103,a,90,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(103,a,91,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(103,a,92,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(103,a,93,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(103,a,94,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(103,a,95,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(103,a,96,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(103,a,97,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(103,a,98,b)].
% 2.47/2.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(103,a,99,b)].
% 2.47/2.81 104 -class_Ring__and__Field_Osemiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0_0) # label(axiom). [assumption].
% 2.47/2.81 105 -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].
% 2.47/2.81 106 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1_4) # label(axiom). [assumption].
% 2.47/2.81 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(106,b,101,a)].
% 2.47/2.81 107 -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].
% 2.47/2.81 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(107,b,102,a)].
% 2.47/2.81 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(107,b,103,a)].
% 2.47/2.81 108 -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].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.47/2.81 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)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(108,b,88,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(108,b,89,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(108,b,90,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(108,b,91,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(108,b,92,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(108,b,93,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(108,b,94,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(108,b,95,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(108,b,96,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(108,b,97,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring(A). [resolve(108,b,98,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(108,b,99,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__0(A). [resolve(108,b,104,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(108,b,105,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(108,b,106,b)].
% 2.59/2.82 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(108,b,107,b)].
% 2.59/2.83 109 -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].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.59/2.83 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)].
% 2.78/3.06 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)].
% 2.78/3.06 110 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_0) # label(axiom). [assumption].
% 2.78/3.06 111 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom). [assumption].
% 2.78/3.06 112 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom). [assumption].
% 2.78/3.06 113 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom). [assumption].
% 2.78/3.06 114 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom). [assumption].
% 2.78/3.06 115 -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].
% 2.78/3.06 116 -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].
% 2.78/3.06 117 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom). [assumption].
% 2.78/3.06 118 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom). [assumption].
% 2.78/3.06 119 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_3) # label(axiom). [assumption].
% 2.78/3.06 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(119,a,111,a)].
% 2.78/3.06 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(119,a,112,a)].
% 2.78/3.06 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(119,a,113,b)].
% 2.78/3.06 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Power_Orecpower(A). [resolve(119,a,114,b)].
% 2.78/3.06 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(119,a,115,b)].
% 2.78/3.06 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(119,a,116,b)].
% 2.78/3.06 120 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom). [assumption].
% 2.78/3.06 121 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom). [assumption].
% 2.78/3.06 122 -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].
% 2.78/3.06 123 -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].
% 2.78/3.06 124 -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].
% 2.78/3.06 125 -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].
% 2.78/3.06 126 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom). [assumption].
% 2.78/3.06 127 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom). [assumption].
% 2.78/3.06 128 -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].
% 2.99/3.23 129 -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].
% 2.99/3.23 130 -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].
% 2.99/3.23 131 -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].
% 2.99/3.23 132 -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].
% 2.99/3.23 133 -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].
% 2.99/3.23 134 -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].
% 2.99/3.23 135 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(71,a,78,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(135,b,111,a)].
% 2.99/3.23 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(135,b,112,a)].
% 2.99/3.23 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(135,b,113,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(135,b,114,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(135,b,115,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(135,b,116,b)].
% 2.99/3.23 136 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(100,a,78,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(136,b,111,a)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(136,b,112,a)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(136,b,113,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(136,b,114,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(136,b,115,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(136,b,116,b)].
% 2.99/3.23 137 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(101,a,78,b)].
% 2.99/3.23 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(137,b,111,a)].
% 2.99/3.23 Derived: class_HOL_Oplus(tc_nat). [resolve(137,b,112,a)].
% 2.99/3.23 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(137,b,113,b)].
% 2.99/3.23 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(137,b,114,b)].
% 2.99/3.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(137,b,115,b)].
% 2.99/3.23 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(137,b,116,b)].
% 2.99/3.23 138 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(102,a,78,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(138,b,111,a)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(138,b,112,a)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(138,b,113,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(138,b,114,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(138,b,115,b)].
% 2.99/3.23 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(138,b,116,b)].
% 2.99/3.23 139 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(103,a,78,b)].
% 2.99/3.30 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(139,b,111,a)].
% 2.99/3.30 Derived: class_HOL_Otimes(tc_nat). [resolve(139,b,112,a)].
% 2.99/3.30 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(139,b,113,b)].
% 2.99/3.30 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(139,b,114,b)].
% 2.99/3.30 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(139,b,115,b)].
% 2.99/3.30 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(139,b,116,b)].
% 2.99/3.30 140 -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)].
% 2.99/3.30 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(140,c,111,a)].
% 2.99/3.30 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(140,c,112,a)].
% 2.99/3.30 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)].
% 2.99/3.30 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)].
% 2.99/3.30 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)].
% 2.99/3.30 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)].
% 2.99/3.30 141 -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)].
% 2.99/3.30 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(141,c,111,a)].
% 2.99/3.30 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(141,c,112,a)].
% 2.99/3.30 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)].
% 2.99/3.30 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)].
% 2.99/3.30 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)].
% 2.99/3.30 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)].
% 2.99/3.30 142 -class_OrderedGroup_Ocomm__monoid__add(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_0) # label(axiom). [assumption].
% 3.08/3.31 143 class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_12) # label(axiom). [assumption].
% 3.08/3.31 144 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat_20) # label(axiom). [assumption].
% 3.08/3.31 145 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom). [assumption].
% 3.08/3.31 146 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Oab__group__add_1) # label(axiom). [assumption].
% 3.08/3.31 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(142,a,143,a)].
% 3.08/3.31 Derived: class_HOL_Ozero(tc_nat). [resolve(142,a,144,a)].
% 3.08/3.31 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(142,a,145,b)].
% 3.08/3.31 Derived: class_HOL_Ozero(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(142,a,146,b)].
% 3.08/3.31 147 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom). [assumption].
% 3.08/3.32 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(147,a,146,b)].
% 3.08/3.32 148 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_2) # label(axiom). [assumption].
% 3.08/3.32 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(148,a,146,b)].
% 3.08/3.32 149 -class_OrderedGroup_Ocomm__monoid__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_3) # label(axiom). [assumption].
% 3.08/3.32 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(149,a,146,b)].
% 3.08/3.32 150 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom). [assumption].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(150,b,147,a)].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(150,b,148,a)].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A). [resolve(150,b,149,a)].
% 3.08/3.32 151 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_4) # label(axiom). [assumption].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(151,b,147,a)].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(151,b,148,a)].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(151,b,149,a)].
% 3.08/3.32 152 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_3) # label(axiom). [assumption].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(152,b,147,a)].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(152,b,148,a)].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A). [resolve(152,b,149,a)].
% 3.08/3.32 153 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_3) # label(axiom). [assumption].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(153,b,147,a)].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(153,b,148,a)].
% 3.08/3.32 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A). [resolve(153,b,149,a)].
% 3.08/3.32 154 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_2) # label(axiom). [assumption].
% 3.08/3.33 155 -class_Power_Orecpower(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Power_Orecpower_12) # label(axiom). [assumption].
% 3.08/3.33 Derived: -class_Power_Orecpower(A) | class_HOL_Ozero(A). [resolve(155,b,142,a)].
% 3.08/3.33 156 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_7) # label(axiom). [assumption].
% 3.08/3.33 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(156,b,142,a)].
% 3.08/3.33 157 -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].
% 3.08/3.33 158 -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].
% 3.08/3.33 159 -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].
% 3.08/3.33 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(159,b,142,a)].
% 3.08/3.33 160 -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].
% 3.08/3.33 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A). [resolve(160,b,142,a)].
% 3.08/3.33 161 -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].
% 3.08/3.33 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Ozero(A). [resolve(161,b,142,a)].
% 3.08/3.33 162 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ofield_23) # label(axiom). [assumption].
% 3.08/3.33 163 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom). [assumption].
% 3.08/3.33 164 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_17) # label(axiom). [assumption].
% 3.08/3.33 165 -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].
% 3.08/3.33 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Ozero(A). [resolve(165,b,142,a)].
% 3.08/3.33 166 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__field_25) # label(axiom). [assumption].
% 3.08/3.33 167 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_23) # label(axiom). [assumption].
% 3.08/3.33 168 -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].
% 3.08/3.33 169 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_17) # label(axiom). [assumption].
% 3.08/3.33 170 -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].
% 3.08/3.33 171 -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].
% 3.08/3.33 172 -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].
% 3.08/3.33 173 -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].
% 3.08/3.33 174 -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].
% 3.08/3.39 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Ozero(A). [resolve(174,b,142,a)].
% 3.08/3.39 175 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_10) # label(axiom). [assumption].
% 3.08/3.39 176 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_4) # label(axiom). [assumption].
% 3.08/3.39 177 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom). [assumption].
% 3.08/3.39 178 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring__1_10) # label(axiom). [assumption].
% 3.08/3.39 179 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_6) # label(axiom). [assumption].
% 3.08/3.39 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(179,b,147,a)].
% 3.08/3.39 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(179,b,148,a)].
% 3.08/3.39 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A). [resolve(179,b,149,a)].
% 3.08/3.39 180 -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].
% 3.08/3.39 181 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_7) # label(axiom). [assumption].
% 3.08/3.39 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(181,b,142,a)].
% 3.08/3.39 182 -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].
% 3.08/3.39 183 -class_OrderedGroup_Ocomm__monoid__add(A) | c_plus(B,c_0,A) = B # label(cls_OrderedGroup_Oadd__0__right_0) # label(axiom). [assumption].
% 3.08/3.39 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(183,a,143,a)].
% 3.08/3.39 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(183,a,144,a)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(183,a,145,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Oab__group__add(B). [resolve(183,a,146,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(183,a,150,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(183,a,151,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(183,a,152,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(183,a,153,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(183,a,154,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(183,a,155,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(183,a,156,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(183,a,157,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(183,a,158,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(183,a,159,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(183,a,160,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(183,a,161,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(183,a,162,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(183,a,163,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(183,a,164,b)].
% 3.08/3.39 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(183,a,165,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(183,a,166,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(183,a,167,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(183,a,168,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(183,a,169,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(183,a,170,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(183,a,171,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(183,a,172,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(183,a,173,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(183,a,174,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(183,a,175,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(183,a,176,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(183,a,177,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(183,a,178,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(183,a,179,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(183,a,180,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(183,a,181,b)].
% 3.17/3.40 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(183,a,182,b)].
% 3.17/3.40 184 -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].
% 3.17/3.40 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(184,a,143,a)].
% 3.17/3.40 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(184,a,144,a)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(184,a,145,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Oab__group__add(B). [resolve(184,a,146,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(184,a,150,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(184,a,151,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(184,a,152,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(184,a,153,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(184,a,154,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(184,a,155,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(184,a,156,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(184,a,157,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(184,a,158,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(184,a,159,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(184,a,160,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(184,a,161,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(184,a,162,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(184,a,163,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(184,a,164,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(184,a,165,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(184,a,166,b)].
% 3.17/3.40 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(184,a,167,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(184,a,168,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(184,a,169,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(184,a,170,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(184,a,171,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(184,a,172,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(184,a,173,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(184,a,174,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(184,a,175,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(184,a,176,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(184,a,177,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(184,a,178,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(184,a,179,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(184,a,180,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(184,a,181,b)].
% 3.38/3.63 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(184,a,182,b)].
% 3.38/3.63 185 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_1) # label(axiom). [assumption].
% 3.38/3.63 186 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom). [assumption].
% 3.38/3.63 187 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom). [assumption].
% 3.38/3.63 188 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom). [assumption].
% 3.38/3.63 189 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom). [assumption].
% 3.38/3.63 190 -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].
% 3.38/3.63 191 -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].
% 3.38/3.63 192 -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].
% 3.38/3.63 193 -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].
% 3.38/3.63 194 -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].
% 3.38/3.63 195 -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].
% 3.38/3.63 196 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom). [assumption].
% 3.38/3.63 197 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom). [assumption].
% 3.38/3.63 198 -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].
% 3.38/3.63 199 -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].
% 3.38/3.63 200 -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].
% 3.45/3.68 201 -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].
% 3.45/3.68 202 -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].
% 3.45/3.68 203 -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].
% 3.45/3.68 204 -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].
% 3.45/3.68 205 -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].
% 3.45/3.68 206 -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].
% 3.45/3.68 207 -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].
% 3.45/3.68 208 -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].
% 3.45/3.68 209 -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].
% 3.45/3.68 210 -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].
% 3.45/3.68 211 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom). [assumption].
% 3.45/3.68 212 -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].
% 3.45/3.68 213 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom). [assumption].
% 3.45/3.68 214 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom). [assumption].
% 3.45/3.68 215 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom). [assumption].
% 3.45/3.68 216 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom). [assumption].
% 3.45/3.68 217 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom). [assumption].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(217,a,191,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(217,a,192,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(217,a,196,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(217,a,197,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(217,a,198,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(217,a,200,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(217,a,201,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(217,a,202,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(217,a,203,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(217,a,204,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(217,a,205,b)].
% 3.45/3.68 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(217,a,206,b)].
% 3.60/3.85 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(217,a,207,b)].
% 3.60/3.85 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(217,a,209,b)].
% 3.60/3.85 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(217,a,210,b)].
% 3.60/3.85 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(217,a,211,b)].
% 3.60/3.85 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(217,a,212,b)].
% 3.60/3.85 218 -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].
% 3.60/3.85 219 -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].
% 3.60/3.85 220 -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].
% 3.60/3.85 221 -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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 222 -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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.85 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 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)].
% 3.60/3.86 223 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(179,b,147,a)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(223,a,186,a)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(223,a,187,a)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(223,a,188,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(223,a,189,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(223,a,190,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(223,a,191,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(223,a,192,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(223,a,193,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(223,a,194,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(223,a,195,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(223,a,196,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(223,a,197,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(223,a,198,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(223,a,199,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(223,a,200,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(223,a,201,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(223,a,202,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(223,a,203,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(223,a,204,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(223,a,205,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(223,a,206,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(223,a,207,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(223,a,208,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(223,a,209,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(223,a,210,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(223,a,211,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(223,a,212,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(223,a,218,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(223,a,219,b)].
% 3.60/3.86 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(223,a,220,b)].
% 3.60/3.86 224 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(179,b,148,a)].
% 3.60/3.86 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(224,a,186,a)].
% 3.60/3.86 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(224,a,187,a)].
% 3.60/3.86 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(224,a,188,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(224,a,189,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(224,a,190,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(224,a,191,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(224,a,192,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(224,a,193,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(224,a,194,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(224,a,195,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(224,a,196,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(224,a,197,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(224,a,198,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(224,a,199,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(224,a,200,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(224,a,201,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(224,a,202,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(224,a,203,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(224,a,204,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(224,a,205,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(224,a,206,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(224,a,207,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(224,a,208,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(224,a,209,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(224,a,210,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(224,a,211,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(224,a,212,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(224,a,218,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(224,a,219,b)].
% 3.60/3.87 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(224,a,220,b)].
% 3.60/3.87 225 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A). [resolve(179,b,149,a)].
% 3.60/3.87 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(225,a,186,a)].
% 3.60/3.87 Derived: class_HOL_Oplus(tc_nat). [resolve(225,a,187,a)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(225,a,188,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(225,a,189,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(225,a,190,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(225,a,191,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(225,a,192,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(225,a,193,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(225,a,194,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(225,a,195,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(225,a,196,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(225,a,197,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(225,a,198,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(225,a,199,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(225,a,200,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(225,a,201,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(225,a,202,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(225,a,203,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(225,a,204,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(225,a,205,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(225,a,206,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(225,a,207,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(225,a,208,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(225,a,209,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(225,a,210,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(225,a,211,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(225,a,212,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(225,a,218,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(225,a,219,b)].
% 3.60/3.87 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(225,a,220,b)].
% 3.60/3.87 226 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(183,a,179,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(226,b,186,a)].
% 3.60/3.87 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(226,b,187,a)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(226,b,188,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(226,b,189,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(226,b,190,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(226,b,191,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(226,b,192,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(226,b,193,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(226,b,194,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(226,b,195,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(226,b,196,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(226,b,197,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(226,b,198,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(226,b,199,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(226,b,200,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(226,b,201,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(226,b,202,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(226,b,203,b)].
% 3.60/3.87 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(226,b,204,b)].
% 3.68/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(226,b,205,b)].
% 3.68/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(226,b,206,b)].
% 3.68/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(226,b,207,b)].
% 3.68/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(226,b,208,b)].
% 3.68/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(226,b,209,b)].
% 3.68/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(226,b,210,b)].
% 3.68/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(226,b,211,b)].
% 3.68/3.96 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(226,b,212,b)].
% 3.68/3.96 227 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(184,a,179,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(227,b,186,a)].
% 3.68/3.96 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(227,b,187,a)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(227,b,188,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(227,b,189,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(227,b,190,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(227,b,191,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(227,b,192,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(227,b,193,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(227,b,194,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(227,b,195,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(227,b,196,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(227,b,197,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(227,b,198,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(227,b,199,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(227,b,200,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(227,b,201,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(227,b,202,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(227,b,203,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(227,b,204,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(227,b,205,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(227,b,206,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(227,b,207,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(227,b,208,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(227,b,209,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(227,b,210,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(227,b,211,b)].
% 3.68/3.96 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(227,b,212,b)].
% 3.68/3.96 228 -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].
% 3.68/3.96 229 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom). [assumption].
% 3.68/3.96 230 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom). [assumption].
% 3.91/4.16 231 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom). [assumption].
% 3.91/4.16 232 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom). [assumption].
% 3.91/4.16 233 -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].
% 3.91/4.16 234 -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].
% 3.91/4.16 235 -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].
% 3.91/4.16 236 -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].
% 3.91/4.16 237 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_5) # label(axiom). [assumption].
% 3.91/4.16 238 -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].
% 3.91/4.16 239 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_7) # label(axiom). [assumption].
% 3.91/4.16 240 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_9) # label(axiom). [assumption].
% 3.91/4.16 241 -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].
% 3.91/4.16 242 -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].
% 3.91/4.16 243 -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].
% 3.91/4.16 244 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ofield_15) # label(axiom). [assumption].
% 3.91/4.16 245 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oidom_15) # label(axiom). [assumption].
% 3.91/4.16 246 -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].
% 3.91/4.16 247 -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].
% 3.91/4.16 248 -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].
% 3.91/4.16 249 -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].
% 3.91/4.16 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(249,b,228,a)].
% 3.91/4.16 250 -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].
% 3.91/4.16 251 -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].
% 3.91/4.16 252 -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].
% 3.91/4.16 253 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(71,a,79,b)].
% 3.91/4.20 254 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(100,a,79,b)].
% 3.91/4.20 255 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(101,a,79,b)].
% 3.91/4.20 256 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(102,a,79,b)].
% 3.91/4.20 257 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(103,a,79,b)].
% 3.91/4.20 258 -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)].
% 3.91/4.20 259 -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)].
% 3.91/4.20 260 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(183,a,158,b)].
% 3.91/4.20 261 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(184,a,158,b)].
% 3.91/4.20 262 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(217,a,192,b)].
% 3.91/4.20 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(262,b,229,a)].
% 3.91/4.20 Derived: class_HOL_Ozero(tc_nat). [resolve(262,b,230,a)].
% 3.91/4.20 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(262,b,231,b)].
% 3.91/4.20 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(262,b,232,b)].
% 3.91/4.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(262,b,233,b)].
% 3.91/4.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(262,b,234,b)].
% 3.91/4.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(262,b,241,b)].
% 3.91/4.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(262,b,242,b)].
% 3.91/4.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(262,b,243,b)].
% 3.91/4.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(262,b,246,b)].
% 3.91/4.20 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(262,b,252,b)].
% 3.91/4.20 263 -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)].
% 3.91/4.20 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)].
% 3.91/4.20 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)].
% 3.91/4.20 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)].
% 3.91/4.20 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)].
% 3.91/4.20 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)].
% 3.91/4.20 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)].
% 3.91/4.22 264 -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)].
% 3.91/4.22 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)].
% 3.91/4.22 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)].
% 3.91/4.22 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)].
% 3.91/4.22 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)].
% 3.91/4.22 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)].
% 3.91/4.22 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)].
% 3.91/4.22 265 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(223,a,192,b)].
% 3.91/4.22 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(265,b,229,a)].
% 3.91/4.22 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(265,b,230,a)].
% 3.91/4.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(265,b,231,b)].
% 3.91/4.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(265,b,232,b)].
% 3.91/4.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(265,b,233,b)].
% 3.91/4.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(265,b,234,b)].
% 3.91/4.22 266 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(224,a,192,b)].
% 3.91/4.22 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(266,b,229,a)].
% 3.91/4.22 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(266,b,230,a)].
% 3.91/4.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(266,b,231,b)].
% 3.91/4.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(266,b,232,b)].
% 3.91/4.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(266,b,233,b)].
% 3.91/4.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(266,b,234,b)].
% 3.91/4.22 267 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(225,a,192,b)].
% 3.91/4.22 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(267,b,229,a)].
% 3.91/4.22 Derived: class_HOL_Oplus(tc_nat). [resolve(267,b,230,a)].
% 3.91/4.22 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(267,b,231,b)].
% 3.91/4.22 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(267,b,232,b)].
% 3.91/4.22 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(267,b,233,b)].
% 3.91/4.22 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(267,b,234,b)].
% 3.91/4.22 268 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(226,b,192,b)].
% 3.91/4.22 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(268,b,229,a)].
% 3.91/4.22 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(268,b,230,a)].
% 3.91/4.22 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(268,b,231,b)].
% 4.07/4.29 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(268,b,232,b)].
% 4.07/4.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(268,b,233,b)].
% 4.07/4.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(268,b,234,b)].
% 4.07/4.29 269 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(227,b,192,b)].
% 4.07/4.29 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(269,b,229,a)].
% 4.07/4.29 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(269,b,230,a)].
% 4.07/4.29 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(269,b,231,b)].
% 4.07/4.29 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(269,b,232,b)].
% 4.07/4.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(269,b,233,b)].
% 4.07/4.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(269,b,234,b)].
% 4.07/4.29 270 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom). [assumption].
% 4.07/4.29 271 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom). [assumption].
% 4.07/4.29 272 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom). [assumption].
% 4.07/4.29 273 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom). [assumption].
% 4.07/4.29 274 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom). [assumption].
% 4.07/4.29 275 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 4.07/4.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(270,a,275,b)].
% 4.07/4.29 276 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom). [assumption].
% 4.07/4.29 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(276,a,275,b)].
% 4.07/4.29 277 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom). [assumption].
% 4.07/4.29 278 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_11) # label(axiom). [assumption].
% 4.07/4.29 279 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_12) # label(axiom). [assumption].
% 4.07/4.29 280 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_12) # label(axiom). [assumption].
% 4.07/4.29 281 -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].
% 4.07/4.29 282 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_6) # label(axiom). [assumption].
% 4.07/4.29 283 -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].
% 4.07/4.29 284 -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].
% 4.07/4.29 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(284,b,270,a)].
% 4.07/4.29 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(284,b,276,a)].
% 4.07/4.34 285 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom). [assumption].
% 4.07/4.34 286 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_15) # label(axiom). [assumption].
% 4.07/4.34 287 -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].
% 4.07/4.34 288 -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].
% 4.07/4.34 289 -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].
% 4.07/4.34 290 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom). [assumption].
% 4.07/4.34 291 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom). [assumption].
% 4.07/4.34 292 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_21) # label(axiom). [assumption].
% 4.07/4.34 293 -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].
% 4.07/4.34 294 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_28) # label(axiom). [assumption].
% 4.07/4.34 295 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_27) # label(axiom). [assumption].
% 4.07/4.34 296 -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].
% 4.07/4.34 297 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_21) # label(axiom). [assumption].
% 4.07/4.34 298 -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].
% 4.07/4.34 299 -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].
% 4.07/4.34 300 -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].
% 4.07/4.34 301 -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].
% 4.07/4.34 302 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_5) # label(axiom). [assumption].
% 4.07/4.34 303 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom). [assumption].
% 4.07/4.34 304 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_5) # label(axiom). [assumption].
% 4.07/4.34 305 -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].
% 4.07/4.34 306 -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].
% 4.07/4.34 307 -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].
% 4.07/4.35 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(307,a,271,a)].
% 4.07/4.35 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(307,a,272,a)].
% 4.07/4.35 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(307,a,273,b)].
% 4.07/4.35 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(307,a,274,b)].
% 4.07/4.35 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)].
% 4.07/4.35 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(307,a,277,b)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(307,a,285,b)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(307,a,290,b)].
% 4.07/4.35 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(307,a,291,b)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.07/4.35 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(307,a,303,b)].
% 4.07/4.35 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)].
% 4.07/4.35 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)].
% 4.14/4.36 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)].
% 4.14/4.36 308 -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].
% 4.14/4.36 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(308,a,271,a)].
% 4.14/4.36 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(308,a,272,a)].
% 4.14/4.36 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(308,a,273,b)].
% 4.14/4.36 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(308,a,274,b)].
% 4.14/4.36 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)].
% 4.14/4.36 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(308,a,277,b)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(308,a,285,b)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(308,a,290,b)].
% 4.14/4.36 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(308,a,291,b)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.14/4.36 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)].
% 4.37/4.61 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(308,a,303,b)].
% 4.37/4.61 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)].
% 4.37/4.61 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)].
% 4.37/4.61 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)].
% 4.37/4.61 309 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) # label(axiom). [assumption].
% 4.37/4.61 310 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom). [assumption].
% 4.37/4.61 311 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom). [assumption].
% 4.37/4.61 312 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom). [assumption].
% 4.37/4.61 313 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom). [assumption].
% 4.37/4.61 314 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 4.37/4.61 315 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 4.37/4.61 316 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom). [assumption].
% 4.37/4.61 317 -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].
% 4.37/4.61 318 -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].
% 4.37/4.61 319 -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].
% 4.37/4.61 320 -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].
% 4.37/4.61 321 -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].
% 4.37/4.61 322 -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].
% 4.37/4.61 323 -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].
% 4.37/4.61 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(323,b,309,a)].
% 4.37/4.61 324 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom). [assumption].
% 4.37/4.61 325 -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].
% 4.37/4.61 326 -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].
% 4.37/4.61 327 -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].
% 4.59/4.84 328 -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].
% 4.59/4.84 329 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom). [assumption].
% 4.59/4.84 330 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom). [assumption].
% 4.59/4.84 331 -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].
% 4.59/4.84 332 -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].
% 4.59/4.84 333 -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].
% 4.59/4.84 334 -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].
% 4.59/4.84 335 -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].
% 4.59/4.84 336 -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].
% 4.59/4.84 337 -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].
% 4.59/4.84 338 -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].
% 4.59/4.84 339 -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].
% 4.59/4.84 340 -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].
% 4.59/4.84 341 -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].
% 4.59/4.84 342 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom). [assumption].
% 4.59/4.84 343 -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].
% 4.59/4.84 344 -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].
% 4.59/4.84 345 -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].
% 4.59/4.84 346 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(270,a,275,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(346,b,310,a)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(346,b,311,a)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(346,b,312,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(346,b,313,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(346,b,316,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(346,b,317,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(346,b,318,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(346,b,319,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(346,b,320,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(346,b,321,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(346,b,322,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(346,b,324,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(346,b,325,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(346,b,326,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(346,b,327,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(346,b,328,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(346,b,329,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(346,b,330,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(346,b,331,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(346,b,332,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(346,b,333,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(346,b,334,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(346,b,335,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(346,b,336,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(346,b,337,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(346,b,338,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(346,b,339,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(346,b,340,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(346,b,341,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(346,b,342,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(346,b,343,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(346,b,344,b)].
% 4.59/4.84 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(346,b,345,b)].
% 4.59/4.84 347 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(276,a,275,b)].
% 4.59/4.84 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(347,b,310,a)].
% 4.59/4.84 Derived: class_HOL_Oplus(tc_nat). [resolve(347,b,311,a)].
% 4.59/4.84 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(347,b,312,b)].
% 4.59/4.84 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(347,b,313,b)].
% 4.59/4.84 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(347,b,316,b)].
% 4.59/4.84 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(347,b,317,b)].
% 4.59/4.84 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(347,b,318,b)].
% 4.59/4.84 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(347,b,319,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(347,b,320,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(347,b,321,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(347,b,322,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(347,b,324,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(347,b,325,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(347,b,326,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(347,b,327,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(347,b,328,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(347,b,329,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(347,b,330,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(347,b,331,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(347,b,332,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(347,b,333,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(347,b,334,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(347,b,335,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(347,b,336,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(347,b,337,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(347,b,338,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(347,b,339,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(347,b,340,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(347,b,341,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(347,b,342,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(347,b,343,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(347,b,344,b)].
% 4.65/4.93 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(347,b,345,b)].
% 4.65/4.93 348 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Ocancel__ab__semigroup__add(C). [resolve(307,a,275,b)].
% 4.65/4.93 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(348,c,310,a)].
% 4.65/4.93 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(348,c,311,a)].
% 4.65/4.93 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(348,c,312,b)].
% 4.65/4.93 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(348,c,313,b)].
% 4.65/4.93 349 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Ocancel__ab__semigroup__add(C). [resolve(308,a,275,b)].
% 4.65/4.93 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(349,c,310,a)].
% 4.65/4.93 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(349,c,311,a)].
% 4.65/4.93 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(349,c,312,b)].
% 4.65/4.93 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(349,c,313,b)].
% 4.65/4.93 350 -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].
% 4.65/4.93 351 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom). [assumption].
% 4.65/4.93 352 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom). [assumption].
% 4.65/4.94 353 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom). [assumption].
% 4.65/4.94 354 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom). [assumption].
% 4.65/4.94 355 -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].
% 4.65/4.94 356 -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].
% 4.65/4.94 357 -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].
% 4.65/4.94 358 -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].
% 4.65/4.94 359 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_18) # label(axiom). [assumption].
% 4.65/4.94 360 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_18) # label(axiom). [assumption].
% 4.65/4.94 361 -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].
% 4.65/4.94 362 -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].
% 4.65/4.94 363 -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].
% 4.65/4.94 364 -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].
% 4.65/4.94 365 -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].
% 4.65/4.94 366 -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].
% 4.65/4.94 367 -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].
% 4.65/4.94 368 -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].
% 4.65/4.94 369 -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].
% 4.65/4.94 370 -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].
% 4.65/4.94 371 -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].
% 4.65/4.94 372 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring_12) # label(axiom). [assumption].
% 4.65/4.94 373 -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].
% 4.65/4.94 374 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_3) # label(axiom). [assumption].
% 4.65/4.94 375 -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].
% 4.81/5.03 376 -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].
% 4.81/5.03 377 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_7) # label(axiom). [assumption].
% 4.81/5.03 378 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_8) # label(axiom). [assumption].
% 4.81/5.03 379 -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].
% 4.81/5.03 380 -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].
% 4.81/5.03 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(380,a,351,a)].
% 4.81/5.03 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(380,a,352,a)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(380,a,353,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(380,a,354,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(380,a,355,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(380,a,356,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(380,a,357,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(380,a,358,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(380,a,359,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(380,a,360,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(380,a,361,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(380,a,362,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(380,a,363,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(380,a,364,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(380,a,365,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(380,a,366,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(380,a,367,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(380,a,368,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(380,a,369,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(380,a,370,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(380,a,371,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(380,a,372,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(380,a,373,b)].
% 4.81/5.03 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(380,a,379,b)].
% 4.81/5.03 381 -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].
% 4.81/5.03 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(381,a,351,a)].
% 4.81/5.03 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(381,a,352,a)].
% 4.81/5.03 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(381,a,353,b)].
% 4.81/5.03 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(381,a,354,b)].
% 4.81/5.03 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(381,a,355,b)].
% 4.81/5.03 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(381,a,356,b)].
% 4.81/5.03 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(381,a,357,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(381,a,358,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(381,a,359,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(381,a,360,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(381,a,361,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(381,a,362,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(381,a,363,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(381,a,364,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(381,a,365,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(381,a,366,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(381,a,367,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(381,a,368,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(381,a,369,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(381,a,370,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(381,a,371,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(381,a,372,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(381,a,373,b)].
% 4.90/5.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(381,a,379,b)].
% 4.90/5.16 382 -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)].
% 4.90/5.16 383 -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)].
% 4.90/5.16 384 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(183,a,180,b)].
% 4.90/5.16 385 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(184,a,180,b)].
% 4.90/5.16 386 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(223,a,218,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(386,b,357,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(386,b,358,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(386,b,359,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(386,b,360,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(386,b,361,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(386,b,362,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(386,b,363,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(386,b,364,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(386,b,365,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(386,b,366,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(386,b,367,b)].
% 4.90/5.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(386,b,368,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(386,b,369,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(386,b,370,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(386,b,371,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(386,b,372,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(386,b,373,b)].
% 4.97/5.19 387 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(224,a,218,b)].
% 4.97/5.19 388 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(225,a,218,b)].
% 4.97/5.19 389 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)].
% 4.97/5.19 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(389,c,354,b)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(389,c,359,b)].
% 4.97/5.19 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(389,c,360,b)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(389,c,372,b)].
% 4.97/5.19 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)].
% 4.97/5.19 390 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)].
% 4.97/5.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(390,c,354,b)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(390,c,359,b)].
% 4.97/5.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(390,c,360,b)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 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)].
% 4.97/5.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(390,c,372,b)].
% 4.97/5.19 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)].
% 4.97/5.19 391 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(346,b,344,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(391,b,351,a)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(391,b,352,a)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(391,b,353,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(391,b,354,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(391,b,355,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(391,b,356,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(391,b,357,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(391,b,358,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(391,b,359,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(391,b,360,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(391,b,361,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(391,b,362,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(391,b,363,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(391,b,364,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(391,b,365,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(391,b,366,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(391,b,367,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(391,b,368,b)].
% 4.97/5.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(391,b,369,b)].
% 5.06/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(391,b,370,b)].
% 5.06/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(391,b,371,b)].
% 5.06/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(391,b,372,b)].
% 5.06/5.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(391,b,373,b)].
% 5.06/5.29 392 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(347,b,344,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(392,b,351,a)].
% 5.06/5.29 Derived: class_HOL_Oplus(tc_nat). [resolve(392,b,352,a)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(392,b,353,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(392,b,354,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(392,b,355,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(392,b,356,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(392,b,357,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(392,b,358,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(392,b,359,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(392,b,360,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(392,b,361,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(392,b,362,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(392,b,363,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(392,b,364,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(392,b,365,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(392,b,366,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(392,b,367,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(392,b,368,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(392,b,369,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(392,b,370,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(392,b,371,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(392,b,372,b)].
% 5.06/5.29 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(392,b,373,b)].
% 5.06/5.29 393 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_1) # label(axiom). [assumption].
% 5.06/5.29 394 class_Ring__and__Field_Oring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_19) # label(axiom). [assumption].
% 5.06/5.29 395 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom). [assumption].
% 5.06/5.29 396 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_16) # label(axiom). [assumption].
% 5.06/5.29 397 -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].
% 5.06/5.29 398 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ofield_3) # label(axiom). [assumption].
% 5.06/5.29 399 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom). [assumption].
% 5.06/5.29 400 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Olordered__ring_1) # label(axiom). [assumption].
% 5.06/5.29 401 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__field_6) # label(axiom). [assumption].
% 5.11/5.34 402 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__idom_3) # label(axiom). [assumption].
% 5.11/5.34 403 -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].
% 5.11/5.34 404 -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].
% 5.11/5.34 405 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__ring_0) # label(axiom). [assumption].
% 5.11/5.34 406 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring_2) # label(axiom). [assumption].
% 5.11/5.34 407 -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring_3) # label(axiom). [assumption].
% 5.11/5.34 408 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring_4) # label(axiom). [assumption].
% 5.11/5.34 409 -class_Ring__and__Field_Oring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring_5) # label(axiom). [assumption].
% 5.11/5.34 410 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring_6) # label(axiom). [assumption].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(410,a,394,a)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(410,a,395,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(410,a,396,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(410,a,397,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(410,a,398,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(410,a,399,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(410,a,400,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(410,a,401,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(410,a,402,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(410,a,403,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(410,a,404,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(410,a,405,b)].
% 5.11/5.34 411 -class_Ring__and__Field_Oring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring_9) # label(axiom). [assumption].
% 5.11/5.34 412 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oring__1_0) # label(axiom). [assumption].
% 5.11/5.34 413 -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].
% 5.11/5.34 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)].
% 5.11/5.34 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)].
% 5.11/5.34 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 414 -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].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.35 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 415 -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].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.11/5.38 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)].
% 5.20/5.47 416 -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].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ocomm__ring(B). [resolve(416,a,396,b)].
% 5.20/5.47 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(416,a,397,b)].
% 5.20/5.47 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(416,a,398,b)].
% 5.20/5.47 Derived: c_times(c_uminus(A,B),C,B) = c_uminus(c_times(A,C,B),B) | -class_Ring__and__Field_Oidom(B). [resolve(416,a,399,b)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 417 -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].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 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)].
% 5.20/5.47 418 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(71,a,98,b)].
% 5.20/5.47 419 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(100,a,98,b)].
% 5.28/5.51 420 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(101,a,98,b)].
% 5.28/5.51 421 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(102,a,98,b)].
% 5.28/5.51 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(421,b,398,b)].
% 5.28/5.51 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(421,b,399,b)].
% 5.28/5.51 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(421,b,400,b)].
% 5.28/5.51 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(421,b,401,b)].
% 5.28/5.51 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(421,b,402,b)].
% 5.28/5.51 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(421,b,403,b)].
% 5.28/5.51 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(421,b,404,b)].
% 5.28/5.51 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(421,b,405,b)].
% 5.28/5.51 422 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(103,a,98,b)].
% 5.28/5.51 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(422,b,398,b)].
% 5.28/5.51 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(422,b,399,b)].
% 5.28/5.51 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(422,b,400,b)].
% 5.28/5.51 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(422,b,401,b)].
% 5.28/5.51 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(422,b,402,b)].
% 5.28/5.51 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(422,b,403,b)].
% 5.28/5.51 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(422,b,404,b)].
% 5.28/5.51 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(422,b,405,b)].
% 5.28/5.51 423 -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)].
% 5.28/5.51 424 -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)].
% 5.28/5.51 425 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(183,a,177,b)].
% 5.28/5.51 426 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(184,a,177,b)].
% 5.28/5.51 427 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(217,a,211,b)].
% 5.28/5.51 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(427,b,398,b)].
% 5.28/5.51 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(427,b,399,b)].
% 5.28/5.51 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(427,b,400,b)].
% 5.28/5.51 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(427,b,401,b)].
% 5.28/5.51 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(427,b,402,b)].
% 5.28/5.51 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(427,b,403,b)].
% 5.28/5.51 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(427,b,404,b)].
% 5.28/5.51 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(427,b,405,b)].
% 5.28/5.51 428 -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)].
% 5.28/5.51 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)].
% 5.28/5.51 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 429 -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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 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)].
% 5.28/5.52 430 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(223,a,211,b)].
% 5.28/5.52 431 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(224,a,211,b)].
% 5.28/5.56 432 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(225,a,211,b)].
% 5.28/5.56 433 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(226,b,211,b)].
% 5.28/5.56 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(433,b,398,b)].
% 5.28/5.56 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(433,b,399,b)].
% 5.28/5.56 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(433,b,400,b)].
% 5.28/5.56 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(433,b,401,b)].
% 5.28/5.56 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(433,b,402,b)].
% 5.28/5.56 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(433,b,403,b)].
% 5.28/5.56 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(433,b,404,b)].
% 5.28/5.56 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(433,b,405,b)].
% 5.28/5.56 434 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(227,b,211,b)].
% 5.28/5.56 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(434,b,398,b)].
% 5.28/5.56 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(434,b,399,b)].
% 5.28/5.56 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(434,b,400,b)].
% 5.28/5.56 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(434,b,401,b)].
% 5.28/5.56 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(434,b,402,b)].
% 5.28/5.56 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(434,b,403,b)].
% 5.28/5.56 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(434,b,404,b)].
% 5.28/5.56 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(434,b,405,b)].
% 5.28/5.56 435 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(307,a,303,b)].
% 5.28/5.56 436 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(308,a,303,b)].
% 5.28/5.56 437 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(346,b,342,b)].
% 5.28/5.56 438 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(347,b,342,b)].
% 5.28/5.56 439 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(380,a,372,b)].
% 5.28/5.56 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(439,b,394,a)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(439,b,395,b)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(439,b,396,b)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(439,b,397,b)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(439,b,398,b)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(439,b,399,b)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(439,b,400,b)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(439,b,401,b)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(439,b,402,b)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(439,b,403,b)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(439,b,404,b)].
% 5.28/5.56 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(439,b,405,b)].
% 5.28/5.56 440 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(381,a,372,b)].
% 5.28/5.56 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(440,b,394,a)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(440,b,395,b)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(440,b,396,b)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(440,b,397,b)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(440,b,398,b)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(440,b,399,b)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(440,b,400,b)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(440,b,401,b)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(440,b,402,b)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(440,b,403,b)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(440,b,404,b)].
% 5.28/5.56 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(440,b,405,b)].
% 5.28/5.56 441 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(386,b,372,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(441,b,394,a)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(441,b,395,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(441,b,396,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(441,b,397,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(441,b,398,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(441,b,399,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(441,b,400,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(441,b,401,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(441,b,402,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(441,b,403,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(441,b,404,b)].
% 5.28/5.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(441,b,405,b)].
% 5.28/5.56 442 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(389,c,372,b)].
% 5.28/5.56 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(442,c,394,a)].
% 5.28/5.56 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(442,c,395,b)].
% 5.28/5.56 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)].
% 5.28/5.56 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)].
% 5.28/5.56 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(442,c,398,b)].
% 5.28/5.56 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(442,c,399,b)].
% 5.28/5.56 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)].
% 5.28/5.56 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)].
% 5.28/5.56 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)].
% 5.28/5.56 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)].
% 5.28/5.56 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)].
% 5.28/5.56 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)].
% 5.28/5.56 443 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(390,c,372,b)].
% 5.28/5.56 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(443,c,394,a)].
% 5.28/5.56 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(443,c,395,b)].
% 5.28/5.56 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)].
% 5.69/5.98 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)].
% 5.69/5.98 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(443,c,398,b)].
% 5.69/5.98 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(443,c,399,b)].
% 5.69/5.98 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)].
% 5.69/5.98 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)].
% 5.69/5.98 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)].
% 5.69/5.98 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)].
% 5.69/5.98 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)].
% 5.69/5.98 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)].
% 5.69/5.98 444 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(391,b,372,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(444,b,394,a)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(444,b,395,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(444,b,396,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(444,b,397,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(444,b,398,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(444,b,399,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(444,b,400,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(444,b,401,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(444,b,402,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(444,b,403,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(444,b,404,b)].
% 5.69/5.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(444,b,405,b)].
% 5.69/5.98 445 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(392,b,372,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(445,b,394,a)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(445,b,395,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(445,b,396,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(445,b,397,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(445,b,398,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(445,b,399,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(445,b,400,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(445,b,401,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(445,b,402,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(445,b,403,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(445,b,404,b)].
% 5.69/5.98 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(445,b,405,b)].
% 5.69/5.98 446 -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].
% 5.69/5.98 447 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom). [assumption].
% 5.88/6.14 448 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom). [assumption].
% 5.88/6.14 449 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom). [assumption].
% 5.88/6.14 450 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom). [assumption].
% 5.88/6.14 451 -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].
% 5.88/6.14 452 -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].
% 5.88/6.14 453 -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].
% 5.88/6.14 454 -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].
% 5.88/6.14 455 -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].
% 5.88/6.14 456 -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].
% 5.88/6.14 457 -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].
% 5.88/6.14 458 -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].
% 5.88/6.14 459 -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].
% 5.88/6.14 460 -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].
% 5.88/6.14 461 -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].
% 5.88/6.14 462 -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].
% 5.88/6.14 463 -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].
% 5.88/6.14 464 -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].
% 5.88/6.14 465 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(71,a,80,b)].
% 5.88/6.14 466 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(100,a,80,b)].
% 5.88/6.14 467 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(102,a,80,b)].
% 5.88/6.14 468 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(103,a,80,b)].
% 5.88/6.14 469 -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)].
% 5.88/6.14 470 -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)].
% 5.88/6.14 471 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(159,b,142,a)].
% 5.98/6.19 472 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(183,a,159,b)].
% 5.98/6.19 473 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(184,a,159,b)].
% 5.98/6.19 474 -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)].
% 5.98/6.19 475 -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)].
% 5.98/6.19 476 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(223,a,193,b)].
% 5.98/6.19 477 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(224,a,193,b)].
% 5.98/6.19 478 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(226,b,193,b)].
% 5.98/6.19 479 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(227,b,193,b)].
% 5.98/6.19 480 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(262,b,241,b)].
% 5.98/6.19 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(480,b,447,a)].
% 5.98/6.19 Derived: class_HOL_Ozero(tc_nat). [resolve(480,b,448,a)].
% 5.98/6.19 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(480,b,449,b)].
% 5.98/6.19 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(480,b,450,b)].
% 5.98/6.19 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(480,b,451,b)].
% 5.98/6.19 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(480,b,452,b)].
% 5.98/6.19 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(480,b,463,b)].
% 5.98/6.19 481 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)].
% 5.98/6.19 482 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)].
% 5.98/6.19 483 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(346,b,327,b)].
% 5.98/6.19 484 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(380,a,357,b)].
% 5.98/6.19 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(484,b,448,a)].
% 5.98/6.19 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(484,b,450,b)].
% 5.98/6.19 485 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(381,a,357,b)].
% 5.98/6.19 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(485,b,448,a)].
% 5.98/6.19 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(485,b,450,b)].
% 5.98/6.19 486 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(386,b,357,b)].
% 5.98/6.19 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(486,b,448,a)].
% 5.98/6.19 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(486,b,450,b)].
% 5.98/6.19 487 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)].
% 5.98/6.19 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(487,c,448,a)].
% 5.98/6.19 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(487,c,450,b)].
% 5.98/6.19 488 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)].
% 5.98/6.19 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(488,c,448,a)].
% 5.98/6.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(488,c,450,b)].
% 5.98/6.19 489 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(391,b,357,b)].
% 5.98/6.19 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(489,b,448,a)].
% 5.98/6.19 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(489,b,450,b)].
% 6.20/6.44 490 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom). [assumption].
% 6.20/6.44 491 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom). [assumption].
% 6.20/6.44 492 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom). [assumption].
% 6.20/6.44 493 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_12) # label(axiom). [assumption].
% 6.20/6.44 494 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_2) # label(axiom). [assumption].
% 6.20/6.44 495 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom). [assumption].
% 6.20/6.44 496 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom). [assumption].
% 6.20/6.44 497 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_8) # label(axiom). [assumption].
% 6.20/6.44 498 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom). [assumption].
% 6.20/6.44 499 -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].
% 6.20/6.44 500 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom). [assumption].
% 6.20/6.44 501 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom). [assumption].
% 6.20/6.44 502 -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].
% 6.20/6.44 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(502,b,494,a)].
% 6.20/6.44 503 -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].
% 6.20/6.44 504 -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].
% 6.20/6.44 505 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(71,a,76,b)].
% 6.20/6.44 506 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(100,a,76,b)].
% 6.20/6.44 507 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(102,a,76,b)].
% 6.20/6.44 508 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(103,a,76,b)].
% 6.20/6.44 509 -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)].
% 6.20/6.44 510 -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)].
% 6.20/6.44 511 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(119,a,115,b)].
% 6.20/6.44 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(511,b,491,a)].
% 6.20/6.44 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(511,b,492,b)].
% 6.20/6.44 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(511,b,500,b)].
% 6.20/6.44 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(511,b,501,b)].
% 6.20/6.44 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(511,b,503,b)].
% 6.20/6.44 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(511,b,504,b)].
% 6.20/6.48 512 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(135,b,115,b)].
% 6.20/6.48 513 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(136,b,115,b)].
% 6.20/6.48 514 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(138,b,115,b)].
% 6.20/6.48 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(514,b,491,a)].
% 6.20/6.48 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(514,b,492,b)].
% 6.20/6.48 515 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(139,b,115,b)].
% 6.20/6.48 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(515,b,491,a)].
% 6.20/6.48 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(515,b,492,b)].
% 6.20/6.48 516 -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)].
% 6.20/6.48 517 -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)].
% 6.20/6.48 518 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(156,b,142,a)].
% 6.20/6.48 519 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(183,a,156,b)].
% 6.20/6.48 520 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(184,a,156,b)].
% 6.20/6.48 521 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(223,a,190,b)].
% 6.20/6.48 522 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(224,a,190,b)].
% 6.20/6.48 523 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(226,b,190,b)].
% 6.20/6.48 524 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(227,b,190,b)].
% 6.20/6.48 525 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(262,b,233,b)].
% 6.20/6.48 526 -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)].
% 6.20/6.48 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)].
% 6.20/6.48 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Numeral_Onumber__ring(A). [resolve(526,c,492,b)].
% 6.20/6.48 527 -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)].
% 6.20/6.48 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)].
% 6.20/6.48 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)].
% 6.20/6.48 528 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(265,b,233,b)].
% 6.20/6.48 529 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(266,b,233,b)].
% 6.20/6.48 530 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(268,b,233,b)].
% 6.20/6.48 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(530,b,491,a)].
% 6.29/6.52 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(530,b,492,b)].
% 6.29/6.52 531 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(269,b,233,b)].
% 6.29/6.52 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(531,b,491,a)].
% 6.29/6.52 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(531,b,492,b)].
% 6.29/6.52 532 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(307,a,286,b)].
% 6.29/6.52 533 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(308,a,286,b)].
% 6.29/6.52 534 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(346,b,325,b)].
% 6.29/6.52 535 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(380,a,355,b)].
% 6.29/6.52 536 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(381,a,355,b)].
% 6.29/6.52 537 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(389,c,355,b)].
% 6.29/6.52 538 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(390,c,355,b)].
% 6.29/6.52 539 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(391,b,355,b)].
% 6.29/6.52 540 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(410,a,396,b)].
% 6.29/6.52 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(540,b,491,a)].
% 6.29/6.52 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(540,b,492,b)].
% 6.29/6.52 541 -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)].
% 6.29/6.52 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)].
% 6.29/6.52 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)].
% 6.29/6.52 542 -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)].
% 6.29/6.52 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)].
% 6.29/6.52 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)].
% 6.29/6.52 543 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)].
% 6.29/6.52 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)].
% 6.29/6.52 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)].
% 6.29/6.52 544 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)].
% 6.29/6.52 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)].
% 6.29/6.52 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)].
% 6.29/6.52 545 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)].
% 6.29/6.52 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)].
% 6.38/6.61 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)].
% 6.38/6.61 546 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(439,b,396,b)].
% 6.38/6.61 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(546,b,491,a)].
% 6.38/6.61 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(546,b,492,b)].
% 6.38/6.61 547 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(440,b,396,b)].
% 6.38/6.61 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(547,b,491,a)].
% 6.38/6.61 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(547,b,492,b)].
% 6.38/6.61 548 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(441,b,396,b)].
% 6.38/6.61 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(548,b,491,a)].
% 6.38/6.61 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(548,b,492,b)].
% 6.38/6.61 549 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(442,c,396,b)].
% 6.38/6.61 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(549,c,491,a)].
% 6.38/6.61 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(549,c,492,b)].
% 6.38/6.61 550 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(443,c,396,b)].
% 6.38/6.61 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(550,c,491,a)].
% 6.38/6.61 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(550,c,492,b)].
% 6.38/6.61 551 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(444,b,396,b)].
% 6.38/6.61 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(551,b,491,a)].
% 6.38/6.61 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(551,b,492,b)].
% 6.38/6.61 552 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(480,b,451,b)].
% 6.38/6.61 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(552,b,491,a)].
% 6.38/6.61 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(552,b,492,b)].
% 6.38/6.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(552,b,500,b)].
% 6.38/6.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(552,b,501,b)].
% 6.38/6.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(552,b,502,b)].
% 6.38/6.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(552,b,503,b)].
% 6.38/6.61 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(552,b,504,b)].
% 6.38/6.61 553 -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].
% 6.38/6.61 554 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom). [assumption].
% 6.38/6.61 555 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom). [assumption].
% 6.38/6.61 556 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom). [assumption].
% 6.38/6.61 557 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom). [assumption].
% 6.38/6.61 558 -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].
% 6.38/6.61 559 -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].
% 6.38/6.61 560 -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].
% 6.38/6.61 561 -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].
% 6.52/6.73 562 -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].
% 6.52/6.73 563 -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].
% 6.52/6.73 564 -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].
% 6.52/6.73 565 -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].
% 6.52/6.73 566 -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].
% 6.52/6.73 567 -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].
% 6.52/6.73 568 -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].
% 6.52/6.73 569 -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].
% 6.52/6.73 Derived: c_0 != c_1. [resolve(569,a,554,a)].
% 6.52/6.73 570 -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].
% 6.52/6.73 Derived: c_1 != c_0. [resolve(570,a,554,a)].
% 6.52/6.73 571 -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)].
% 6.52/6.73 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)].
% 6.52/6.73 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)].
% 6.52/6.73 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)].
% 6.52/6.73 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)].
% 6.52/6.73 572 -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)].
% 6.52/6.73 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)].
% 6.52/6.73 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)].
% 6.52/6.73 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)].
% 6.52/6.73 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)].
% 6.52/6.73 573 -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)].
% 6.52/6.73 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)].
% 6.52/6.73 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)].
% 6.52/6.73 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)].
% 6.52/6.74 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)].
% 6.52/6.74 574 -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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 575 -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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 576 -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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 577 -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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 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)].
% 6.52/6.74 578 -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)].
% 6.70/6.91 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)].
% 6.70/6.91 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)].
% 6.70/6.91 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)].
% 6.70/6.91 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)].
% 6.70/6.91 579 -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)].
% 6.70/6.91 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)].
% 6.70/6.91 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)].
% 6.70/6.91 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)].
% 6.70/6.91 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)].
% 6.70/6.91 580 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom). [assumption].
% 6.70/6.91 581 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom). [assumption].
% 6.70/6.91 582 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom). [assumption].
% 6.70/6.91 583 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom). [assumption].
% 6.70/6.91 584 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom). [assumption].
% 6.70/6.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(580,a,584,b)].
% 6.70/6.91 585 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom). [assumption].
% 6.70/6.91 Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(585,a,584,b)].
% 6.70/6.91 586 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom). [assumption].
% 6.70/6.91 587 -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].
% 6.70/6.91 588 -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].
% 6.70/6.91 589 -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].
% 6.70/6.91 590 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom). [assumption].
% 6.70/6.91 591 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom). [assumption].
% 6.70/6.91 592 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom). [assumption].
% 6.70/6.91 593 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom). [assumption].
% 6.83/7.03 594 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom). [assumption].
% 6.83/7.03 595 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom). [assumption].
% 6.83/7.03 596 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom). [assumption].
% 6.83/7.03 597 -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].
% 6.83/7.03 598 -class_OrderedGroup_Omonoid__mult(A) | c_times(c_1,B,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) # label(axiom). [assumption].
% 6.83/7.03 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(598,a,581,a)].
% 6.83/7.03 Derived: c_times(c_1,A,tc_nat) = A. [resolve(598,a,582,a)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(598,a,583,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(598,a,584,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(598,a,586,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(598,a,587,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(598,a,588,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(598,a,589,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(598,a,590,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(598,a,591,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(598,a,592,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(598,a,593,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(598,a,594,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(598,a,595,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(598,a,596,b)].
% 6.83/7.03 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(598,a,597,b)].
% 6.83/7.03 599 -class_OrderedGroup_Omonoid__mult(A) | c_times(B,c_1,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) # label(axiom). [assumption].
% 6.83/7.03 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(599,a,581,a)].
% 6.83/7.03 Derived: c_times(A,c_1,tc_nat) = A. [resolve(599,a,582,a)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(599,a,583,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(599,a,584,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(599,a,586,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(599,a,587,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(599,a,588,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(599,a,589,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(599,a,590,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(599,a,591,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(599,a,592,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(599,a,593,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(599,a,594,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(599,a,595,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(599,a,596,b)].
% 6.83/7.03 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(599,a,597,b)].
% 6.83/7.03 600 -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)].
% 6.98/7.22 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)].
% 6.98/7.22 601 -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)].
% 6.98/7.22 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)].
% 6.98/7.22 602 -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)].
% 6.98/7.22 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)].
% 6.98/7.22 603 -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)].
% 6.98/7.22 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)].
% 6.98/7.22 604 -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)].
% 6.98/7.22 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)].
% 6.98/7.22 605 -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)].
% 6.98/7.22 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)].
% 6.98/7.22 606 -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)].
% 6.98/7.22 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)].
% 6.98/7.22 607 -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)].
% 6.98/7.22 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)].
% 6.98/7.22 608 -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)].
% 6.98/7.22 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)].
% 6.98/7.22 609 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom). [assumption].
% 6.98/7.22 610 class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_24) # label(axiom). [assumption].
% 6.98/7.22 611 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat_24) # label(axiom). [assumption].
% 6.98/7.22 612 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom). [assumption].
% 6.98/7.22 613 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_2) # label(axiom). [assumption].
% 6.98/7.22 614 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_3) # label(axiom). [assumption].
% 7.21/7.44 615 -class_Power_Orecpower(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Power_Orecpower_16) # label(axiom). [assumption].
% 7.21/7.44 616 -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].
% 7.21/7.44 617 -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].
% 7.21/7.44 618 -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].
% 7.21/7.44 619 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_8) # label(axiom). [assumption].
% 7.21/7.44 620 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom). [assumption].
% 7.21/7.44 621 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_11) # label(axiom). [assumption].
% 7.21/7.44 622 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_8) # label(axiom). [assumption].
% 7.21/7.44 623 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_2) # label(axiom). [assumption].
% 7.21/7.44 624 -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)].
% 7.21/7.44 625 -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)].
% 7.21/7.44 626 -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)].
% 7.21/7.44 627 -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)].
% 7.21/7.44 628 -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)].
% 7.21/7.44 629 -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)].
% 7.21/7.44 630 -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)].
% 7.21/7.44 631 -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)].
% 7.21/7.44 632 -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)].
% 7.21/7.44 633 class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(580,a,584,b)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(633,b,610,a)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(633,b,611,a)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(633,b,612,b)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(633,b,615,b)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(633,b,616,b)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(633,b,617,b)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(633,b,618,b)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(633,b,619,b)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(633,b,620,b)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(633,b,621,b)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(633,b,622,b)].
% 7.21/7.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(633,b,623,b)].
% 7.21/7.44 634 class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(585,a,584,b)].
% 7.21/7.44 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(634,b,610,a)].
% 7.21/7.44 Derived: class_HOL_Otimes(tc_nat). [resolve(634,b,611,a)].
% 7.21/7.44 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(634,b,612,b)].
% 7.21/7.44 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(634,b,615,b)].
% 7.21/7.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(634,b,616,b)].
% 7.21/7.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(634,b,617,b)].
% 7.21/7.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(634,b,618,b)].
% 7.21/7.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(634,b,619,b)].
% 7.21/7.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(634,b,620,b)].
% 7.21/7.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(634,b,621,b)].
% 7.21/7.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(634,b,622,b)].
% 7.21/7.44 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(634,b,623,b)].
% 7.21/7.44 635 c_times(c_1,A,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(598,a,584,b)].
% 7.21/7.44 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(635,b,610,a)].
% 7.21/7.44 Derived: c_times(c_1,A,tc_nat) = A. [resolve(635,b,611,a)].
% 7.21/7.44 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(635,b,612,b)].
% 7.21/7.44 636 c_times(A,c_1,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(599,a,584,b)].
% 7.21/7.44 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(636,b,610,a)].
% 7.21/7.44 Derived: c_times(A,c_1,tc_nat) = A. [resolve(636,b,611,a)].
% 7.21/7.44 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(636,b,612,b)].
% 7.21/7.44 637 -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)].
% 7.21/7.44 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)].
% 7.21/7.44 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)].
% 7.21/7.44 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)].
% 7.21/7.44 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 638 -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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 639 -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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 640 -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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 641 -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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 642 -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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 643 -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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 644 -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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.21/7.45 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 645 -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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 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)].
% 7.28/7.54 646 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom). [assumption].
% 7.44/7.68 647 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom). [assumption].
% 7.44/7.68 648 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom). [assumption].
% 7.44/7.68 649 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom). [assumption].
% 7.44/7.68 650 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom). [assumption].
% 7.44/7.68 651 -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].
% 7.44/7.68 652 -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].
% 7.44/7.68 653 -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].
% 7.44/7.68 654 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom). [assumption].
% 7.44/7.68 655 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom). [assumption].
% 7.44/7.68 656 -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].
% 7.44/7.68 657 -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].
% 7.44/7.68 658 -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].
% 7.44/7.68 659 -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].
% 7.44/7.68 660 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom). [assumption].
% 7.44/7.68 661 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom). [assumption].
% 7.44/7.68 662 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_8) # label(axiom). [assumption].
% 7.44/7.68 663 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom). [assumption].
% 7.44/7.68 664 -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].
% 7.44/7.68 665 -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)].
% 7.44/7.68 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)].
% 7.44/7.68 666 -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)].
% 7.44/7.68 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)].
% 7.44/7.68 667 -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)].
% 7.44/7.68 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)].
% 7.44/7.68 668 -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)].
% 7.60/7.80 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)].
% 7.60/7.80 669 -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)].
% 7.60/7.80 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)].
% 7.60/7.80 670 -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)].
% 7.60/7.80 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)].
% 7.60/7.80 671 -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)].
% 7.60/7.80 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)].
% 7.60/7.80 672 -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)].
% 7.60/7.80 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)].
% 7.60/7.80 673 -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)].
% 7.60/7.80 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)].
% 7.60/7.80 674 -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)].
% 7.60/7.80 675 -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)].
% 7.60/7.80 676 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(181,b,142,a)].
% 7.60/7.80 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(676,a,664,b)].
% 7.60/7.80 677 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(183,a,181,b)].
% 7.60/7.80 678 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(184,a,181,b)].
% 7.60/7.80 679 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(223,a,219,b)].
% 7.60/7.80 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(679,b,652,b)].
% 7.60/7.80 680 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(224,a,219,b)].
% 7.60/7.80 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(680,b,652,b)].
% 7.60/7.80 681 c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(598,a,596,b)].
% 7.60/7.80 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(681,b,650,b)].
% 7.60/7.80 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(681,b,651,b)].
% 7.60/7.80 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(681,b,652,b)].
% 7.60/7.80 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(681,b,653,b)].
% 7.60/7.80 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(681,b,654,b)].
% 7.71/7.90 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(681,b,655,b)].
% 7.71/7.90 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(681,b,656,b)].
% 7.71/7.90 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(681,b,657,b)].
% 7.71/7.90 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(681,b,658,b)].
% 7.71/7.90 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(681,b,659,b)].
% 7.71/7.90 682 c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(599,a,596,b)].
% 7.71/7.90 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(682,b,650,b)].
% 7.71/7.90 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(682,b,651,b)].
% 7.71/7.90 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(682,b,652,b)].
% 7.71/7.90 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(682,b,653,b)].
% 7.71/7.90 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(682,b,654,b)].
% 7.71/7.90 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(682,b,655,b)].
% 7.71/7.90 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(682,b,656,b)].
% 7.71/7.90 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(682,b,657,b)].
% 7.71/7.90 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(682,b,658,b)].
% 7.71/7.90 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(682,b,659,b)].
% 7.71/7.90 683 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_1) # label(axiom). [assumption].
% 7.71/7.90 684 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom). [assumption].
% 7.71/7.90 685 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom). [assumption].
% 7.71/7.90 686 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom). [assumption].
% 7.71/7.90 687 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom). [assumption].
% 7.71/7.90 688 -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].
% 7.71/7.90 689 -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].
% 7.71/7.90 690 -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].
% 7.71/7.90 691 -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].
% 7.71/7.90 692 -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].
% 7.71/7.90 693 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_9) # label(axiom). [assumption].
% 7.71/7.90 694 -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].
% 7.71/7.90 695 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ofield_7) # label(axiom). [assumption].
% 7.71/7.90 696 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oidom_7) # label(axiom). [assumption].
% 7.71/7.90 697 -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].
% 7.71/7.90 698 -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].
% 7.83/8.06 699 -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].
% 7.83/8.06 700 -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)].
% 7.83/8.06 701 -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)].
% 7.83/8.06 702 -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)].
% 7.83/8.06 703 -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)].
% 7.83/8.06 704 -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)].
% 7.83/8.06 705 -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)].
% 7.83/8.06 706 -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)].
% 7.83/8.06 707 -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)].
% 7.83/8.06 708 -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)].
% 7.83/8.06 709 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(71,a,81,b)].
% 7.83/8.06 710 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(100,a,81,b)].
% 7.83/8.06 711 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(102,a,81,b)].
% 7.83/8.06 712 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(103,a,81,b)].
% 7.83/8.06 713 -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)].
% 7.83/8.06 714 -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)].
% 7.83/8.06 715 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A). [resolve(160,b,142,a)].
% 7.83/8.06 716 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(183,a,160,b)].
% 7.83/8.06 717 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(184,a,160,b)].
% 7.83/8.06 718 -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)].
% 7.83/8.06 719 -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)].
% 7.83/8.06 720 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(223,a,194,b)].
% 7.83/8.06 721 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(224,a,194,b)].
% 7.83/8.06 722 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(226,b,194,b)].
% 7.83/8.06 723 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(227,b,194,b)].
% 7.90/8.13 724 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(262,b,242,b)].
% 7.90/8.13 725 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(598,a,588,b)].
% 7.90/8.13 726 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(599,a,588,b)].
% 7.90/8.13 727 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(633,b,617,b)].
% 7.90/8.13 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(727,b,684,a)].
% 7.90/8.13 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(727,b,685,a)].
% 7.90/8.13 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(727,b,686,b)].
% 7.90/8.13 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(727,b,687,b)].
% 7.90/8.13 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(727,b,688,b)].
% 7.90/8.13 728 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(634,b,617,b)].
% 7.90/8.13 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(728,b,684,a)].
% 7.90/8.13 Derived: class_HOL_Otimes(tc_nat). [resolve(728,b,685,a)].
% 7.90/8.13 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(728,b,686,b)].
% 7.90/8.13 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(728,b,687,b)].
% 7.90/8.13 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(728,b,688,b)].
% 7.90/8.13 729 -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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 730 -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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 731 -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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 732 -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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 733 -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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 734 -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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 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)].
% 7.90/8.13 735 -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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 736 -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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 737 -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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 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)].
% 7.90/8.14 738 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(679,b,652,b)].
% 7.90/8.14 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(738,b,684,a)].
% 7.90/8.14 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(738,b,685,a)].
% 7.90/8.14 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(738,b,686,b)].
% 7.90/8.14 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(738,b,687,b)].
% 7.90/8.14 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(738,b,688,b)].
% 7.90/8.14 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(738,b,694,b)].
% 7.90/8.14 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(738,b,695,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(738,b,696,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(738,b,697,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(738,b,698,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(738,b,699,b)].
% 8.03/8.22 739 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(680,b,652,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(739,b,684,a)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(739,b,685,a)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(739,b,686,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(739,b,687,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(739,b,688,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(739,b,694,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(739,b,695,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(739,b,696,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(739,b,697,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(739,b,698,b)].
% 8.03/8.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(739,b,699,b)].
% 8.03/8.22 740 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(681,b,652,b)].
% 8.03/8.22 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(740,b,684,a)].
% 8.03/8.22 Derived: c_times(c_1,A,tc_nat) = A. [resolve(740,b,685,a)].
% 8.03/8.22 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(740,b,686,b)].
% 8.03/8.22 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(740,b,687,b)].
% 8.03/8.22 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(740,b,688,b)].
% 8.03/8.22 741 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(682,b,652,b)].
% 8.03/8.22 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(741,b,684,a)].
% 8.03/8.22 Derived: c_times(A,c_1,tc_nat) = A. [resolve(741,b,685,a)].
% 8.03/8.22 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(741,b,686,b)].
% 8.03/8.22 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(741,b,687,b)].
% 8.03/8.22 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(741,b,688,b)].
% 8.03/8.22 742 -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].
% 8.03/8.22 743 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom). [assumption].
% 8.03/8.22 744 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom). [assumption].
% 8.03/8.22 745 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom). [assumption].
% 8.03/8.22 746 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom). [assumption].
% 8.03/8.22 747 -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].
% 8.03/8.22 748 -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].
% 8.03/8.22 749 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_9) # label(axiom). [assumption].
% 8.18/8.38 750 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_9) # label(axiom). [assumption].
% 8.18/8.38 751 -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].
% 8.18/8.38 752 -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].
% 8.18/8.38 753 -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].
% 8.18/8.38 754 -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].
% 8.18/8.38 755 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_12) # label(axiom). [assumption].
% 8.18/8.38 756 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_5) # label(axiom). [assumption].
% 8.18/8.38 757 -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].
% 8.18/8.38 758 -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].
% 8.18/8.38 759 -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)].
% 8.18/8.38 760 -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)].
% 8.18/8.38 761 -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)].
% 8.18/8.38 762 -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)].
% 8.18/8.38 763 -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)].
% 8.18/8.38 764 -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)].
% 8.18/8.38 765 -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)].
% 8.18/8.38 766 -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)].
% 8.18/8.38 767 -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)].
% 8.18/8.38 768 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(107,b,102,a)].
% 8.18/8.38 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(768,a,754,b)].
% 8.18/8.38 769 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(107,b,103,a)].
% 8.18/8.38 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(769,a,754,b)].
% 8.18/8.38 770 -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)].
% 8.18/8.38 771 -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)].
% 8.34/8.57 772 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(183,a,182,b)].
% 8.34/8.57 773 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(184,a,182,b)].
% 8.34/8.57 774 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(223,a,220,b)].
% 8.34/8.57 775 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(224,a,220,b)].
% 8.34/8.57 776 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)].
% 8.34/8.57 777 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)].
% 8.34/8.57 778 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(346,b,345,b)].
% 8.34/8.57 779 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(380,a,379,b)].
% 8.34/8.57 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(779,b,748,b)].
% 8.34/8.57 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(779,b,753,b)].
% 8.34/8.57 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(779,b,754,b)].
% 8.34/8.57 780 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(381,a,379,b)].
% 8.34/8.57 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(780,b,748,b)].
% 8.34/8.57 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(780,b,753,b)].
% 8.34/8.57 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(780,b,754,b)].
% 8.34/8.57 781 c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(598,a,597,b)].
% 8.34/8.57 782 c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(599,a,597,b)].
% 8.34/8.57 783 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(676,a,664,b)].
% 8.34/8.57 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(783,b,743,a)].
% 8.34/8.57 Derived: class_HOL_Ozero(tc_nat). [resolve(783,b,744,a)].
% 8.34/8.57 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(783,b,745,b)].
% 8.34/8.57 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(783,b,746,b)].
% 8.34/8.57 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(783,b,747,b)].
% 8.34/8.57 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(783,b,748,b)].
% 8.34/8.57 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(783,b,749,b)].
% 8.34/8.57 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(783,b,750,b)].
% 8.34/8.57 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(783,b,751,b)].
% 8.34/8.57 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(783,b,752,b)].
% 8.34/8.57 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(783,b,753,b)].
% 8.34/8.57 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(783,b,754,b)].
% 8.34/8.57 784 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring__1_1) # label(axiom). [assumption].
% 8.34/8.57 785 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom). [assumption].
% 8.34/8.57 786 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom). [assumption].
% 8.34/8.57 787 -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].
% 8.34/8.57 788 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom). [assumption].
% 8.34/8.57 789 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom). [assumption].
% 8.34/8.57 790 -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].
% 8.49/8.73 791 -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].
% 8.49/8.73 792 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_11) # label(axiom). [assumption].
% 8.49/8.73 793 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom). [assumption].
% 8.49/8.73 794 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom). [assumption].
% 8.49/8.73 795 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom). [assumption].
% 8.49/8.73 796 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom). [assumption].
% 8.49/8.73 797 -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)].
% 8.49/8.73 798 -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)].
% 8.49/8.73 799 -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)].
% 8.49/8.73 800 -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)].
% 8.49/8.73 801 -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)].
% 8.49/8.73 802 -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)].
% 8.49/8.73 803 -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)].
% 8.49/8.73 804 -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)].
% 8.49/8.73 805 -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)].
% 8.49/8.73 806 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(71,a,99,b)].
% 8.49/8.73 807 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(100,a,99,b)].
% 8.49/8.73 808 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(102,a,99,b)].
% 8.49/8.73 809 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(103,a,99,b)].
% 8.49/8.73 810 -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)].
% 8.49/8.73 811 -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)].
% 8.49/8.73 812 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(183,a,178,b)].
% 8.49/8.73 813 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(184,a,178,b)].
% 8.49/8.73 814 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(217,a,212,b)].
% 8.49/8.73 815 -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)].
% 8.49/8.73 816 -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)].
% 8.49/8.76 817 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(223,a,212,b)].
% 8.49/8.76 818 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(224,a,212,b)].
% 8.49/8.76 819 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(226,b,212,b)].
% 8.49/8.76 820 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(227,b,212,b)].
% 8.49/8.76 821 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(307,a,304,b)].
% 8.49/8.76 822 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(308,a,304,b)].
% 8.49/8.76 823 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(346,b,343,b)].
% 8.49/8.76 824 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(380,a,373,b)].
% 8.49/8.76 825 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(381,a,373,b)].
% 8.49/8.76 826 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(386,b,373,b)].
% 8.49/8.76 827 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(389,c,373,b)].
% 8.49/8.76 828 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(390,c,373,b)].
% 8.49/8.76 829 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(391,b,373,b)].
% 8.49/8.76 830 -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)].
% 8.49/8.76 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)].
% 8.49/8.76 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)].
% 8.49/8.76 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)].
% 8.49/8.76 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)].
% 8.49/8.76 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)].
% 8.49/8.76 831 -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)].
% 8.49/8.76 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)].
% 8.49/8.76 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)].
% 8.49/8.76 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)].
% 8.49/8.76 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)].
% 8.61/8.81 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)].
% 8.61/8.81 832 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 833 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 834 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 835 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(598,a,595,b)].
% 8.61/8.81 836 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(599,a,595,b)].
% 8.61/8.81 837 -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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 838 -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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 839 -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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 840 -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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 841 -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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 842 -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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.61/8.81 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)].
% 8.63/8.83 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_Oordered__idom(A). [resolve(842,d,791,b)].
% 8.63/8.83 843 -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)].
% 8.63/8.83 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(843,d,788,b)].
% 8.63/8.83 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_Oidom(A). [resolve(843,d,789,b)].
% 8.63/8.83 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_Oordered__field(A). [resolve(843,d,790,b)].
% 8.63/8.83 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_Oordered__idom(A). [resolve(843,d,791,b)].
% 8.63/8.83 844 -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)].
% 8.63/8.83 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(844,d,788,b)].
% 8.63/8.83 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_Oidom(A). [resolve(844,d,789,b)].
% 8.63/8.83 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_Oordered__field(A). [resolve(844,d,790,b)].
% 8.63/8.83 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_Oordered__idom(A). [resolve(844,d,791,b)].
% 8.63/8.83 845 -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)].
% 8.63/8.83 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(845,d,788,b)].
% 8.63/8.83 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(845,d,789,b)].
% 8.63/8.83 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(845,d,790,b)].
% 8.63/8.83 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(845,d,791,b)].
% 8.63/8.83 846 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(681,b,659,b)].
% 8.63/8.83 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(846,b,788,b)].
% 8.63/8.83 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(846,b,789,b)].
% 8.63/8.83 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(846,b,790,b)].
% 8.63/8.83 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(846,b,791,b)].
% 8.63/8.83 847 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(682,b,659,b)].
% 8.63/8.83 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(847,b,788,b)].
% 8.63/8.83 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(847,b,789,b)].
% 8.63/8.83 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(847,b,790,b)].
% 8.63/8.83 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(847,b,791,b)].
% 8.63/8.83 848 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(768,a,754,b)].
% 8.63/8.91 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(848,b,785,a)].
% 8.63/8.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(848,b,786,b)].
% 8.63/8.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(848,b,787,b)].
% 8.63/8.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(848,b,788,b)].
% 8.63/8.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(848,b,789,b)].
% 8.63/8.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(848,b,790,b)].
% 8.63/8.91 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(848,b,791,b)].
% 8.63/8.91 849 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(769,a,754,b)].
% 8.63/8.91 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(849,b,785,a)].
% 8.63/8.91 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(849,b,786,b)].
% 8.63/8.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(849,b,787,b)].
% 8.63/8.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(849,b,788,b)].
% 8.63/8.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(849,b,789,b)].
% 8.63/8.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(849,b,790,b)].
% 8.63/8.91 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(849,b,791,b)].
% 8.63/8.91 850 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(779,b,754,b)].
% 8.63/8.91 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(850,b,785,a)].
% 8.63/8.91 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(850,b,786,b)].
% 8.63/8.91 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(850,b,787,b)].
% 8.63/8.91 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(850,b,788,b)].
% 8.63/8.91 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(850,b,789,b)].
% 8.63/8.91 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(850,b,790,b)].
% 8.63/8.91 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(850,b,791,b)].
% 8.63/8.91 851 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(780,b,754,b)].
% 8.63/8.91 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(851,b,785,a)].
% 8.63/8.91 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(851,b,786,b)].
% 8.63/8.91 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(851,b,787,b)].
% 8.63/8.91 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(851,b,788,b)].
% 8.63/8.91 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(851,b,789,b)].
% 8.63/8.91 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(851,b,790,b)].
% 8.63/8.91 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(851,b,791,b)].
% 8.63/8.91 852 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(783,b,754,b)].
% 8.63/8.91 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(852,b,785,a)].
% 8.63/8.91 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(852,b,786,b)].
% 8.63/8.91 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(852,b,787,b)].
% 8.63/8.91 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(852,b,788,b)].
% 8.63/8.91 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(852,b,789,b)].
% 8.63/8.91 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(852,b,790,b)].
% 8.63/8.91 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(852,b,791,b)].
% 8.63/8.91 853 -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].
% 8.63/8.91 854 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom). [assumption].
% 8.63/8.91 855 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom). [assumption].
% 8.73/8.94 856 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom). [assumption].
% 8.73/8.94 857 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom). [assumption].
% 8.73/8.94 858 -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].
% 8.73/8.94 859 -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].
% 8.73/8.94 860 -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].
% 8.73/8.94 861 -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].
% 8.73/8.94 862 -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].
% 8.73/8.94 863 -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].
% 8.73/8.94 864 -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].
% 8.73/8.94 865 -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].
% 8.73/8.94 866 -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].
% 8.73/8.94 867 -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].
% 8.73/8.94 868 -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].
% 8.73/8.94 869 -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].
% 8.73/8.94 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(869,a,854,a)].
% 8.73/8.94 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(869,a,855,a)].
% 8.73/8.94 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(869,a,856,b)].
% 8.73/8.94 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Power_Orecpower(A). [resolve(869,a,857,b)].
% 8.73/8.94 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(869,a,858,b)].
% 8.73/8.94 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(869,a,864,b)].
% 8.73/8.94 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(869,a,865,b)].
% 8.73/8.94 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(869,a,866,b)].
% 8.73/8.94 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(869,a,867,b)].
% 8.73/8.94 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(869,a,868,b)].
% 8.73/8.94 870 -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].
% 8.73/8.94 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(870,a,854,a)].
% 8.73/8.94 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(870,a,855,a)].
% 8.73/8.94 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(870,a,856,b)].
% 8.73/8.94 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Power_Orecpower(A). [resolve(870,a,857,b)].
% 8.73/8.94 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(870,a,858,b)].
% 8.73/8.94 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(870,a,864,b)].
% 8.73/8.95 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(870,a,865,b)].
% 8.73/8.95 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(870,a,866,b)].
% 8.73/8.95 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(870,a,867,b)].
% 8.73/8.95 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(870,a,868,b)].
% 8.73/8.95 871 -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].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 872 -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].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.95 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)].
% 8.73/8.97 873 -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].
% 8.73/8.97 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(873,a,854,a)].
% 8.73/8.97 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(873,a,855,a)].
% 8.73/8.97 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Numeral_Onumber__ring(B). [resolve(873,a,856,b)].
% 8.73/8.97 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Power_Orecpower(B). [resolve(873,a,857,b)].
% 8.73/8.97 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)].
% 8.73/8.97 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(873,a,864,b)].
% 8.73/8.97 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oidom(B). [resolve(873,a,865,b)].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 874 -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].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 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)].
% 8.73/8.97 875 -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].
% 8.73/8.97 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(875,a,854,a)].
% 8.73/8.97 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(875,a,855,a)].
% 8.73/8.97 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Numeral_Onumber__ring(A). [resolve(875,a,856,b)].
% 8.73/8.97 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Power_Orecpower(A). [resolve(875,a,857,b)].
% 8.73/8.97 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(875,a,858,b)].
% 8.73/8.97 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(875,a,864,b)].
% 8.73/8.97 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(875,a,865,b)].
% 8.73/8.97 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(875,a,866,b)].
% 8.73/8.98 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(875,a,867,b)].
% 8.73/8.98 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__semidom(A). [resolve(875,a,868,b)].
% 8.73/8.98 876 -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].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 877 -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].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.73/8.98 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)].
% 8.92/9.11 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)].
% 8.92/9.11 878 -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].
% 8.92/9.11 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(878,a,854,a)].
% 8.92/9.11 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(878,a,855,a)].
% 8.92/9.11 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(878,a,856,b)].
% 8.92/9.11 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Power_Orecpower(A). [resolve(878,a,857,b)].
% 8.92/9.11 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(878,a,858,b)].
% 8.92/9.11 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(878,a,864,b)].
% 8.92/9.11 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(878,a,865,b)].
% 8.92/9.11 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(878,a,866,b)].
% 8.92/9.11 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(878,a,867,b)].
% 8.92/9.11 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(878,a,868,b)].
% 8.92/9.11 879 -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)].
% 8.92/9.11 880 -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)].
% 8.92/9.11 881 -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)].
% 8.92/9.11 882 -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)].
% 8.92/9.11 883 -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)].
% 8.92/9.11 884 -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)].
% 8.92/9.11 885 -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)].
% 8.92/9.11 886 -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)].
% 8.92/9.11 887 -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)].
% 8.92/9.11 888 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(71,a,82,b)].
% 8.92/9.11 889 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(100,a,82,b)].
% 8.92/9.11 890 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(102,a,82,b)].
% 8.92/9.11 891 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(103,a,82,b)].
% 8.92/9.11 892 -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)].
% 8.92/9.11 893 -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)].
% 8.92/9.11 894 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Ozero(A). [resolve(161,b,142,a)].
% 8.94/9.20 895 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(183,a,161,b)].
% 8.94/9.20 896 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(184,a,161,b)].
% 8.94/9.20 897 -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)].
% 8.94/9.20 898 -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)].
% 8.94/9.20 899 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(223,a,195,b)].
% 8.94/9.20 900 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(224,a,195,b)].
% 8.94/9.20 901 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(226,b,195,b)].
% 8.94/9.20 902 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(227,b,195,b)].
% 8.94/9.20 903 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(262,b,243,b)].
% 8.94/9.20 904 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)].
% 8.94/9.20 905 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)].
% 8.94/9.20 906 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(346,b,328,b)].
% 8.94/9.20 907 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(380,a,358,b)].
% 8.94/9.20 908 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(381,a,358,b)].
% 8.94/9.20 909 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(386,b,358,b)].
% 8.94/9.20 910 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)].
% 8.94/9.20 911 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)].
% 8.94/9.20 912 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(391,b,358,b)].
% 8.94/9.20 913 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(598,a,589,b)].
% 8.94/9.20 914 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(599,a,589,b)].
% 8.94/9.20 915 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(633,b,618,b)].
% 8.94/9.20 916 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(634,b,618,b)].
% 8.94/9.20 917 -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)].
% 8.94/9.20 918 -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)].
% 8.94/9.20 919 -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)].
% 8.94/9.20 920 -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)].
% 8.94/9.20 921 -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)].
% 8.94/9.20 922 -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)].
% 8.94/9.20 923 -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)].
% 9.41/9.62 924 -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)].
% 9.41/9.62 925 -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)].
% 9.41/9.62 926 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(681,b,653,b)].
% 9.41/9.62 927 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(682,b,653,b)].
% 9.41/9.62 928 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(738,b,694,b)].
% 9.41/9.62 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(928,b,854,a)].
% 9.41/9.62 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(928,b,855,a)].
% 9.41/9.62 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(928,b,856,b)].
% 9.41/9.62 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(928,b,857,b)].
% 9.41/9.62 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(928,b,858,b)].
% 9.41/9.62 929 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(739,b,694,b)].
% 9.41/9.62 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(929,b,854,a)].
% 9.41/9.62 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(929,b,855,a)].
% 9.41/9.62 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(929,b,856,b)].
% 9.41/9.62 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(929,b,857,b)].
% 9.41/9.62 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(929,b,858,b)].
% 9.41/9.62 930 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(779,b,748,b)].
% 9.41/9.62 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(930,b,855,a)].
% 9.41/9.62 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(930,b,857,b)].
% 9.41/9.62 931 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(780,b,748,b)].
% 9.41/9.62 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(931,b,855,a)].
% 9.41/9.62 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(931,b,857,b)].
% 9.41/9.62 932 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(783,b,748,b)].
% 9.41/9.62 Derived: class_HOL_Ozero(tc_nat). [resolve(932,b,855,a)].
% 9.41/9.62 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(932,b,857,b)].
% 9.41/9.62 933 -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].
% 9.41/9.62 934 class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_30) # label(axiom). [assumption].
% 9.41/9.62 935 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom). [assumption].
% 9.41/9.62 936 -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_14) # label(axiom). [assumption].
% 9.41/9.62 937 -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].
% 9.41/9.62 938 -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].
% 9.41/9.62 939 -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].
% 9.41/9.62 940 -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].
% 9.41/9.62 941 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Ofield_0) # label(axiom). [assumption].
% 9.41/9.63 942 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oidom_0) # label(axiom). [assumption].
% 9.41/9.63 943 -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].
% 9.41/9.63 944 -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].
% 9.41/9.63 945 -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].
% 9.41/9.63 Derived: c_in(c_0,c_IntDef_OInts,tc_IntDef_Oint). [resolve(945,a,934,a)].
% 9.41/9.63 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Numeral_Onumber__ring(A). [resolve(945,a,935,b)].
% 9.41/9.63 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(945,a,941,b)].
% 9.41/9.63 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(945,a,942,b)].
% 9.41/9.63 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(945,a,943,b)].
% 9.41/9.63 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(945,a,944,b)].
% 9.41/9.63 946 -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].
% 9.41/9.63 Derived: c_in(c_1,c_IntDef_OInts,tc_IntDef_Oint). [resolve(946,a,934,a)].
% 9.41/9.63 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Numeral_Onumber__ring(A). [resolve(946,a,935,b)].
% 9.41/9.63 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(946,a,941,b)].
% 9.41/9.63 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(946,a,942,b)].
% 9.41/9.63 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(946,a,943,b)].
% 9.41/9.63 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(946,a,944,b)].
% 9.41/9.63 947 -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].
% 9.41/9.63 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)].
% 9.41/9.63 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)].
% 9.41/9.63 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)].
% 9.41/9.63 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)].
% 9.41/9.63 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)].
% 9.41/9.63 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)].
% 9.41/9.63 948 -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].
% 9.41/9.63 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)].
% 9.41/9.63 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)].
% 9.41/9.63 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)].
% 9.41/9.63 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)].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 949 -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].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 950 -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].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 951 -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].
% 9.41/9.64 Derived: c_IntDef_Oof__int(c_1,tc_IntDef_Oint) = c_1. [resolve(951,a,934,a)].
% 9.41/9.64 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Numeral_Onumber__ring(A). [resolve(951,a,935,b)].
% 9.41/9.64 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(951,a,941,b)].
% 9.41/9.64 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(951,a,942,b)].
% 9.41/9.64 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(951,a,943,b)].
% 9.41/9.64 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(951,a,944,b)].
% 9.41/9.64 952 -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].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.64 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 953 -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].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 954 -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].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 955 -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].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.65 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)].
% 9.41/9.67 956 -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].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 957 -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].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 958 -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].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 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)].
% 9.41/9.67 959 -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].
% 9.52/9.70 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)].
% 9.52/9.70 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)].
% 9.52/9.70 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)].
% 9.52/9.70 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)].
% 9.52/9.70 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)].
% 9.52/9.70 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)].
% 9.52/9.70 960 -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].
% 9.52/9.70 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)].
% 9.52/9.70 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)].
% 9.52/9.70 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)].
% 9.52/9.70 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)].
% 9.52/9.70 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)].
% 9.52/9.70 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)].
% 9.53/9.71 961 -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].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 962 -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].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 963 -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].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.71 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)].
% 9.53/9.81 964 -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)].
% 9.53/9.81 965 -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)].
% 9.53/9.81 966 -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)].
% 9.53/9.81 967 -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)].
% 9.53/9.81 968 -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)].
% 9.53/9.81 969 -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)].
% 9.53/9.81 970 -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)].
% 9.53/9.81 971 -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)].
% 9.53/9.81 972 -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)].
% 9.53/9.81 973 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(71,a,77,b)].
% 9.53/9.81 974 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(100,a,77,b)].
% 9.53/9.81 975 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(102,a,77,b)].
% 9.53/9.81 976 -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)].
% 9.53/9.81 977 -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)].
% 9.53/9.81 978 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(119,a,116,b)].
% 9.53/9.81 979 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(135,b,116,b)].
% 9.53/9.81 980 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(136,b,116,b)].
% 9.53/9.81 981 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(138,b,116,b)].
% 9.53/9.81 982 -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)].
% 9.53/9.81 983 -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)].
% 9.53/9.81 984 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(183,a,157,b)].
% 9.53/9.81 985 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(184,a,157,b)].
% 9.53/9.81 986 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(217,a,191,b)].
% 9.53/9.81 987 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(223,a,191,b)].
% 9.53/9.81 988 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(224,a,191,b)].
% 9.53/9.81 989 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(226,b,191,b)].
% 9.53/9.81 990 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(227,b,191,b)].
% 9.64/9.87 991 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(262,b,234,b)].
% 9.64/9.87 992 -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)].
% 9.64/9.87 993 -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)].
% 9.64/9.87 994 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(265,b,234,b)].
% 9.64/9.87 995 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(266,b,234,b)].
% 9.64/9.87 996 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(268,b,234,b)].
% 9.64/9.87 997 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(269,b,234,b)].
% 9.64/9.87 998 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)].
% 9.64/9.87 999 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)].
% 9.64/9.87 1000 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(346,b,326,b)].
% 9.64/9.87 1001 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(380,a,356,b)].
% 9.64/9.87 1002 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(381,a,356,b)].
% 9.64/9.87 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)].
% 9.64/9.87 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)].
% 9.64/9.87 1005 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(391,b,356,b)].
% 9.64/9.87 1006 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(410,a,397,b)].
% 9.64/9.87 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)].
% 9.64/9.87 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)].
% 9.64/9.87 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)].
% 9.64/9.87 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)].
% 9.64/9.87 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)].
% 9.64/9.87 1012 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(439,b,397,b)].
% 9.64/9.87 1013 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(440,b,397,b)].
% 9.64/9.87 1014 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(441,b,397,b)].
% 9.64/9.87 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)].
% 9.64/9.87 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)].
% 9.64/9.87 1017 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(444,b,397,b)].
% 9.64/9.87 1018 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(480,b,452,b)].
% 9.64/9.87 1019 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(598,a,587,b)].
% 9.64/9.87 1020 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(599,a,587,b)].
% 9.64/9.87 1021 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(633,b,616,b)].
% 9.64/9.87 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 1031 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(681,b,651,b)].
% 9.64/9.89 1032 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(682,b,651,b)].
% 9.64/9.89 1033 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(727,b,688,b)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.89 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 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)].
% 9.64/9.90 1043 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(738,b,688,b)].
% 9.64/9.90 1044 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(739,b,688,b)].
% 9.64/9.90 1045 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(740,b,688,b)].
% 9.64/9.90 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(1045,b,934,a)].
% 9.64/9.90 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(1045,b,935,b)].
% 9.64/9.90 1046 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(741,b,688,b)].
% 9.64/9.90 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(1046,b,934,a)].
% 9.64/9.90 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(1046,b,935,b)].
% 9.64/9.90 1047 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(783,b,747,b)].
% 9.64/9.90 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 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)].
% 9.73/9.92 1053 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(848,b,787,b)].
% 9.73/9.92 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1053,b,934,a)].
% 9.73/9.92 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(1053,b,935,b)].
% 9.73/9.92 1054 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(850,b,787,b)].
% 9.73/9.92 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1054,b,934,a)].
% 9.73/9.92 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(1054,b,935,b)].
% 9.73/9.92 1055 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(851,b,787,b)].
% 9.73/9.92 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1055,b,934,a)].
% 9.73/9.92 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(1055,b,935,b)].
% 9.73/9.92 1056 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(852,b,787,b)].
% 9.73/9.92 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1056,b,934,a)].
% 9.73/9.92 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(1056,b,935,b)].
% 9.73/9.92 1057 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(869,a,858,b)].
% 9.73/9.92 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1057,b,934,a)].
% 9.73/9.92 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(1057,b,935,b)].
% 9.73/9.92 1058 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(870,a,858,b)].
% 9.73/9.93 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1058,b,934,a)].
% 9.73/9.93 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(1058,b,935,b)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(1061,b,934,a)].
% 9.73/9.93 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Numeral_Onumber__ring(B). [resolve(1061,b,935,b)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 1063 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(875,a,858,b)].
% 9.73/9.93 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(1063,b,934,a)].
% 9.73/9.93 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Numeral_Onumber__ring(A). [resolve(1063,b,935,b)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 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)].
% 9.73/9.93 1066 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(878,a,858,b)].
% 9.73/9.93 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(1066,b,934,a)].
% 9.73/9.93 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(1066,b,935,b)].
% 9.73/9.93 1067 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(928,b,858,b)].
% 9.73/9.93 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1067,b,934,a)].
% 9.73/9.93 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(1067,b,935,b)].
% 9.73/9.93 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1067,b,941,b)].
% 9.73/9.93 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1067,b,942,b)].
% 9.83/10.02 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1067,b,943,b)].
% 9.83/10.02 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1067,b,944,b)].
% 9.83/10.02 1068 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(929,b,858,b)].
% 9.83/10.02 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1068,b,934,a)].
% 9.83/10.02 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(1068,b,935,b)].
% 9.83/10.02 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1068,b,941,b)].
% 9.83/10.02 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1068,b,942,b)].
% 9.83/10.02 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1068,b,943,b)].
% 9.83/10.02 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1068,b,944,b)].
% 9.83/10.02 1069 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom). [assumption].
% 9.83/10.02 1070 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom). [assumption].
% 9.83/10.02 1071 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom). [assumption].
% 9.83/10.02 1072 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom). [assumption].
% 9.83/10.02 1073 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom). [assumption].
% 9.83/10.02 1074 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom). [assumption].
% 9.83/10.02 1075 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom). [assumption].
% 9.83/10.02 1076 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom). [assumption].
% 9.83/10.02 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].
% 9.83/10.02 1078 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom). [assumption].
% 9.83/10.02 1079 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom). [assumption].
% 9.83/10.02 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1079,b,1069,a)].
% 9.83/10.02 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].
% 9.83/10.02 1081 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom). [assumption].
% 9.83/10.02 1082 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom). [assumption].
% 9.83/10.02 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].
% 9.83/10.02 1084 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom). [assumption].
% 9.83/10.02 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].
% 9.83/10.02 1086 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom). [assumption].
% 9.92/10.11 1087 -class_LOrder_Omeet__semilorder(A) | c_LOrder_Omeet(B,B,A) = B # label(cls_LOrder_Omeet__idempotent_0) # label(axiom). [assumption].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1087,a,1070,a)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1087,a,1071,a)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1087,a,1072,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1087,a,1073,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1087,a,1074,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1087,a,1075,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1087,a,1076,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1087,a,1077,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1087,a,1078,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1087,a,1079,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1087,a,1080,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1087,a,1081,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1087,a,1082,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1087,a,1083,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1087,a,1084,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1087,a,1085,b)].
% 9.92/10.11 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1087,a,1086,b)].
% 9.92/10.11 1088 -class_LOrder_Omeet__semilorder(A) | c_lessequals(B,B,A). [resolve(7,b,2,a)].
% 9.92/10.11 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1088,a,1070,a)].
% 9.92/10.11 Derived: c_lessequals(A,A,tc_nat). [resolve(1088,a,1071,a)].
% 9.92/10.11 Derived: c_lessequals(A,A,B) | -class_LOrder_Olorder(B). [resolve(1088,a,1072,b)].
% 9.92/10.11 1089 class_Orderings_Oord(A) | -class_LOrder_Omeet__semilorder(A). [resolve(18,a,7,b)].
% 9.92/10.11 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1089,b,1070,a)].
% 9.92/10.11 Derived: class_Orderings_Oord(tc_nat). [resolve(1089,b,1071,a)].
% 9.92/10.11 Derived: class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(1089,b,1072,b)].
% 9.92/10.11 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1089,b,1080,b)].
% 9.92/10.11 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1089,b,1081,b)].
% 9.92/10.11 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1089,b,1082,b)].
% 9.92/10.11 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1089,b,1083,b)].
% 9.92/10.11 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1089,b,1084,b)].
% 9.92/10.11 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1089,b,1085,b)].
% 9.92/10.11 1090 -c_less(A,A,B) | -class_LOrder_Omeet__semilorder(B). [resolve(33,a,7,b)].
% 9.92/10.11 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1090,b,1070,a)].
% 9.92/10.11 Derived: -c_less(A,A,tc_nat). [resolve(1090,b,1071,a)].
% 9.92/10.11 Derived: -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(1090,b,1072,b)].
% 9.92/10.11 1091 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(34,a,7,b)].
% 9.92/10.11 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1091,c,1070,a)].
% 9.92/10.11 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1091,c,1071,a)].
% 9.92/10.11 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1091,c,1072,b)].
% 9.92/10.11 1092 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Omeet__semilorder(B). [resolve(35,a,7,b)].
% 9.92/10.13 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1092,b,1070,a)].
% 9.92/10.13 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1092,b,1071,a)].
% 9.92/10.13 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(1092,b,1072,b)].
% 9.92/10.13 1093 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(36,a,7,b)].
% 9.92/10.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1093,c,1070,a)].
% 9.92/10.13 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1093,c,1071,a)].
% 9.92/10.13 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1093,c,1072,b)].
% 9.92/10.13 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)].
% 9.92/10.13 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1094,c,1070,a)].
% 9.92/10.13 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1094,c,1071,a)].
% 9.92/10.13 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)].
% 9.92/10.13 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)].
% 9.92/10.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1095,c,1070,a)].
% 9.92/10.13 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(1095,c,1071,a)].
% 9.92/10.13 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)].
% 9.92/10.13 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)].
% 9.92/10.13 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1096,c,1070,a)].
% 9.92/10.13 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(1096,c,1071,a)].
% 9.92/10.13 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)].
% 9.92/10.13 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)].
% 9.92/10.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1097,c,1070,a)].
% 9.92/10.13 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(1097,c,1071,a)].
% 9.92/10.13 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)].
% 9.92/10.13 1098 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(41,a,7,b)].
% 9.92/10.13 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1098,c,1070,a)].
% 9.92/10.13 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1098,c,1071,a)].
% 10.13/10.36 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1098,c,1072,b)].
% 10.13/10.36 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)].
% 10.13/10.36 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)].
% 10.13/10.36 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)].
% 10.13/10.36 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)].
% 10.13/10.36 1100 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom). [assumption].
% 10.13/10.36 1101 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom). [assumption].
% 10.13/10.36 1102 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom). [assumption].
% 10.13/10.36 1103 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom). [assumption].
% 10.13/10.36 1104 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom). [assumption].
% 10.13/10.36 1105 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom). [assumption].
% 10.13/10.36 1106 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom). [assumption].
% 10.13/10.36 1107 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom). [assumption].
% 10.13/10.36 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].
% 10.13/10.36 1109 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom). [assumption].
% 10.13/10.36 1110 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom). [assumption].
% 10.13/10.36 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].
% 10.13/10.36 1112 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom). [assumption].
% 10.13/10.36 1113 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 10.13/10.36 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].
% 10.13/10.36 1115 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom). [assumption].
% 10.13/10.36 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].
% 10.13/10.36 1117 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom). [assumption].
% 10.13/10.36 1118 -class_LOrder_Ojoin__semilorder(A) | c_LOrder_Ojoin(B,B,A) = B # label(cls_LOrder_Ojoin__idempotent_0) # label(axiom). [assumption].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1118,a,1101,a)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1118,a,1102,a)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1118,a,1103,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1118,a,1104,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1118,a,1105,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1118,a,1106,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1118,a,1107,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1118,a,1108,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1118,a,1109,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1118,a,1110,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1118,a,1111,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1118,a,1112,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1118,a,1113,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1118,a,1114,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1118,a,1115,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1118,a,1116,b)].
% 10.50/10.68 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1118,a,1117,b)].
% 10.50/10.68 1119 -class_LOrder_Ojoin__semilorder(A) | c_lessequals(B,B,A). [resolve(5,b,2,a)].
% 10.50/10.68 1120 class_Orderings_Oord(A) | -class_LOrder_Ojoin__semilorder(A). [resolve(18,a,5,b)].
% 10.50/10.68 1121 -c_less(A,A,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(33,a,5,b)].
% 10.50/10.68 1122 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(34,a,5,b)].
% 10.50/10.68 1123 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(35,a,5,b)].
% 10.50/10.68 1124 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(36,a,5,b)].
% 10.50/10.68 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)].
% 10.50/10.68 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)].
% 10.50/10.68 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)].
% 10.50/10.68 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)].
% 10.50/10.68 1129 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(41,a,5,b)].
% 10.50/10.68 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)].
% 10.50/10.68 1131 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom). [assumption].
% 10.50/10.68 1132 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom). [assumption].
% 10.50/10.68 1133 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom). [assumption].
% 10.50/10.68 1134 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom). [assumption].
% 10.50/10.68 1135 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom). [assumption].
% 10.50/10.68 1136 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom). [assumption].
% 10.74/10.92 1137 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom). [assumption].
% 10.74/10.92 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].
% 10.74/10.92 1139 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom). [assumption].
% 10.74/10.92 1140 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom). [assumption].
% 10.74/10.92 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].
% 10.74/10.92 1142 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom). [assumption].
% 10.74/10.92 1143 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom). [assumption].
% 10.74/10.92 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].
% 10.74/10.92 1145 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom). [assumption].
% 10.74/10.92 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].
% 10.74/10.92 1147 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom). [assumption].
% 10.74/10.92 1148 -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(6,b,2,a)].
% 10.74/10.92 1149 class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(18,a,6,b)].
% 10.74/10.92 1150 -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(33,a,6,b)].
% 10.74/10.92 1151 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(34,a,6,b)].
% 10.74/10.92 1152 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(35,a,6,b)].
% 10.74/10.92 1153 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(36,a,6,b)].
% 10.74/10.92 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)].
% 10.74/10.92 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)].
% 10.74/10.92 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)].
% 10.74/10.92 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)].
% 10.74/10.92 1158 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(41,a,6,b)].
% 10.74/10.93 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)].
% 10.74/10.93 1160 c_LOrder_Omeet(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1087,a,1072,b)].
% 10.74/10.93 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1160,b,1132,a)].
% 10.74/10.93 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1160,b,1133,a)].
% 10.74/10.93 1161 c_lessequals(A,A,B) | -class_LOrder_Olorder(B). [resolve(1088,a,1072,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1161,b,1132,a)].
% 10.74/10.93 Derived: c_lessequals(A,A,tc_nat). [resolve(1161,b,1133,a)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1161,b,1134,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1161,b,1135,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1161,b,1136,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1161,b,1137,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1161,b,1138,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1161,b,1139,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1161,b,1140,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1161,b,1141,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1161,b,1142,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1161,b,1143,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1161,b,1144,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1161,b,1145,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1161,b,1146,b)].
% 10.74/10.93 Derived: c_lessequals(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1161,b,1147,b)].
% 10.74/10.93 1162 class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(1089,b,1072,b)].
% 10.74/10.93 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1162,b,1132,a)].
% 10.74/10.93 Derived: class_Orderings_Oord(tc_nat). [resolve(1162,b,1133,a)].
% 10.74/10.93 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1162,b,1134,b)].
% 10.74/10.93 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1162,b,1135,b)].
% 10.74/10.93 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1162,b,1136,b)].
% 10.74/10.93 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1162,b,1137,b)].
% 10.74/10.93 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1162,b,1138,b)].
% 10.74/10.93 Derived: class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(1162,b,1139,b)].
% 10.74/10.93 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1162,b,1140,b)].
% 10.74/10.93 Derived: class_Orderings_Oord(A) | -class_Wellfounded__Recursion_Owellorder(A). [resolve(1162,b,1147,b)].
% 10.74/10.93 1163 -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(1090,b,1072,b)].
% 10.74/10.93 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1163,b,1132,a)].
% 10.74/10.93 Derived: -c_less(A,A,tc_nat). [resolve(1163,b,1133,a)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1163,b,1134,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1163,b,1135,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1163,b,1136,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1163,b,1137,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1163,b,1138,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1163,b,1139,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1163,b,1140,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1163,b,1141,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1163,b,1142,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1163,b,1143,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1163,b,1144,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1163,b,1145,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1163,b,1146,b)].
% 10.74/10.93 Derived: -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1163,b,1147,b)].
% 10.74/10.93 1164 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1091,c,1072,b)].
% 10.74/10.93 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1164,c,1132,a)].
% 10.74/10.93 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1164,c,1133,a)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1164,c,1139,b)].
% 10.74/10.93 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)].
% 10.74/10.93 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1164,c,1141,b)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1164,c,1147,b)].
% 10.74/10.93 1165 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(1092,b,1072,b)].
% 10.74/10.93 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1165,b,1132,a)].
% 10.74/10.93 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1165,b,1133,a)].
% 10.74/10.93 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1165,b,1134,b)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(1165,b,1139,b)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1165,b,1147,b)].
% 10.74/10.93 1166 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1093,c,1072,b)].
% 10.74/10.93 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1166,c,1132,a)].
% 10.74/10.93 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1166,c,1133,a)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1166,c,1139,b)].
% 10.74/10.93 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)].
% 10.74/10.93 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1166,c,1141,b)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1166,c,1147,b)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 1171 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1098,c,1072,b)].
% 10.74/10.93 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1171,c,1132,a)].
% 10.74/10.93 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1171,c,1133,a)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1171,c,1139,b)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1171,c,1147,b)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.93 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)].
% 10.74/10.94 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)].
% 10.74/10.94 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)].
% 10.74/10.94 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)].
% 10.74/10.94 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)].
% 10.74/10.94 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)].
% 10.82/11.04 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)].
% 10.82/11.04 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)].
% 10.82/11.04 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)].
% 10.82/11.04 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)].
% 10.82/11.04 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)].
% 10.82/11.04 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)].
% 10.82/11.04 1173 c_LOrder_Ojoin(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1118,a,1103,b)].
% 10.82/11.04 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1173,b,1132,a)].
% 10.82/11.04 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1173,b,1133,a)].
% 10.82/11.04 1174 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom). [assumption].
% 10.82/11.04 1175 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom). [assumption].
% 10.82/11.04 1176 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom). [assumption].
% 10.82/11.04 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].
% 10.82/11.04 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].
% 10.82/11.04 1179 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom). [assumption].
% 10.82/11.04 1180 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 10.82/11.04 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].
% 10.82/11.04 1182 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom). [assumption].
% 10.82/11.04 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].
% 10.82/11.04 1184 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom). [assumption].
% 10.82/11.04 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].
% 10.82/11.04 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)].
% 10.82/11.04 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)].
% 10.82/11.04 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)].
% 10.82/11.04 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.05 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)].
% 10.82/11.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1187,a,1178,b)].
% 10.82/11.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1187,a,1179,b)].
% 10.82/11.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1187,a,1180,b)].
% 10.82/11.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1187,a,1181,b)].
% 10.82/11.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1187,a,1182,b)].
% 10.82/11.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1187,a,1183,b)].
% 10.82/11.06 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1187,a,1184,b)].
% 10.82/11.06 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].
% 10.82/11.06 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(1188,a,1175,a)].
% 10.82/11.06 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset. [resolve(1188,a,1176,a)].
% 10.82/11.06 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1188,a,1177,b)].
% 10.82/11.06 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1188,a,1178,b)].
% 10.82/11.06 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1188,a,1179,b)].
% 10.82/11.06 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1188,a,1180,b)].
% 10.82/11.06 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1188,a,1181,b)].
% 10.82/11.06 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1188,a,1182,b)].
% 10.82/11.06 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1188,a,1183,b)].
% 10.82/11.07 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)].
% 10.82/11.07 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].
% 10.82/11.07 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)].
% 10.82/11.07 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)].
% 10.82/11.07 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)].
% 10.82/11.07 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)].
% 10.82/11.07 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)].
% 10.82/11.07 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)].
% 10.82/11.07 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)].
% 10.82/11.07 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)].
% 10.82/11.07 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)].
% 10.82/11.07 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)].
% 10.82/11.07 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].
% 10.82/11.07 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)].
% 10.82/11.07 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)].
% 10.82/11.07 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1190,a,1177,b)].
% 10.82/11.07 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1190,a,1178,b)].
% 10.82/11.07 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1190,a,1179,b)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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)].
% 10.82/11.08 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].
% 10.82/11.08 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.09 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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].
% 10.92/11.10 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1194,a,1175,a)].
% 10.92/11.10 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1194,a,1176,a)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1194,a,1184,b)].
% 10.92/11.10 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].
% 10.92/11.10 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(1195,a,1175,a)].
% 10.92/11.10 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(1195,a,1176,a)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.92/11.10 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.11 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].
% 10.95/11.11 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1197,a,1175,a)].
% 10.95/11.11 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)].
% 10.95/11.11 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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].
% 10.95/11.12 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(1198,a,1175,a)].
% 10.95/11.12 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(1198,a,1176,a)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.12 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)].
% 10.95/11.13 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].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.95/11.13 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.14 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)].
% 10.98/11.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1202,a,1178,b)].
% 10.98/11.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1202,a,1179,b)].
% 10.98/11.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1202,a,1180,b)].
% 10.98/11.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1202,a,1181,b)].
% 10.98/11.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1202,a,1182,b)].
% 10.98/11.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1202,a,1183,b)].
% 10.98/11.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1202,a,1184,b)].
% 10.98/11.15 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].
% 10.98/11.15 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1203,a,1175,a)].
% 10.98/11.15 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset. [resolve(1203,a,1176,a)].
% 10.98/11.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1203,a,1177,b)].
% 10.98/11.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1203,a,1178,b)].
% 10.98/11.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1203,a,1179,b)].
% 10.98/11.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1203,a,1180,b)].
% 10.98/11.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1203,a,1181,b)].
% 10.98/11.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1203,a,1182,b)].
% 10.98/11.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1203,a,1183,b)].
% 10.98/11.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1203,a,1184,b)].
% 10.98/11.15 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].
% 10.98/11.15 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1204,a,1175,a)].
% 10.98/11.16 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1204,a,1176,a)].
% 10.98/11.16 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)].
% 10.98/11.16 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)].
% 10.98/11.16 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)].
% 10.98/11.16 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)].
% 10.98/11.16 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)].
% 10.98/11.16 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)].
% 10.98/11.16 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)].
% 10.98/11.16 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1204,a,1184,b)].
% 10.98/11.16 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].
% 10.98/11.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1205,a,1175,a)].
% 10.98/11.16 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)].
% 10.98/11.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1205,a,1177,b)].
% 10.98/11.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1205,a,1178,b)].
% 10.98/11.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1205,a,1179,b)].
% 10.98/11.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1205,a,1180,b)].
% 10.98/11.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1205,a,1181,b)].
% 10.98/11.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1205,a,1182,b)].
% 10.98/11.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1205,a,1183,b)].
% 10.98/11.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1205,a,1184,b)].
% 10.98/11.16 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].
% 10.98/11.16 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1206,a,1175,a)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.17 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.21 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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].
% 10.98/11.22 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)].
% 10.98/11.22 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(1210,a,1176,a)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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].
% 10.98/11.22 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)].
% 10.98/11.22 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(1211,a,1176,a)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 10.98/11.22 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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].
% 11.07/11.23 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)].
% 11.07/11.23 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1213,a,1176,a)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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].
% 11.07/11.23 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)].
% 11.07/11.23 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1214,a,1176,a)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.23 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)].
% 11.07/11.24 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].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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].
% 11.07/11.24 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)].
% 11.07/11.24 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1216,a,1176,a)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.24 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].
% 11.07/11.24 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)].
% 11.07/11.24 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1217,a,1176,a)].
% 11.07/11.24 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)].
% 11.07/11.24 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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)].
% 11.07/11.25 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].
% 11.07/11.25 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1219,a,1175,a)].
% 11.07/11.25 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(1219,a,1176,a)].
% 11.07/11.25 Derived: c_Orderings_Omin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1219,a,1177,b)].
% 11.07/11.25 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1219,a,1178,b)].
% 11.07/11.25 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1219,a,1179,b)].
% 11.07/11.25 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1219,a,1180,b)].
% 11.07/11.25 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1219,a,1181,b)].
% 11.07/11.25 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1219,a,1182,b)].
% 11.07/11.25 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1219,a,1183,b)].
% 11.07/11.27 Derived: c_Orderings_Omin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1219,a,1184,b)].
% 11.07/11.27 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].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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].
% 11.07/11.27 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)].
% 11.07/11.27 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1221,a,1176,a)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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)].
% 11.07/11.27 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].
% 11.07/11.27 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)].
% 11.07/11.27 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1222,a,1176,a)].
% 11.07/11.27 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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)].
% 11.07/11.28 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].
% 11.07/11.28 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1224,a,1175,a)].
% 11.07/11.28 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(1224,a,1176,a)].
% 11.07/11.28 Derived: c_Orderings_Omax(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1224,a,1177,b)].
% 11.07/11.28 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1224,a,1178,b)].
% 11.07/11.28 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1224,a,1179,b)].
% 11.07/11.28 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1224,a,1180,b)].
% 11.07/11.28 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1224,a,1181,b)].
% 11.07/11.28 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1224,a,1182,b)].
% 11.14/11.30 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1224,a,1183,b)].
% 11.14/11.30 Derived: c_Orderings_Omax(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1224,a,1184,b)].
% 11.14/11.30 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].
% 11.14/11.30 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint). [resolve(1225,a,1175,a)].
% 11.14/11.30 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)].
% 11.14/11.30 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)].
% 11.14/11.30 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)].
% 11.14/11.30 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1225,a,1179,b)].
% 11.14/11.30 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1225,a,1180,b)].
% 11.14/11.30 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)].
% 11.14/11.30 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)].
% 11.14/11.30 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)].
% 11.14/11.30 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)].
% 11.14/11.30 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].
% 11.14/11.30 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)].
% 11.14/11.30 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(1226,a,1176,a)].
% 11.14/11.30 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)].
% 11.14/11.30 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)].
% 11.14/11.30 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1226,a,1179,b)].
% 11.14/11.30 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1226,a,1180,b)].
% 11.14/11.30 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)].
% 11.14/11.30 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)].
% 11.14/11.30 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)].
% 11.14/11.30 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)].
% 11.14/11.30 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].
% 11.14/11.30 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)].
% 11.14/11.31 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(1227,a,1176,a)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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].
% 11.14/11.31 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)].
% 11.14/11.31 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(1228,a,1176,a)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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)].
% 11.14/11.31 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].
% 11.14/11.31 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)].
% 11.14/11.31 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(1229,a,1176,a)].
% 11.14/11.31 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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].
% 11.14/11.32 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1230,a,1175,a)].
% 11.14/11.32 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1230,a,1176,a)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1230,a,1184,b)].
% 11.14/11.32 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].
% 11.14/11.32 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1231,a,1175,a)].
% 11.14/11.32 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1231,a,1176,a)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.32 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)].
% 11.14/11.33 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)].
% 11.14/11.33 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1231,a,1184,b)].
% 11.14/11.33 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].
% 11.14/11.33 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1232,a,1175,a)].
% 11.14/11.33 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1232,a,1176,a)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1232,a,1184,b)].
% 11.14/11.33 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].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.33 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.34 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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)].
% 11.14/11.35 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].
% 11.14/11.35 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.14/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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].
% 11.21/11.36 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1240,a,1175,a)].
% 11.21/11.36 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1240,a,1176,a)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.21/11.36 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1240,a,1184,b)].
% 11.22/11.37 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].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.22/11.37 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)].
% 11.44/11.59 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)].
% 11.44/11.59 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)].
% 11.44/11.59 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)].
% 11.44/11.59 1243 -class_Orderings_Olinorder(A) | c_lessequals(B,B,A). [resolve(17,b,2,a)].
% 11.44/11.59 1244 class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(18,a,17,b)].
% 11.44/11.59 1245 -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(33,a,17,b)].
% 11.44/11.59 1246 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(34,a,17,b)].
% 11.44/11.59 1247 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(35,a,17,b)].
% 11.44/11.59 1248 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(36,a,17,b)].
% 11.44/11.59 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)].
% 11.44/11.59 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)].
% 11.44/11.59 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)].
% 11.44/11.59 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)].
% 11.44/11.59 1253 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(41,a,17,b)].
% 11.44/11.59 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)].
% 11.44/11.59 1255 c_LOrder_Omeet(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1087,a,1078,b)].
% 11.44/11.59 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1255,b,1177,b)].
% 11.44/11.59 1256 c_LOrder_Ojoin(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1118,a,1109,b)].
% 11.44/11.59 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1256,b,1177,b)].
% 11.44/11.59 1257 c_lessequals(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1161,b,1139,b)].
% 11.44/11.59 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1257,b,1175,a)].
% 11.44/11.59 Derived: c_lessequals(A,A,tc_nat). [resolve(1257,b,1176,a)].
% 11.44/11.59 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1257,b,1177,b)].
% 11.44/11.59 1258 class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(1162,b,1139,b)].
% 11.44/11.59 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1258,b,1175,a)].
% 11.44/11.59 Derived: class_Orderings_Oord(tc_nat). [resolve(1258,b,1176,a)].
% 11.44/11.59 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1258,b,1177,b)].
% 11.44/11.59 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1258,b,1178,b)].
% 11.44/11.59 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1258,b,1179,b)].
% 11.44/11.59 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1258,b,1180,b)].
% 11.44/11.59 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1258,b,1181,b)].
% 11.44/11.59 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1258,b,1182,b)].
% 11.44/11.59 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1258,b,1183,b)].
% 11.44/11.59 1259 -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1163,b,1139,b)].
% 11.44/11.61 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1259,b,1175,a)].
% 11.44/11.61 Derived: -c_less(A,A,tc_nat). [resolve(1259,b,1176,a)].
% 11.44/11.61 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1259,b,1177,b)].
% 11.44/11.61 1260 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1164,c,1139,b)].
% 11.44/11.61 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1260,c,1175,a)].
% 11.44/11.61 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1260,c,1176,a)].
% 11.44/11.61 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)].
% 11.44/11.61 1261 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(1165,b,1139,b)].
% 11.44/11.61 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1261,b,1175,a)].
% 11.44/11.61 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1261,b,1176,a)].
% 11.44/11.61 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)].
% 11.44/11.61 1262 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1166,c,1139,b)].
% 11.44/11.61 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1262,c,1175,a)].
% 11.44/11.61 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1262,c,1176,a)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.44/11.61 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)].
% 11.59/11.81 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)].
% 11.59/11.81 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)].
% 11.59/11.81 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)].
% 11.59/11.81 1267 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1171,c,1139,b)].
% 11.59/11.81 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1267,c,1175,a)].
% 11.59/11.81 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1267,c,1176,a)].
% 11.59/11.81 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)].
% 11.59/11.81 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)].
% 11.59/11.81 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)].
% 11.59/11.81 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)].
% 11.59/11.81 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)].
% 11.59/11.81 1269 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom). [assumption].
% 11.59/11.81 1270 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom). [assumption].
% 11.59/11.81 1271 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom). [assumption].
% 11.59/11.81 1272 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom). [assumption].
% 11.59/11.81 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].
% 11.59/11.81 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].
% 11.59/11.81 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].
% 11.59/11.81 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].
% 11.59/11.81 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].
% 11.59/11.81 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].
% 11.59/11.81 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1278,a,1276,b)].
% 11.59/11.81 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1278,a,1277,b)].
% 11.59/11.81 1279 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom). [assumption].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A). [resolve(1290,b,1269,a)].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 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].
% 11.73/11.88 Derived: -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A). [resolve(1294,b,1269,a)].
% 11.73/11.88 1295 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(14,b,2,a)].
% 11.73/11.88 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1295,a,1277,b)].
% 11.73/11.88 1296 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(18,a,14,b)].
% 11.73/11.88 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1296,b,1277,b)].
% 11.73/11.88 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1296,b,1289,b)].
% 11.73/11.88 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1296,b,1291,b)].
% 11.73/11.88 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1296,b,1292,b)].
% 12.04/12.28 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1296,b,1293,b)].
% 12.04/12.28 1297 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(33,a,14,b)].
% 12.04/12.28 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1297,b,1277,b)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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)].
% 12.04/12.28 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].
% 12.04/12.28 1308 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom). [assumption].
% 12.04/12.28 1309 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom). [assumption].
% 12.04/12.28 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1317,a,1316,b)].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 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].
% 12.18/12.36 1327 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(16,b,2,a)].
% 12.18/12.36 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1327,a,1316,b)].
% 12.18/12.36 1328 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(18,a,16,b)].
% 12.18/12.36 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1328,b,1316,b)].
% 12.18/12.36 1329 -c_less(A,A,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(33,a,16,b)].
% 12.28/12.44 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1329,b,1316,b)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.28/12.44 1339 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(284,b,270,a)].
% 12.28/12.44 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)].
% 12.28/12.44 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1340,c,1310,b)].
% 12.28/12.44 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)].
% 12.28/12.44 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)].
% 12.58/12.78 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)].
% 12.58/12.78 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)].
% 12.58/12.78 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)].
% 12.58/12.78 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)].
% 12.58/12.78 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)].
% 12.58/12.78 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1341,c,1310,b)].
% 12.58/12.78 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)].
% 12.58/12.78 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)].
% 12.58/12.78 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)].
% 12.58/12.78 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)].
% 12.58/12.78 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)].
% 12.58/12.78 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)].
% 12.58/12.78 1342 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(323,b,309,a)].
% 12.58/12.78 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1342,a,1310,b)].
% 12.58/12.78 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1342,a,1311,b)].
% 12.58/12.78 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1342,a,1312,b)].
% 12.58/12.78 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1342,a,1313,b)].
% 12.58/12.78 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].
% 12.58/12.78 1344 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom). [assumption].
% 12.58/12.78 1345 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom). [assumption].
% 12.58/12.78 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].
% 12.58/12.78 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].
% 12.58/12.78 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].
% 12.58/12.78 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].
% 12.58/12.78 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].
% 12.58/12.78 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].
% 12.58/12.78 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].
% 12.67/12.82 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].
% 12.67/12.82 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].
% 12.67/12.82 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].
% 12.67/12.82 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].
% 12.67/12.82 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].
% 12.67/12.82 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].
% 12.67/12.82 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].
% 12.67/12.82 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].
% 12.67/12.82 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].
% 12.67/12.82 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].
% 12.67/12.82 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1362,a,1344,a)].
% 12.67/12.82 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1362,a,1345,a)].
% 12.67/12.82 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)].
% 12.67/12.82 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)].
% 12.67/12.82 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)].
% 12.67/12.82 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)].
% 12.67/12.82 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)].
% 12.67/12.82 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)].
% 12.67/12.82 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)].
% 12.67/12.82 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1362,a,1355,b)].
% 12.67/12.82 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1362,a,1356,b)].
% 12.67/12.82 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1362,a,1357,b)].
% 12.67/12.82 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1362,a,1358,b)].
% 12.67/12.83 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1362,a,1359,b)].
% 12.67/12.83 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1362,a,1360,b)].
% 12.67/12.83 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)].
% 12.67/12.83 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].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1363,a,1355,b)].
% 12.67/12.83 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1363,a,1356,b)].
% 12.67/12.83 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1363,a,1357,b)].
% 12.67/12.83 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1363,a,1358,b)].
% 12.67/12.83 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1363,a,1359,b)].
% 12.67/12.83 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1363,a,1360,b)].
% 12.67/12.83 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)].
% 12.67/12.83 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].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.83 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.85 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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].
% 12.67/12.86 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1366,a,1344,a)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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].
% 12.67/12.86 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1367,a,1344,a)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.86 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.67/12.87 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 1370 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,B,A). [resolve(15,b,2,a)].
% 12.77/13.00 1371 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(18,a,15,b)].
% 12.77/13.00 1372 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(33,a,15,b)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 12.77/13.00 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)].
% 13.07/13.22 1384 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(346,b,322,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1384,b,1346,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1384,b,1347,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1384,b,1348,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1384,b,1349,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1384,b,1350,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1384,b,1351,b)].
% 13.07/13.22 1385 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1317,a,1316,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1385,b,1344,a)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1385,b,1345,a)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1385,b,1350,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1385,b,1351,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1385,b,1354,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1385,b,1355,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1385,b,1356,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1385,b,1357,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1385,b,1358,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1385,b,1359,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1385,b,1360,b)].
% 13.07/13.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1385,b,1361,b)].
% 13.07/13.22 1386 c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1327,a,1316,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1386,b,1344,a)].
% 13.07/13.22 Derived: c_lessequals(A,A,tc_nat). [resolve(1386,b,1345,a)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1386,b,1346,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1386,b,1347,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1386,b,1348,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1386,b,1349,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1386,b,1350,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1386,b,1351,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1386,b,1354,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1386,b,1355,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1386,b,1356,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1386,b,1357,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1386,b,1358,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1386,b,1359,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1386,b,1360,b)].
% 13.07/13.22 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1386,b,1361,b)].
% 13.07/13.22 1387 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1328,b,1316,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1387,b,1344,a)].
% 13.07/13.22 Derived: class_Orderings_Oord(tc_nat). [resolve(1387,b,1345,a)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1387,b,1346,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1387,b,1347,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1387,b,1348,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1387,b,1349,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1387,b,1350,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1387,b,1351,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1387,b,1354,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1387,b,1355,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1387,b,1356,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1387,b,1357,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1387,b,1358,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1387,b,1359,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1387,b,1360,b)].
% 13.07/13.22 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1387,b,1361,b)].
% 13.07/13.22 1388 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1329,b,1316,b)].
% 13.07/13.22 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1388,b,1344,a)].
% 13.07/13.22 Derived: -c_less(A,A,tc_nat). [resolve(1388,b,1345,a)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1388,b,1346,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1388,b,1347,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1388,b,1348,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1388,b,1349,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1388,b,1350,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1388,b,1351,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1388,b,1354,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1388,b,1355,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1388,b,1356,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1388,b,1357,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1388,b,1358,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1388,b,1359,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1388,b,1360,b)].
% 13.07/13.22 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1388,b,1361,b)].
% 13.07/13.22 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)].
% 13.07/13.22 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1389,c,1344,a)].
% 13.07/13.22 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1389,c,1345,a)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1390,b,1344,a)].
% 13.07/13.23 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1390,b,1345,a)].
% 13.07/13.23 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1390,b,1346,b)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1391,c,1344,a)].
% 13.07/13.23 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1391,c,1345,a)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1396,c,1344,a)].
% 13.07/13.23 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1396,c,1345,a)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.23 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)].
% 13.07/13.24 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1397,b,1354,b)].
% 13.07/13.24 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1397,b,1355,b)].
% 13.07/13.24 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1397,b,1356,b)].
% 13.07/13.24 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1397,b,1357,b)].
% 13.07/13.24 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1397,b,1358,b)].
% 13.07/13.24 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1397,b,1359,b)].
% 13.07/13.24 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1397,b,1360,b)].
% 13.07/13.24 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1397,b,1361,b)].
% 13.07/13.24 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)].
% 13.07/13.24 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1398,c,1344,a)].
% 13.07/13.24 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1398,c,1345,a)].
% 13.07/13.24 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1398,c,1346,b)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 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)].
% 13.07/13.24 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1399,c,1344,a)].
% 13.07/13.24 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1399,c,1345,a)].
% 13.07/13.24 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1399,c,1346,b)].
% 13.07/13.24 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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)].
% 13.27/13.46 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].
% 13.27/13.46 1401 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom). [assumption].
% 13.27/13.46 1402 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom). [assumption].
% 13.27/13.46 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].
% 13.27/13.46 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].
% 13.27/13.46 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].
% 13.27/13.46 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].
% 13.27/13.46 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].
% 13.27/13.46 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].
% 13.27/13.46 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].
% 13.27/13.46 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].
% 13.27/13.46 1411 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(12,b,2,a)].
% 13.27/13.46 1412 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(18,a,12,b)].
% 13.27/13.46 1413 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(33,a,12,b)].
% 13.27/13.46 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 1425 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(346,b,320,b)].
% 13.46/13.64 1426 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1087,a,1077,b)].
% 13.46/13.64 1427 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1118,a,1108,b)].
% 13.46/13.64 1428 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1161,b,1138,b)].
% 13.46/13.64 1429 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1162,b,1138,b)].
% 13.46/13.64 1430 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1163,b,1138,b)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.64 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)].
% 13.46/13.66 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)].
% 13.46/13.66 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) | B = c_emptyset. [resolve(1440,e,1401,a)].
% 13.46/13.66 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset. [resolve(1440,e,1402,a)].
% 13.46/13.66 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)].
% 13.46/13.66 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMax(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(1441,d,1401,a)].
% 13.46/13.66 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(1441,d,1402,a)].
% 13.46/13.66 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)].
% 13.46/13.66 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1442,d,1401,a)].
% 13.46/13.66 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat). [resolve(1442,d,1402,a)].
% 13.46/13.66 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)].
% 13.46/13.66 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(1443,f,1401,a)].
% 13.46/13.66 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset. [resolve(1443,f,1402,a)].
% 13.46/13.66 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)].
% 13.46/13.66 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1444,e,1401,a)].
% 13.46/13.66 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(1444,e,1402,a)].
% 13.46/13.66 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)].
% 13.46/13.66 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1445,e,1401,a)].
% 13.46/13.66 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(1445,e,1402,a)].
% 13.46/13.66 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1449,b,1401,a)].
% 13.46/13.67 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1449,b,1402,a)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.46/13.67 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)].
% 13.55/13.68 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1452,e,1402,a)].
% 13.55/13.68 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)].
% 13.55/13.68 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1453,f,1401,a)].
% 13.55/13.68 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(1453,f,1402,a)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 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)].
% 13.55/13.68 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1458,e,1401,a)].
% 13.55/13.68 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)].
% 13.56/13.70 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)].
% 13.56/13.70 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1459,b,1401,a)].
% 13.56/13.70 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1459,b,1402,a)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(1465,c,1402,a)].
% 13.56/13.70 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)].
% 13.56/13.70 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)].
% 13.56/13.70 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(1466,c,1402,a)].
% 13.56/13.70 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)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1468,c,1402,a)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1469,c,1402,a)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1471,c,1402,a)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1472,c,1402,a)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 1474 c_Orderings_Omin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1219,a,1177,b)].
% 13.57/13.72 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1474,b,1401,a)].
% 13.57/13.72 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(1474,b,1402,a)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 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)].
% 13.57/13.72 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1476,c,1402,a)].
% 13.57/13.72 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)].
% 13.57/13.73 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)].
% 13.57/13.73 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1477,c,1402,a)].
% 13.57/13.73 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)].
% 13.57/13.73 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)].
% 13.57/13.73 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)].
% 13.57/13.73 1479 c_Orderings_Omax(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1224,a,1177,b)].
% 13.57/13.73 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1479,b,1401,a)].
% 13.57/13.73 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(1479,b,1402,a)].
% 13.57/13.73 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)].
% 13.57/13.73 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)].
% 13.57/13.73 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)].
% 13.57/13.73 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)].
% 13.57/13.73 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)].
% 13.57/13.73 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(1481,b,1402,a)].
% 13.57/13.73 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)].
% 13.57/13.73 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)].
% 13.57/13.73 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(1482,b,1402,a)].
% 13.57/13.73 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)].
% 13.57/13.73 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)].
% 13.57/13.73 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(1483,b,1402,a)].
% 13.57/13.73 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)].
% 13.57/13.73 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)].
% 13.57/13.73 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(1484,b,1402,a)].
% 13.57/13.73 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)].
% 13.57/13.73 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1485,c,1401,a)].
% 13.57/13.73 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1485,c,1402,a)].
% 13.57/13.73 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)].
% 13.57/13.73 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1486,c,1401,a)].
% 13.57/13.74 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1486,c,1402,a)].
% 13.57/13.74 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)].
% 13.57/13.74 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1487,c,1401,a)].
% 13.57/13.74 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1487,c,1402,a)].
% 13.57/13.74 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)].
% 13.57/13.74 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1495,c,1401,a)].
% 13.57/13.75 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1495,c,1402,a)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 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)].
% 13.57/13.75 1498 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1255,b,1177,b)].
% 13.57/13.75 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1498,b,1401,a)].
% 13.57/13.75 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1498,b,1402,a)].
% 13.57/13.75 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1498,b,1405,b)].
% 13.57/13.75 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1498,b,1406,b)].
% 13.57/13.75 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1498,b,1407,b)].
% 13.57/13.75 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1498,b,1408,b)].
% 13.57/13.75 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1498,b,1409,b)].
% 13.57/13.75 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1498,b,1410,b)].
% 13.57/13.75 1499 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1256,b,1177,b)].
% 13.57/13.75 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1499,b,1401,a)].
% 13.57/13.75 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1499,b,1402,a)].
% 13.57/13.75 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1499,b,1405,b)].
% 13.57/13.75 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1499,b,1406,b)].
% 13.57/13.75 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1499,b,1407,b)].
% 13.57/13.78 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1499,b,1408,b)].
% 13.57/13.78 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1499,b,1409,b)].
% 13.57/13.78 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1499,b,1410,b)].
% 13.57/13.78 1500 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1257,b,1177,b)].
% 13.57/13.78 1501 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1258,b,1177,b)].
% 13.57/13.78 1502 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1259,b,1177,b)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 1512 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1278,a,1276,b)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.78 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)].
% 13.57/13.80 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)].
% 13.57/13.80 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1518,c,1401,a)].
% 13.57/13.80 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1518,c,1402,a)].
% 13.57/13.80 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)].
% 13.57/13.80 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1519,c,1401,a)].
% 13.57/13.80 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1519,c,1402,a)].
% 13.57/13.80 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)].
% 13.57/13.80 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1520,c,1401,a)].
% 13.57/13.80 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1520,c,1402,a)].
% 13.57/13.80 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)].
% 13.57/13.80 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1521,c,1401,a)].
% 13.57/13.80 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1521,c,1402,a)].
% 13.57/13.80 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)].
% 13.57/13.80 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1522,c,1401,a)].
% 13.57/13.80 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)].
% 13.57/13.80 1523 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1384,b,1350,b)].
% 13.57/13.80 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1523,b,1401,a)].
% 13.57/13.80 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1523,b,1402,a)].
% 13.57/13.80 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1523,b,1405,b)].
% 13.57/13.80 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1523,b,1406,b)].
% 13.57/13.80 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1523,b,1407,b)].
% 13.57/13.80 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1523,b,1408,b)].
% 13.57/13.80 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1523,b,1409,b)].
% 13.57/13.80 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1523,b,1410,b)].
% 13.57/13.80 1524 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1385,b,1350,b)].
% 13.57/13.80 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1524,b,1401,a)].
% 13.57/13.80 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1524,b,1402,a)].
% 13.57/13.80 1525 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1386,b,1350,b)].
% 13.57/13.80 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1525,b,1401,a)].
% 13.57/13.80 Derived: c_lessequals(A,A,tc_nat). [resolve(1525,b,1402,a)].
% 13.57/13.80 1526 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1387,b,1350,b)].
% 13.57/13.80 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1526,b,1401,a)].
% 13.57/13.80 Derived: class_Orderings_Oord(tc_nat). [resolve(1526,b,1402,a)].
% 13.57/13.80 1527 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1388,b,1350,b)].
% 13.68/13.82 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1527,b,1401,a)].
% 13.68/13.82 Derived: -c_less(A,A,tc_nat). [resolve(1527,b,1402,a)].
% 13.68/13.82 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)].
% 13.68/13.82 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1528,c,1401,a)].
% 13.68/13.82 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1528,c,1402,a)].
% 13.68/13.82 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)].
% 13.68/13.82 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1529,b,1401,a)].
% 13.68/13.82 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1529,b,1402,a)].
% 13.68/13.82 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)].
% 13.68/13.82 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1530,c,1401,a)].
% 13.68/13.82 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1530,c,1402,a)].
% 13.68/13.82 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)].
% 13.68/13.82 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1531,c,1401,a)].
% 13.68/13.82 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1531,c,1402,a)].
% 13.68/13.82 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)].
% 13.68/13.82 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1532,c,1401,a)].
% 13.68/13.82 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(1532,c,1402,a)].
% 13.68/13.82 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)].
% 13.68/13.82 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1533,c,1401,a)].
% 13.68/13.82 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(1533,c,1402,a)].
% 13.68/13.82 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)].
% 13.68/13.82 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1534,c,1401,a)].
% 13.68/13.82 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(1534,c,1402,a)].
% 13.68/13.82 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)].
% 13.68/13.82 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1535,c,1401,a)].
% 13.68/13.82 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1535,c,1402,a)].
% 13.68/13.82 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)].
% 14.28/14.47 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)].
% 14.28/14.47 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)].
% 14.28/14.47 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)].
% 14.28/14.47 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1537,c,1401,a)].
% 14.28/14.47 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1537,c,1402,a)].
% 14.28/14.47 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)].
% 14.28/14.47 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1538,c,1401,a)].
% 14.28/14.47 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1538,c,1402,a)].
% 14.28/14.47 1539 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom). [assumption].
% 14.28/14.47 1540 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom). [assumption].
% 14.28/14.47 1541 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom). [assumption].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 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].
% 14.28/14.47 1554 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom). [assumption].
% 14.28/14.47 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].
% 14.35/14.56 1556 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom). [assumption].
% 14.35/14.56 1557 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(31,b,2,a)].
% 14.35/14.56 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1557,a,1549,b)].
% 14.35/14.56 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1557,a,1550,b)].
% 14.35/14.56 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1557,a,1551,b)].
% 14.35/14.56 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1557,a,1552,b)].
% 14.35/14.56 1558 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(33,a,31,b)].
% 14.35/14.56 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1558,b,1549,b)].
% 14.35/14.56 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1558,b,1550,b)].
% 14.35/14.56 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1558,b,1551,b)].
% 14.35/14.56 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1558,b,1552,b)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.35/14.56 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)].
% 14.45/14.59 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1562,c,1551,b)].
% 14.45/14.59 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1562,c,1552,b)].
% 14.45/14.59 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)].
% 14.45/14.59 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1563,c,1549,b)].
% 14.45/14.59 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1563,c,1550,b)].
% 14.45/14.59 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1563,c,1551,b)].
% 14.45/14.59 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1563,c,1552,b)].
% 14.45/14.59 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)].
% 14.45/14.59 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1564,c,1549,b)].
% 14.45/14.59 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1564,c,1550,b)].
% 14.45/14.59 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1564,c,1551,b)].
% 14.45/14.59 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1564,c,1552,b)].
% 14.45/14.59 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)].
% 14.45/14.59 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1565,c,1549,b)].
% 14.45/14.59 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1565,c,1550,b)].
% 14.45/14.59 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1565,c,1551,b)].
% 14.45/14.59 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1565,c,1552,b)].
% 14.45/14.59 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)].
% 14.45/14.59 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)].
% 14.45/14.59 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)].
% 14.45/14.59 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)].
% 14.45/14.59 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)].
% 14.48/14.62 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)].
% 14.48/14.62 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)].
% 14.48/14.62 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)].
% 14.48/14.62 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)].
% 14.48/14.62 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)].
% 14.48/14.62 1568 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(71,a,97,b)].
% 14.48/14.62 1569 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(100,a,97,b)].
% 14.48/14.62 1570 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(102,a,97,b)].
% 14.48/14.62 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1570,b,1543,b)].
% 14.48/14.62 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1570,b,1548,b)].
% 14.48/14.62 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1570,b,1549,b)].
% 14.48/14.62 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1570,b,1550,b)].
% 14.48/14.62 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1570,b,1552,b)].
% 14.48/14.62 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)].
% 14.48/14.62 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)].
% 14.48/14.62 1573 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(183,a,176,b)].
% 14.48/14.62 1574 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(184,a,176,b)].
% 14.48/14.62 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)].
% 14.48/14.62 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__comm__semiring__strict(A). [resolve(1575,c,1543,b)].
% 14.48/14.62 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__semidom(A). [resolve(1575,c,1547,b)].
% 14.48/14.62 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__semiring__strict(A). [resolve(1575,c,1548,b)].
% 14.48/14.62 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__cancel__comm__semiring(A). [resolve(1575,c,1549,b)].
% 14.51/14.64 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)].
% 14.51/14.64 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)].
% 14.51/14.64 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)].
% 14.51/14.64 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1576,c,1543,b)].
% 14.51/14.64 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1576,c,1547,b)].
% 14.51/14.64 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1576,c,1548,b)].
% 14.51/14.64 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1576,c,1549,b)].
% 14.51/14.64 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1576,c,1550,b)].
% 14.51/14.64 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1576,c,1552,b)].
% 14.51/14.64 1577 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(223,a,210,b)].
% 14.51/14.64 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1577,b,1552,b)].
% 14.51/14.64 1578 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(224,a,210,b)].
% 14.51/14.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1578,b,1552,b)].
% 14.51/14.64 1579 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(226,b,210,b)].
% 14.51/14.64 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1579,b,1543,b)].
% 14.51/14.64 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1579,b,1547,b)].
% 14.51/14.64 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1579,b,1548,b)].
% 14.51/14.64 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1579,b,1549,b)].
% 14.51/14.64 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1579,b,1550,b)].
% 14.51/14.64 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1579,b,1552,b)].
% 14.51/14.64 1580 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(227,b,210,b)].
% 14.51/14.64 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1580,b,1543,b)].
% 14.51/14.64 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1580,b,1547,b)].
% 14.51/14.64 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1580,b,1548,b)].
% 14.96/15.12 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1580,b,1549,b)].
% 14.96/15.12 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1580,b,1550,b)].
% 14.96/15.12 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1580,b,1552,b)].
% 14.96/15.12 1581 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A). [resolve(1294,b,1269,a)].
% 14.96/15.12 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1581,a,1550,b)].
% 14.96/15.12 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].
% 14.96/15.12 1583 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom). [assumption].
% 14.96/15.12 1584 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom). [assumption].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 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].
% 14.96/15.12 1597 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(27,b,2,a)].
% 14.96/15.12 1598 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(33,a,27,b)].
% 14.96/15.12 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)].
% 14.96/15.12 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)].
% 14.96/15.12 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)].
% 15.06/15.19 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)].
% 15.06/15.19 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)].
% 15.06/15.19 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)].
% 15.06/15.19 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)].
% 15.06/15.19 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)].
% 15.06/15.19 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)].
% 15.06/15.20 1608 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(71,a,93,b)].
% 15.06/15.20 1609 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(100,a,93,b)].
% 15.06/15.20 1610 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(102,a,93,b)].
% 15.06/15.20 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)].
% 15.06/15.20 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)].
% 15.06/15.20 1613 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(183,a,172,b)].
% 15.06/15.20 1614 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(184,a,172,b)].
% 15.06/15.20 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)].
% 15.06/15.20 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)].
% 15.06/15.20 1617 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(223,a,206,b)].
% 15.06/15.20 1618 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(224,a,206,b)].
% 15.06/15.20 1619 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(226,b,206,b)].
% 15.06/15.20 1620 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(227,b,206,b)].
% 15.06/15.20 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)].
% 15.06/15.20 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)].
% 15.06/15.20 1623 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(346,b,339,b)].
% 15.06/15.20 1624 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(380,a,369,b)].
% 15.06/15.20 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1624,b,1586,b)].
% 15.06/15.20 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1624,b,1591,b)].
% 15.06/15.20 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1624,b,1592,b)].
% 15.06/15.20 1625 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(381,a,369,b)].
% 15.33/15.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1625,b,1586,b)].
% 15.33/15.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1625,b,1591,b)].
% 15.33/15.48 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1625,b,1592,b)].
% 15.33/15.48 1626 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(386,b,369,b)].
% 15.33/15.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1626,b,1592,b)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 1629 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(391,b,369,b)].
% 15.33/15.48 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1629,b,1592,b)].
% 15.33/15.48 1630 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A). [resolve(1290,b,1269,a)].
% 15.33/15.48 1631 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1557,a,1550,b)].
% 15.33/15.48 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1631,b,1583,a)].
% 15.33/15.48 Derived: c_lessequals(A,A,tc_nat). [resolve(1631,b,1584,a)].
% 15.33/15.48 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1631,b,1585,b)].
% 15.33/15.48 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1631,b,1586,b)].
% 15.33/15.48 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1631,b,1587,b)].
% 15.33/15.48 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1631,b,1588,b)].
% 15.33/15.48 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1631,b,1589,b)].
% 15.33/15.48 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1631,b,1590,b)].
% 15.33/15.48 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1631,b,1591,b)].
% 15.33/15.48 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1631,b,1592,b)].
% 15.33/15.48 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1631,b,1596,b)].
% 15.33/15.48 1632 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1558,b,1550,b)].
% 15.33/15.48 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1632,b,1583,a)].
% 15.33/15.48 Derived: -c_less(A,A,tc_nat). [resolve(1632,b,1584,a)].
% 15.33/15.48 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1632,b,1585,b)].
% 15.33/15.48 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1632,b,1586,b)].
% 15.33/15.48 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1632,b,1587,b)].
% 15.33/15.48 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1632,b,1588,b)].
% 15.33/15.48 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1632,b,1589,b)].
% 15.33/15.48 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1632,b,1590,b)].
% 15.33/15.48 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1632,b,1591,b)].
% 15.33/15.48 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1632,b,1592,b)].
% 15.33/15.48 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1632,b,1596,b)].
% 15.33/15.48 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)].
% 15.33/15.48 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1633,c,1583,a)].
% 15.33/15.48 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1633,c,1584,a)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1634,b,1583,a)].
% 15.33/15.48 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1634,b,1584,a)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.33/15.48 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1635,c,1583,a)].
% 15.33/15.48 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1635,c,1584,a)].
% 15.33/15.48 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)].
% 15.33/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.48 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1640,c,1583,a)].
% 15.35/15.49 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1640,c,1584,a)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 1642 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1570,b,1550,b)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1642,b,1583,a)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1642,b,1584,a)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1642,b,1585,b)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1642,b,1586,b)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1642,b,1587,b)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1642,b,1588,b)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1642,b,1589,b)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1642,b,1590,b)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1642,b,1591,b)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1642,b,1592,b)].
% 15.35/15.49 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1642,b,1596,b)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.49 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)].
% 15.35/15.50 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)].
% 15.35/15.50 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)].
% 15.35/15.50 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)].
% 15.35/15.50 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)].
% 15.35/15.50 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)].
% 15.35/15.50 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)].
% 15.35/15.50 1645 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1579,b,1550,b)].
% 15.35/15.50 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(1645,b,1583,a)].
% 15.35/15.50 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(1645,b,1584,a)].
% 15.35/15.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1645,b,1585,b)].
% 15.35/15.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1645,b,1586,b)].
% 15.35/15.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1645,b,1587,b)].
% 15.35/15.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1645,b,1588,b)].
% 15.35/15.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1645,b,1589,b)].
% 15.35/15.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1645,b,1590,b)].
% 15.35/15.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1645,b,1591,b)].
% 15.35/15.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1645,b,1592,b)].
% 15.35/15.50 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1645,b,1596,b)].
% 15.35/15.50 1646 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1580,b,1550,b)].
% 15.35/15.50 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(1646,b,1583,a)].
% 15.35/15.50 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(1646,b,1584,a)].
% 15.35/15.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1646,b,1585,b)].
% 15.35/15.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1646,b,1586,b)].
% 15.35/15.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1646,b,1587,b)].
% 15.35/15.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1646,b,1588,b)].
% 15.35/15.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1646,b,1589,b)].
% 15.35/15.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1646,b,1590,b)].
% 15.35/15.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1646,b,1591,b)].
% 15.35/15.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1646,b,1592,b)].
% 15.35/15.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1646,b,1596,b)].
% 15.56/15.71 1647 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1581,a,1550,b)].
% 15.56/15.71 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1647,b,1583,a)].
% 15.56/15.71 Derived: class_Orderings_Oord(tc_nat). [resolve(1647,b,1584,a)].
% 15.56/15.71 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1647,b,1585,b)].
% 15.56/15.71 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1647,b,1586,b)].
% 15.56/15.71 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1647,b,1587,b)].
% 15.56/15.71 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1647,b,1588,b)].
% 15.56/15.71 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1647,b,1589,b)].
% 15.56/15.71 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1647,b,1590,b)].
% 15.56/15.71 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1647,b,1591,b)].
% 15.56/15.71 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1647,b,1592,b)].
% 15.56/15.71 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1647,b,1596,b)].
% 15.56/15.71 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].
% 15.56/15.71 1649 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom). [assumption].
% 15.56/15.71 1650 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom). [assumption].
% 15.56/15.71 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].
% 15.56/15.71 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].
% 15.56/15.71 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].
% 15.56/15.71 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].
% 15.56/15.71 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].
% 15.56/15.71 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].
% 15.56/15.71 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].
% 15.56/15.71 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].
% 15.56/15.71 1659 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(25,b,2,a)].
% 15.56/15.71 1660 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(33,a,25,b)].
% 15.56/15.71 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)].
% 15.56/15.71 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)].
% 15.56/15.71 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)].
% 15.56/15.71 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)].
% 15.65/15.78 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)].
% 15.65/15.78 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)].
% 15.65/15.78 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)].
% 15.65/15.78 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)].
% 15.65/15.78 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)].
% 15.65/15.78 1670 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(71,a,91,b)].
% 15.65/15.78 1671 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(100,a,91,b)].
% 15.65/15.78 1672 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(102,a,91,b)].
% 15.65/15.78 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)].
% 15.65/15.78 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)].
% 15.65/15.78 1675 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(183,a,170,b)].
% 15.65/15.78 1676 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(184,a,170,b)].
% 15.65/15.78 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)].
% 15.65/15.78 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)].
% 15.65/15.78 1679 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(223,a,204,b)].
% 15.65/15.78 1680 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(224,a,204,b)].
% 15.65/15.78 1681 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(226,b,204,b)].
% 15.65/15.78 1682 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(227,b,204,b)].
% 15.65/15.78 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)].
% 15.65/15.78 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)].
% 15.65/15.78 1685 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(346,b,337,b)].
% 15.65/15.78 1686 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(380,a,367,b)].
% 15.65/15.78 1687 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(381,a,367,b)].
% 15.65/15.78 1688 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(386,b,367,b)].
% 15.65/15.78 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)].
% 15.65/15.78 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)].
% 15.65/15.78 1691 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(391,b,367,b)].
% 15.69/15.90 1692 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1087,a,1085,b)].
% 15.69/15.90 1693 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1089,b,1085,b)].
% 15.69/15.90 1694 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1118,a,1116,b)].
% 15.69/15.90 1695 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1161,b,1146,b)].
% 15.69/15.90 1696 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1163,b,1146,b)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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)].
% 15.69/15.90 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__comm__semiring__strict(B). [resolve(1707,d,1651,b)].
% 15.69/15.90 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(1707,d,1652,b)].
% 15.69/15.90 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__idom(B). [resolve(1707,d,1653,b)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.69/15.91 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.92 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.93 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.94 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.95 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.96 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.97 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.79/15.98 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/15.99 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 1740 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1219,a,1183,b)].
% 15.86/16.00 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1740,b,1651,b)].
% 15.86/16.00 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1740,b,1652,b)].
% 15.86/16.00 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1740,b,1653,b)].
% 15.86/16.00 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1740,b,1654,b)].
% 15.86/16.00 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1740,b,1655,b)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.00 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 1745 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1224,a,1183,b)].
% 15.86/16.01 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1745,b,1651,b)].
% 15.86/16.01 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1745,b,1652,b)].
% 15.86/16.01 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1745,b,1653,b)].
% 15.86/16.01 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1745,b,1654,b)].
% 15.86/16.01 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1745,b,1655,b)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.01 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.02 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.03 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.04 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.05 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)].
% 15.86/16.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1762,c,1652,b)].
% 15.86/16.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1762,c,1653,b)].
% 15.86/16.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1762,c,1654,b)].
% 15.86/16.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1762,c,1655,b)].
% 15.86/16.07 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)].
% 15.86/16.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1763,c,1651,b)].
% 15.86/16.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1763,c,1652,b)].
% 15.86/16.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1763,c,1653,b)].
% 15.86/16.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1763,c,1654,b)].
% 15.86/16.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1763,c,1655,b)].
% 15.86/16.07 1764 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1258,b,1183,b)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.86/16.07 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.95/16.08 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 1773 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1385,b,1360,b)].
% 15.97/16.12 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1773,b,1651,b)].
% 15.97/16.12 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1773,b,1652,b)].
% 15.97/16.12 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1773,b,1653,b)].
% 15.97/16.12 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1773,b,1654,b)].
% 15.97/16.12 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1773,b,1655,b)].
% 15.97/16.12 1774 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1386,b,1360,b)].
% 15.97/16.12 1775 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1387,b,1360,b)].
% 15.97/16.12 1776 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1388,b,1360,b)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.97/16.12 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)].
% 15.99/16.16 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)].
% 15.99/16.16 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)].
% 15.99/16.16 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)].
% 15.99/16.16 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)].
% 15.99/16.16 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)].
% 15.99/16.16 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)].
% 15.99/16.16 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)].
% 15.99/16.16 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)].
% 15.99/16.16 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)].
% 15.99/16.16 1788 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1498,b,1410,b)].
% 15.99/16.16 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1788,b,1649,a)].
% 15.99/16.16 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1788,b,1650,a)].
% 15.99/16.16 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1788,b,1651,b)].
% 15.99/16.16 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1788,b,1652,b)].
% 15.99/16.16 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1788,b,1653,b)].
% 15.99/16.16 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1788,b,1654,b)].
% 15.99/16.16 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1788,b,1655,b)].
% 15.99/16.16 1789 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1499,b,1410,b)].
% 15.99/16.16 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1789,b,1649,a)].
% 15.99/16.16 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1789,b,1650,a)].
% 15.99/16.16 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1789,b,1651,b)].
% 15.99/16.16 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1789,b,1652,b)].
% 15.99/16.16 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1789,b,1653,b)].
% 15.99/16.16 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1789,b,1654,b)].
% 15.99/16.16 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1789,b,1655,b)].
% 15.99/16.16 1790 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1523,b,1410,b)].
% 15.99/16.16 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1790,b,1649,a)].
% 15.99/16.16 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1790,b,1650,a)].
% 15.99/16.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1790,b,1651,b)].
% 15.99/16.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1790,b,1652,b)].
% 15.99/16.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1790,b,1653,b)].
% 15.99/16.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1790,b,1654,b)].
% 15.99/16.16 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1790,b,1655,b)].
% 15.99/16.16 1791 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1570,b,1548,b)].
% 15.99/16.16 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)].
% 15.99/16.17 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)].
% 15.99/16.17 1794 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1579,b,1548,b)].
% 15.99/16.17 1795 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1580,b,1548,b)].
% 15.99/16.17 1796 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1624,b,1591,b)].
% 15.99/16.17 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1796,b,1649,a)].
% 15.99/16.17 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(1796,b,1650,a)].
% 15.99/16.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1796,b,1651,b)].
% 15.99/16.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(1796,b,1652,b)].
% 15.99/16.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1796,b,1653,b)].
% 15.99/16.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1796,b,1654,b)].
% 15.99/16.17 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1796,b,1655,b)].
% 15.99/16.17 1797 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1625,b,1591,b)].
% 15.99/16.17 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1797,b,1649,a)].
% 15.99/16.17 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(1797,b,1650,a)].
% 15.99/16.17 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1797,b,1651,b)].
% 15.99/16.17 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(1797,b,1652,b)].
% 15.99/16.17 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1797,b,1653,b)].
% 15.99/16.17 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1797,b,1654,b)].
% 15.99/16.17 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1797,b,1655,b)].
% 15.99/16.17 1798 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1631,b,1591,b)].
% 15.99/16.17 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1798,b,1649,a)].
% 15.99/16.17 Derived: c_lessequals(A,A,tc_nat). [resolve(1798,b,1650,a)].
% 15.99/16.17 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1798,b,1651,b)].
% 15.99/16.17 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1798,b,1652,b)].
% 15.99/16.17 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1798,b,1653,b)].
% 15.99/16.17 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1798,b,1654,b)].
% 15.99/16.17 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1798,b,1655,b)].
% 15.99/16.17 1799 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1632,b,1591,b)].
% 15.99/16.17 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1799,b,1649,a)].
% 15.99/16.17 Derived: -c_less(A,A,tc_nat). [resolve(1799,b,1650,a)].
% 15.99/16.17 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1799,b,1651,b)].
% 15.99/16.17 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1799,b,1652,b)].
% 15.99/16.17 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1799,b,1653,b)].
% 15.99/16.17 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1799,b,1654,b)].
% 15.99/16.17 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1799,b,1655,b)].
% 15.99/16.17 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)].
% 15.99/16.17 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1800,c,1649,a)].
% 15.99/16.17 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1800,c,1650,a)].
% 15.99/16.17 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1800,c,1651,b)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1801,b,1649,a)].
% 15.99/16.18 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1801,b,1650,a)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1802,c,1649,a)].
% 15.99/16.18 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1802,c,1650,a)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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)].
% 15.99/16.18 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(1803,c,1649,a)].
% 15.99/16.18 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(1803,c,1650,a)].
% 15.99/16.18 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(1803,c,1651,b)].
% 15.99/16.18 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(1803,c,1652,b)].
% 15.99/16.18 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(1803,c,1653,b)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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)].
% 15.99/16.19 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_Oordered__comm__semiring__strict(B). [resolve(1805,c,1651,b)].
% 15.99/16.19 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_Oordered__field(B). [resolve(1805,c,1652,b)].
% 15.99/16.19 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_Oordered__idom(B). [resolve(1805,c,1653,b)].
% 15.99/16.19 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_Oordered__ring__strict(B). [resolve(1805,c,1654,b)].
% 15.99/16.19 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_Oordered__semidom(B). [resolve(1805,c,1655,b)].
% 15.99/16.19 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)].
% 15.99/16.19 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(1806,c,1649,a)].
% 15.99/16.19 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(1806,c,1650,a)].
% 15.99/16.19 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(1806,c,1651,b)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1807,c,1649,a)].
% 15.99/16.20 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1807,c,1650,a)].
% 15.99/16.20 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1807,c,1651,b)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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(1808,b,1649,a)].
% 15.99/16.20 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(1808,b,1650,a)].
% 15.99/16.20 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(1808,b,1651,b)].
% 15.99/16.20 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(1808,b,1652,b)].
% 15.99/16.20 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(1808,b,1653,b)].
% 15.99/16.20 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(1808,b,1654,b)].
% 15.99/16.20 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(1808,b,1655,b)].
% 15.99/16.20 1809 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1642,b,1591,b)].
% 15.99/16.20 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1809,b,1649,a)].
% 15.99/16.20 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1809,b,1650,a)].
% 15.99/16.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1809,b,1651,b)].
% 15.99/16.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1809,b,1652,b)].
% 15.99/16.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1809,b,1653,b)].
% 15.99/16.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1809,b,1654,b)].
% 15.99/16.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1809,b,1655,b)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 15.99/16.20 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)].
% 16.28/16.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1811,c,1654,b)].
% 16.28/16.42 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1811,c,1655,b)].
% 16.28/16.42 1812 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1645,b,1591,b)].
% 16.28/16.42 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(1812,b,1649,a)].
% 16.28/16.42 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(1812,b,1650,a)].
% 16.28/16.42 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1812,b,1651,b)].
% 16.28/16.42 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1812,b,1652,b)].
% 16.28/16.42 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1812,b,1653,b)].
% 16.28/16.42 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1812,b,1654,b)].
% 16.28/16.42 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1812,b,1655,b)].
% 16.28/16.42 1813 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1646,b,1591,b)].
% 16.28/16.42 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(1813,b,1649,a)].
% 16.28/16.42 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(1813,b,1650,a)].
% 16.28/16.42 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1813,b,1651,b)].
% 16.28/16.42 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1813,b,1652,b)].
% 16.28/16.42 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1813,b,1653,b)].
% 16.28/16.42 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1813,b,1654,b)].
% 16.28/16.42 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1813,b,1655,b)].
% 16.28/16.42 1814 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1647,b,1591,b)].
% 16.28/16.42 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1814,b,1649,a)].
% 16.28/16.42 Derived: class_Orderings_Oord(tc_nat). [resolve(1814,b,1650,a)].
% 16.28/16.42 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1814,b,1651,b)].
% 16.28/16.42 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1814,b,1652,b)].
% 16.28/16.42 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1814,b,1653,b)].
% 16.28/16.42 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1814,b,1654,b)].
% 16.28/16.42 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1814,b,1655,b)].
% 16.28/16.42 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].
% 16.28/16.42 1816 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom). [assumption].
% 16.28/16.42 1817 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom). [assumption].
% 16.28/16.42 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].
% 16.28/16.42 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].
% 16.28/16.42 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].
% 16.28/16.42 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].
% 16.37/16.53 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].
% 16.37/16.53 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].
% 16.37/16.53 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].
% 16.37/16.53 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1824,a,1818,b)].
% 16.37/16.53 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1824,a,1822,b)].
% 16.37/16.53 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].
% 16.37/16.53 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].
% 16.37/16.53 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].
% 16.37/16.53 1828 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(29,b,2,a)].
% 16.37/16.53 1829 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(33,a,29,b)].
% 16.37/16.53 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)].
% 16.37/16.53 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)].
% 16.37/16.53 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)].
% 16.37/16.53 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)].
% 16.37/16.53 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)].
% 16.37/16.53 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)].
% 16.37/16.53 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)].
% 16.37/16.53 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)].
% 16.37/16.53 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)].
% 16.37/16.53 1839 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(71,a,95,b)].
% 16.37/16.53 1840 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(100,a,95,b)].
% 16.37/16.53 1841 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(102,a,95,b)].
% 16.37/16.53 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)].
% 16.37/16.53 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)].
% 16.68/16.82 1844 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(183,a,174,b)].
% 16.68/16.82 1845 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(184,a,174,b)].
% 16.68/16.82 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)].
% 16.68/16.82 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)].
% 16.68/16.82 1848 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(223,a,208,b)].
% 16.68/16.82 1849 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(224,a,208,b)].
% 16.68/16.82 1850 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(226,b,208,b)].
% 16.68/16.82 1851 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(227,b,208,b)].
% 16.68/16.82 1852 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1296,b,1292,b)].
% 16.68/16.82 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1852,b,1823,b)].
% 16.68/16.82 1853 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1557,a,1552,b)].
% 16.68/16.82 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1853,b,1823,b)].
% 16.68/16.82 1854 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1558,b,1552,b)].
% 16.68/16.82 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1854,b,1823,b)].
% 16.68/16.82 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)].
% 16.68/16.82 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)].
% 16.68/16.82 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)].
% 16.68/16.82 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)].
% 16.68/16.82 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)].
% 16.68/16.82 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)].
% 16.68/16.82 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)].
% 16.68/16.82 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1858,c,1823,b)].
% 16.68/16.82 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)].
% 16.68/16.82 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1859,c,1823,b)].
% 16.68/16.82 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)].
% 16.68/16.82 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1860,c,1823,b)].
% 16.68/16.82 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)].
% 16.88/17.06 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)].
% 16.88/17.06 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)].
% 16.88/17.06 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)].
% 16.88/17.06 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)].
% 16.88/17.06 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)].
% 16.88/17.06 1864 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1570,b,1552,b)].
% 16.88/17.06 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1864,b,1823,b)].
% 16.88/17.06 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)].
% 16.88/17.06 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)].
% 16.88/17.06 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)].
% 16.88/17.06 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)].
% 16.88/17.06 1867 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1577,b,1552,b)].
% 16.88/17.06 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1867,b,1816,a)].
% 16.88/17.06 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1867,b,1817,a)].
% 16.88/17.06 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1867,b,1823,b)].
% 16.88/17.06 1868 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1578,b,1552,b)].
% 16.88/17.06 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1868,b,1823,b)].
% 16.88/17.06 1869 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1579,b,1552,b)].
% 16.88/17.06 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1869,b,1823,b)].
% 16.88/17.06 1870 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1580,b,1552,b)].
% 16.88/17.06 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1870,b,1823,b)].
% 16.88/17.06 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].
% 16.88/17.06 1872 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom). [assumption].
% 16.88/17.06 1873 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom). [assumption].
% 16.88/17.06 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].
% 16.88/17.06 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].
% 16.96/17.17 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].
% 16.96/17.17 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].
% 16.96/17.17 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].
% 16.96/17.17 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].
% 16.96/17.17 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].
% 16.96/17.17 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].
% 16.96/17.17 1882 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(26,b,2,a)].
% 16.96/17.17 1883 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(33,a,26,b)].
% 16.96/17.17 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)].
% 16.96/17.17 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)].
% 16.96/17.17 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)].
% 16.96/17.17 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)].
% 16.96/17.17 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)].
% 16.96/17.17 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)].
% 16.96/17.17 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)].
% 16.96/17.17 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)].
% 16.96/17.17 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)].
% 16.96/17.17 1893 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(71,a,92,b)].
% 16.96/17.17 1894 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(100,a,92,b)].
% 16.96/17.17 1895 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(102,a,92,b)].
% 16.96/17.17 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)].
% 16.96/17.17 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)].
% 17.26/17.46 1898 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(183,a,171,b)].
% 17.26/17.46 1899 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(184,a,171,b)].
% 17.26/17.46 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)].
% 17.26/17.46 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)].
% 17.26/17.46 1902 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(223,a,205,b)].
% 17.26/17.46 1903 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(224,a,205,b)].
% 17.26/17.46 1904 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(226,b,205,b)].
% 17.26/17.46 1905 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(227,b,205,b)].
% 17.26/17.46 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)].
% 17.26/17.46 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)].
% 17.26/17.46 1908 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(346,b,338,b)].
% 17.26/17.46 1909 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(380,a,368,b)].
% 17.26/17.46 1910 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(381,a,368,b)].
% 17.26/17.46 1911 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(386,b,368,b)].
% 17.26/17.46 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)].
% 17.26/17.46 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)].
% 17.26/17.46 1914 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(391,b,368,b)].
% 17.26/17.46 1915 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1296,b,1289,b)].
% 17.26/17.46 1916 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1557,a,1549,b)].
% 17.26/17.46 1917 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1558,b,1549,b)].
% 17.26/17.46 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)].
% 17.26/17.46 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)].
% 17.26/17.46 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)].
% 17.26/17.46 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)].
% 17.26/17.46 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)].
% 17.26/17.46 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)].
% 17.26/17.46 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)].
% 17.36/17.49 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)].
% 17.36/17.49 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)].
% 17.36/17.49 1927 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1570,b,1549,b)].
% 17.36/17.49 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)].
% 17.36/17.49 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)].
% 17.36/17.49 1930 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1579,b,1549,b)].
% 17.36/17.49 1931 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1580,b,1549,b)].
% 17.36/17.49 1932 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1624,b,1592,b)].
% 17.36/17.49 1933 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1625,b,1592,b)].
% 17.36/17.49 1934 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1626,b,1592,b)].
% 17.36/17.49 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)].
% 17.36/17.49 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1935,c,1872,a)].
% 17.36/17.49 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1935,c,1873,a)].
% 17.36/17.49 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)].
% 17.36/17.49 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1936,c,1872,a)].
% 17.36/17.49 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1936,c,1873,a)].
% 17.36/17.49 1937 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1629,b,1592,b)].
% 17.36/17.49 1938 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1631,b,1592,b)].
% 17.36/17.49 1939 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1632,b,1592,b)].
% 17.36/17.49 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)].
% 17.36/17.49 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)].
% 17.36/17.49 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)].
% 17.36/17.49 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)].
% 17.36/17.49 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)].
% 17.36/17.49 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)].
% 17.36/17.49 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)].
% 17.36/17.49 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)].
% 17.64/17.77 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)].
% 17.64/17.77 1949 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1642,b,1592,b)].
% 17.64/17.77 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)].
% 17.64/17.77 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)].
% 17.64/17.77 1952 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1645,b,1592,b)].
% 17.64/17.77 1953 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1646,b,1592,b)].
% 17.64/17.77 1954 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1647,b,1592,b)].
% 17.64/17.77 1955 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1824,a,1822,b)].
% 17.64/17.77 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(1955,b,1872,a)].
% 17.64/17.77 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(1955,b,1873,a)].
% 17.64/17.77 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1955,b,1874,b)].
% 17.64/17.77 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1955,b,1875,b)].
% 17.64/17.77 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1955,b,1876,b)].
% 17.64/17.77 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1955,b,1877,b)].
% 17.64/17.77 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].
% 17.64/17.77 1957 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom). [assumption].
% 17.64/17.77 1958 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom). [assumption].
% 17.64/17.77 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].
% 17.64/17.77 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].
% 17.64/17.77 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].
% 17.64/17.77 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].
% 17.64/17.77 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].
% 17.64/17.77 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].
% 17.64/17.77 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].
% 17.64/17.77 1966 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(20,b,2,a)].
% 17.64/17.77 1967 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(33,a,20,b)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 1977 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(71,a,86,b)].
% 17.66/17.81 1978 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(100,a,86,b)].
% 17.66/17.81 1979 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(102,a,86,b)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 1982 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(183,a,165,b)].
% 17.66/17.81 1983 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(184,a,165,b)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 1986 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(223,a,199,b)].
% 17.66/17.81 1987 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(224,a,199,b)].
% 17.66/17.81 1988 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(226,b,199,b)].
% 17.66/17.81 1989 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(227,b,199,b)].
% 17.66/17.81 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)].
% 17.66/17.81 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)].
% 17.66/17.81 1992 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(346,b,332,b)].
% 17.78/17.93 1993 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(380,a,362,b)].
% 17.78/17.93 1994 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(381,a,362,b)].
% 17.78/17.93 1995 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(386,b,362,b)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 1998 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(391,b,362,b)].
% 17.78/17.93 1999 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1087,a,1080,b)].
% 17.78/17.93 2000 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1089,b,1080,b)].
% 17.78/17.93 2001 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1118,a,1111,b)].
% 17.78/17.93 2002 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1161,b,1141,b)].
% 17.78/17.93 2003 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1163,b,1141,b)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.93 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.78/17.96 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 2047 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1219,a,1178,b)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 2052 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1224,a,1178,b)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/17.99 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 2071 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1258,b,1178,b)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 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)].
% 17.86/18.04 2080 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1385,b,1355,b)].
% 17.86/18.04 2081 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1386,b,1355,b)].
% 17.86/18.04 2082 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1387,b,1355,b)].
% 17.86/18.04 2083 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1388,b,1355,b)].
% 17.86/18.04 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 2095 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1498,b,1405,b)].
% 17.97/18.11 2096 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1499,b,1405,b)].
% 17.97/18.11 2097 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1523,b,1405,b)].
% 17.97/18.11 2098 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1570,b,1543,b)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 2101 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1579,b,1543,b)].
% 17.97/18.11 2102 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1580,b,1543,b)].
% 17.97/18.11 2103 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1624,b,1586,b)].
% 17.97/18.11 2104 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1625,b,1586,b)].
% 17.97/18.11 2105 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1631,b,1586,b)].
% 17.97/18.11 2106 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1632,b,1586,b)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 17.97/18.11 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 2116 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1642,b,1586,b)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 2119 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1645,b,1586,b)].
% 18.00/18.13 2120 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1646,b,1586,b)].
% 18.00/18.13 2121 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1647,b,1586,b)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.00/18.13 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)].
% 18.03/18.14 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(2125,f,1957,a)].
% 18.03/18.14 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset. [resolve(2125,f,1958,a)].
% 18.03/18.14 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)].
% 18.03/18.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(2126,e,1957,a)].
% 18.03/18.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2126,e,1958,a)].
% 18.03/18.14 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)].
% 18.03/18.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(2127,e,1957,a)].
% 18.03/18.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2127,e,1958,a)].
% 18.03/18.14 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)].
% 18.03/18.14 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)].
% 18.03/18.14 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)].
% 18.03/18.14 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)].
% 18.03/18.14 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)].
% 18.03/18.14 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)].
% 18.03/18.14 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)].
% 18.03/18.14 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)].
% 18.03/18.14 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)].
% 18.03/18.14 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)].
% 18.03/18.15 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2131,b,1957,a)].
% 18.03/18.15 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2131,b,1958,a)].
% 18.03/18.15 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)].
% 18.03/18.15 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(2132,f,1957,a)].
% 18.03/18.15 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset. [resolve(2132,f,1958,a)].
% 18.03/18.15 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)].
% 18.03/18.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2133,e,1957,a)].
% 18.03/18.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2133,e,1958,a)].
% 18.03/18.15 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)].
% 18.03/18.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2134,e,1957,a)].
% 18.03/18.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2134,e,1958,a)].
% 18.03/18.15 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)].
% 18.03/18.15 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(2135,f,1957,a)].
% 18.03/18.15 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(2135,f,1958,a)].
% 18.03/18.15 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)].
% 18.03/18.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2136,e,1957,a)].
% 18.03/18.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2136,e,1958,a)].
% 18.03/18.15 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)].
% 18.03/18.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2137,e,1957,a)].
% 18.03/18.16 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)].
% 18.03/18.16 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)].
% 18.03/18.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(2138,d,1957,a)].
% 18.03/18.16 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)].
% 18.03/18.16 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)].
% 18.03/18.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2139,d,1957,a)].
% 18.03/18.16 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)].
% 18.03/18.16 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)].
% 18.03/18.16 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(2140,e,1957,a)].
% 18.03/18.16 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)].
% 18.03/18.16 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)].
% 18.03/18.16 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2141,b,1957,a)].
% 18.03/18.16 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2141,b,1958,a)].
% 18.03/18.16 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)].
% 18.03/18.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2142,d,1957,a)].
% 18.03/18.16 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)].
% 18.03/18.16 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)].
% 18.03/18.16 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2143,e,1957,a)].
% 18.03/18.16 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)].
% 18.03/18.16 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)].
% 18.03/18.16 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2144,e,1957,a)].
% 18.03/18.16 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_nat),tc_nat) = A. [resolve(2144,e,1958,a)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(2147,c,1958,a)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(2148,c,1958,a)].
% 18.03/18.17 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)].
% 18.03/18.17 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(2149,d,1957,a)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2150,c,1958,a)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2151,c,1958,a)].
% 18.03/18.17 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)].
% 18.03/18.17 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2152,d,1957,a)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 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)].
% 18.03/18.17 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2153,c,1958,a)].
% 18.03/18.17 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)].
% 18.03/18.18 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)].
% 18.03/18.18 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2154,c,1958,a)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | c_lessequals(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(2155,d,1958,a)].
% 18.03/18.18 2156 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1740,b,1651,b)].
% 18.03/18.18 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(2156,b,1957,a)].
% 18.03/18.18 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(2156,b,1958,a)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2158,c,1958,a)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2159,c,1958,a)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | c_lessequals(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(2160,d,1958,a)].
% 18.03/18.18 2161 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1745,b,1651,b)].
% 18.03/18.18 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(2161,b,1957,a)].
% 18.03/18.18 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(2161,b,1958,a)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 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)].
% 18.03/18.18 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(2163,b,1958,a)].
% 18.03/18.19 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)].
% 18.03/18.19 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)].
% 18.03/18.19 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(2164,b,1958,a)].
% 18.03/18.19 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)].
% 18.03/18.19 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)].
% 18.03/18.19 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(2165,b,1958,a)].
% 18.03/18.19 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)].
% 18.03/18.19 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)].
% 18.03/18.19 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(2166,b,1958,a)].
% 18.03/18.19 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)].
% 18.03/18.19 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(2167,c,1957,a)].
% 18.03/18.19 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(2167,c,1958,a)].
% 18.03/18.19 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)].
% 18.03/18.19 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(2168,c,1957,a)].
% 18.03/18.19 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(2168,c,1958,a)].
% 18.03/18.19 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)].
% 18.03/18.19 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(2169,c,1957,a)].
% 18.03/18.19 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(2169,c,1958,a)].
% 18.03/18.19 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)].
% 18.03/18.19 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)].
% 18.03/18.19 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(2170,c,1958,a)].
% 18.03/18.19 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)].
% 18.03/18.19 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)].
% 18.03/18.19 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_nat),c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)). [resolve(2171,c,1958,a)].
% 18.03/18.19 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)].
% 18.03/18.19 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)].
% 18.03/18.20 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)].
% 18.03/18.20 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)].
% 18.03/18.20 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)].
% 18.03/18.20 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)].
% 18.03/18.20 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)].
% 18.03/18.20 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)].
% 18.03/18.20 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)].
% 18.03/18.20 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)].
% 18.03/18.20 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)].
% 18.03/18.20 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)].
% 18.03/18.20 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)].
% 18.03/18.20 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2176,d,1957,a)].
% 18.03/18.20 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)). [resolve(2176,d,1958,a)].
% 18.03/18.20 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)].
% 18.03/18.20 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(2177,c,1957,a)].
% 18.03/18.20 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(2177,c,1958,a)].
% 18.03/18.20 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)].
% 18.03/18.20 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2178,c,1957,a)].
% 18.03/18.20 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(2178,c,1958,a)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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(2180,c,1957,a)].
% 18.03/18.21 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2180,c,1958,a)].
% 18.03/18.21 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)].
% 18.03/18.21 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(2181,c,1957,a)].
% 18.03/18.21 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(2181,c,1958,a)].
% 18.03/18.21 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)].
% 18.03/18.21 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(2182,c,1957,a)].
% 18.03/18.21 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2182,c,1958,a)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 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)].
% 18.03/18.21 2188 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1773,b,1651,b)].
% 18.11/18.23 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)].
% 18.11/18.23 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)].
% 18.11/18.23 2191 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1788,b,1651,b)].
% 18.11/18.23 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(2191,b,1957,a)].
% 18.11/18.23 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(2191,b,1958,a)].
% 18.11/18.23 2192 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1789,b,1651,b)].
% 18.11/18.23 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(2192,b,1957,a)].
% 18.11/18.23 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(2192,b,1958,a)].
% 18.11/18.23 2193 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1790,b,1651,b)].
% 18.11/18.23 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2193,b,1957,a)].
% 18.11/18.23 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2193,b,1958,a)].
% 18.11/18.23 2194 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1796,b,1651,b)].
% 18.11/18.23 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2194,b,1957,a)].
% 18.11/18.23 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2194,b,1958,a)].
% 18.11/18.23 2195 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1797,b,1651,b)].
% 18.11/18.23 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2195,b,1957,a)].
% 18.11/18.23 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2195,b,1958,a)].
% 18.11/18.23 2196 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1798,b,1651,b)].
% 18.11/18.23 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2196,b,1957,a)].
% 18.11/18.23 Derived: c_lessequals(A,A,tc_nat). [resolve(2196,b,1958,a)].
% 18.11/18.23 2197 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1799,b,1651,b)].
% 18.11/18.23 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2197,b,1957,a)].
% 18.11/18.23 Derived: -c_less(A,A,tc_nat). [resolve(2197,b,1958,a)].
% 18.11/18.23 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)].
% 18.11/18.23 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2198,c,1957,a)].
% 18.11/18.23 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2198,c,1958,a)].
% 18.11/18.23 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)].
% 18.11/18.23 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2199,b,1957,a)].
% 18.11/18.23 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2199,b,1958,a)].
% 18.11/18.23 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)].
% 18.11/18.23 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2200,c,1957,a)].
% 18.11/18.23 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2200,c,1958,a)].
% 18.11/18.23 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)].
% 18.11/18.23 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)].
% 18.11/18.23 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)].
% 18.11/18.23 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)].
% 18.11/18.23 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2205,c,1957,a)].
% 18.11/18.24 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2205,c,1958,a)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 2207 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1809,b,1651,b)].
% 18.11/18.24 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2207,b,1957,a)].
% 18.11/18.24 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2207,b,1958,a)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.11/18.24 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)].
% 18.75/18.94 Derived: -class_Numeral_Onumber(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(2209,c,1958,a)].
% 18.75/18.94 2210 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1812,b,1651,b)].
% 18.75/18.94 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(2210,b,1957,a)].
% 18.75/18.94 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(2210,b,1958,a)].
% 18.75/18.94 2211 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1813,b,1651,b)].
% 18.75/18.94 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(2211,b,1957,a)].
% 18.75/18.94 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(2211,b,1958,a)].
% 18.75/18.94 2212 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1814,b,1651,b)].
% 18.75/18.94 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(2212,b,1957,a)].
% 18.75/18.94 Derived: class_Orderings_Oord(tc_nat). [resolve(2212,b,1958,a)].
% 18.75/18.94 2213 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1824,a,1818,b)].
% 18.75/18.94 2214 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1955,b,1874,b)].
% 18.75/18.94 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(2214,b,1957,a)].
% 18.75/18.94 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(2214,b,1958,a)].
% 18.75/18.94 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].
% 18.75/18.94 2216 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom). [assumption].
% 18.75/18.94 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].
% 18.75/18.94 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].
% 18.75/18.94 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].
% 18.75/18.94 2220 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom). [assumption].
% 18.75/18.94 2221 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom). [assumption].
% 18.75/18.94 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(2220,a,2221,a)].
% 18.75/18.94 2222 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom). [assumption].
% 18.75/18.94 2223 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom). [assumption].
% 18.75/18.94 2224 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom). [assumption].
% 18.75/18.94 2225 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom). [assumption].
% 18.75/18.94 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].
% 18.75/18.94 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].
% 18.75/18.94 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2227,b,2220,a)].
% 18.75/18.94 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2227,b,2222,a)].
% 18.75/18.94 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].
% 18.84/18.98 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2228,b,2220,a)].
% 18.84/18.98 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2228,b,2222,a)].
% 18.84/18.98 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].
% 18.84/18.98 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2229,b,2220,a)].
% 18.84/18.98 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].
% 18.84/18.98 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].
% 18.84/18.98 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].
% 18.84/18.98 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].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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)].
% 18.84/18.98 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].
% 18.87/19.00 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2235,a,2221,a)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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].
% 18.87/19.00 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2236,a,2221,a)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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].
% 18.87/19.00 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2237,a,2221,a)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.00 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].
% 18.87/19.00 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2238,a,2221,a)].
% 18.87/19.00 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)].
% 18.87/19.00 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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].
% 18.87/19.01 Derived: c_uminus(c_LOrder_Ojoin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Omeet(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2239,a,2221,a)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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].
% 18.87/19.01 Derived: c_uminus(c_LOrder_Omeet(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Ojoin(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2240,a,2221,a)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 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)].
% 18.87/19.01 2241 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Onprt(c_0,A) = c_0 # label(cls_OrderedGroup_Onprt__0_0) # label(axiom). [assumption].
% 18.87/19.01 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2241,a,2221,a)].
% 18.87/19.01 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2241,a,2226,b)].
% 18.87/19.03 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2241,a,2227,b)].
% 18.87/19.03 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2241,a,2228,b)].
% 18.87/19.03 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2241,a,2229,b)].
% 18.87/19.03 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2241,a,2230,b)].
% 18.87/19.03 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2241,a,2231,b)].
% 18.87/19.03 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2241,a,2232,b)].
% 18.87/19.03 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].
% 18.87/19.03 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(2242,a,2221,a)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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].
% 18.87/19.03 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(2243,a,2221,a)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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)].
% 18.87/19.03 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].
% 18.87/19.03 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2244,a,2221,a)].
% 18.87/19.03 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2244,a,2226,b)].
% 18.87/19.03 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2244,a,2227,b)].
% 18.87/19.03 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2244,a,2228,b)].
% 18.87/19.03 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2244,a,2229,b)].
% 18.93/19.04 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2244,a,2230,b)].
% 18.93/19.04 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2244,a,2231,b)].
% 18.93/19.04 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2244,a,2232,b)].
% 18.93/19.04 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].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.93/19.04 2246 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Opprt(c_0,A) = c_0 # label(cls_OrderedGroup_Opprt__0_0) # label(axiom). [assumption].
% 18.93/19.04 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2246,a,2221,a)].
% 18.93/19.04 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2246,a,2226,b)].
% 18.93/19.04 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2246,a,2227,b)].
% 18.93/19.04 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2246,a,2228,b)].
% 18.93/19.04 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2246,a,2229,b)].
% 18.93/19.04 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2246,a,2230,b)].
% 18.93/19.04 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2246,a,2231,b)].
% 18.93/19.04 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2246,a,2232,b)].
% 18.93/19.04 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].
% 18.93/19.04 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(2247,a,2221,a)].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.93/19.04 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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].
% 18.94/19.05 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(2248,a,2221,a)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 18.94/19.05 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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].
% 19.01/19.11 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2251,a,2221,a)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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].
% 19.01/19.11 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2252,a,2221,a)].
% 19.01/19.11 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2252,a,2226,b)].
% 19.01/19.11 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2252,a,2227,b)].
% 19.01/19.11 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2252,a,2228,b)].
% 19.01/19.11 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2252,a,2229,b)].
% 19.01/19.11 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2252,a,2230,b)].
% 19.01/19.11 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2252,a,2231,b)].
% 19.01/19.11 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2252,a,2232,b)].
% 19.01/19.11 2253 -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(B,B,A). [resolve(8,b,2,a)].
% 19.01/19.11 2254 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(18,a,8,b)].
% 19.01/19.11 2255 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(33,a,8,b)].
% 19.01/19.11 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)].
% 19.01/19.11 2257 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(35,a,8,b)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.01/19.11 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)].
% 19.20/19.32 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)].
% 19.20/19.32 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)].
% 19.20/19.32 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)].
% 19.20/19.32 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)].
% 19.20/19.32 2265 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(150,b,147,a)].
% 19.20/19.32 2266 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(150,b,148,a)].
% 19.20/19.32 2267 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(183,a,150,b)].
% 19.20/19.32 2268 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(184,a,150,b)].
% 19.20/19.32 2269 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(307,a,277,b)].
% 19.20/19.32 2270 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(308,a,277,b)].
% 19.20/19.32 2271 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(346,b,316,b)].
% 19.20/19.32 2272 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1087,a,1073,b)].
% 19.20/19.32 2273 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1118,a,1104,b)].
% 19.20/19.32 2274 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1161,b,1134,b)].
% 19.20/19.32 2275 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1162,b,1134,b)].
% 19.20/19.32 2276 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1163,b,1134,b)].
% 19.20/19.32 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)].
% 19.20/19.32 2278 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1165,b,1134,b)].
% 19.20/19.32 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)].
% 19.20/19.32 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)].
% 19.20/19.32 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)].
% 19.20/19.32 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)].
% 19.20/19.32 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)].
% 19.20/19.32 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)].
% 19.20/19.32 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)].
% 19.20/19.32 2286 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1340,c,1310,b)].
% 19.20/19.32 2287 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1341,c,1310,b)].
% 19.20/19.32 2288 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1342,a,1310,b)].
% 19.20/19.32 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)].
% 19.20/19.32 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)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 2297 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1384,b,1346,b)].
% 19.53/19.65 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2297,b,2229,b)].
% 19.53/19.65 2298 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1386,b,1346,b)].
% 19.53/19.65 2299 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1387,b,1346,b)].
% 19.53/19.65 2300 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1388,b,1346,b)].
% 19.53/19.65 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)].
% 19.53/19.65 2302 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1390,b,1346,b)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 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)].
% 19.53/19.65 2310 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1398,c,1346,b)].
% 19.53/19.66 2311 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1399,c,1346,b)].
% 19.53/19.66 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].
% 19.53/19.66 2313 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom). [assumption].
% 19.53/19.66 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].
% 19.53/19.66 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].
% 19.53/19.66 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].
% 19.53/19.66 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].
% 19.62/19.76 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].
% 19.62/19.76 2319 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom). [assumption].
% 19.62/19.76 2320 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom). [assumption].
% 19.62/19.76 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].
% 19.62/19.76 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2321,a,2315,b)].
% 19.62/19.76 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2321,a,2316,b)].
% 19.62/19.76 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2321,a,2317,b)].
% 19.62/19.76 2322 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom). [assumption].
% 19.62/19.76 2323 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(30,b,2,a)].
% 19.62/19.76 2324 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(33,a,30,b)].
% 19.62/19.76 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)].
% 19.62/19.76 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)].
% 19.62/19.76 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)].
% 19.62/19.76 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)].
% 19.62/19.76 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)].
% 19.62/19.76 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)].
% 19.62/19.76 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)].
% 19.62/19.76 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)].
% 19.62/19.76 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)].
% 19.62/19.76 2334 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(71,a,96,b)].
% 19.62/19.76 2335 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(100,a,96,b)].
% 19.62/19.76 2336 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(102,a,96,b)].
% 19.62/19.76 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)].
% 19.62/19.76 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)].
% 19.62/19.76 2339 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(183,a,175,b)].
% 19.62/19.76 2340 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(184,a,175,b)].
% 19.62/19.76 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)].
% 19.62/19.78 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)].
% 19.62/19.78 2343 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(223,a,209,b)].
% 19.62/19.78 2344 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(224,a,209,b)].
% 19.62/19.78 2345 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(226,b,209,b)].
% 19.62/19.78 2346 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(227,b,209,b)].
% 19.62/19.78 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)].
% 19.62/19.78 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)].
% 19.62/19.78 2349 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(346,b,341,b)].
% 19.62/19.78 2350 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(380,a,371,b)].
% 19.62/19.78 2351 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(381,a,371,b)].
% 19.62/19.78 2352 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(386,b,371,b)].
% 19.62/19.78 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)].
% 19.62/19.78 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)].
% 19.62/19.78 2355 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(391,b,371,b)].
% 19.62/19.78 2356 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(410,a,405,b)].
% 19.62/19.78 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2356,b,2314,b)].
% 19.62/19.78 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2356,b,2315,b)].
% 19.62/19.78 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2356,b,2316,b)].
% 19.62/19.78 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2356,b,2317,b)].
% 19.62/19.78 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)].
% 19.62/19.78 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)].
% 19.62/19.78 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)].
% 19.62/19.78 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)].
% 19.62/19.78 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)].
% 19.62/19.78 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)].
% 19.62/19.78 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 2362 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(421,b,405,b)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 2365 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(433,b,405,b)].
% 19.81/19.96 2366 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(434,b,405,b)].
% 19.81/19.96 2367 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(439,b,405,b)].
% 19.81/19.96 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2367,b,2314,b)].
% 19.81/19.96 2368 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(440,b,405,b)].
% 19.81/19.96 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2368,b,2314,b)].
% 19.81/19.96 2369 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(441,b,405,b)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 2372 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(444,b,405,b)].
% 19.81/19.96 2373 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1296,b,1293,b)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.81/19.96 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 2382 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1385,b,1361,b)].
% 19.91/20.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2382,b,2314,b)].
% 19.91/20.03 2383 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1386,b,1361,b)].
% 19.91/20.03 2384 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1387,b,1361,b)].
% 19.91/20.03 2385 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1388,b,1361,b)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 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)].
% 19.91/20.03 2397 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1631,b,1596,b)].
% 19.91/20.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2397,b,2314,b)].
% 19.91/20.03 2398 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1632,b,1596,b)].
% 19.91/20.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2398,b,2314,b)].
% 19.91/20.03 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 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)].
% 19.91/20.05 2408 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1642,b,1596,b)].
% 19.91/20.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2408,b,2314,b)].
% 19.91/20.05 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)].
% 19.91/20.05 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2409,c,2314,b)].
% 19.91/20.05 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)].
% 19.91/20.05 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2410,c,2314,b)].
% 20.23/20.34 2411 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1645,b,1596,b)].
% 20.23/20.34 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2411,b,2314,b)].
% 20.23/20.34 2412 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1646,b,1596,b)].
% 20.23/20.34 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2412,b,2314,b)].
% 20.23/20.34 2413 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1647,b,1596,b)].
% 20.23/20.34 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2413,b,2314,b)].
% 20.23/20.34 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].
% 20.23/20.34 2415 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom). [assumption].
% 20.23/20.34 2416 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom). [assumption].
% 20.23/20.34 2417 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom). [assumption].
% 20.23/20.34 2418 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom). [assumption].
% 20.23/20.34 2419 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom). [assumption].
% 20.23/20.34 2420 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom). [assumption].
% 20.23/20.34 2421 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom). [assumption].
% 20.23/20.34 2422 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom). [assumption].
% 20.23/20.34 2423 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom). [assumption].
% 20.23/20.34 2424 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom). [assumption].
% 20.23/20.34 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].
% 20.23/20.34 2426 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom). [assumption].
% 20.23/20.34 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].
% 20.23/20.34 2428 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom). [assumption].
% 20.23/20.34 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)].
% 20.23/20.34 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2414,a,2416,a)].
% 20.23/20.34 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)].
% 20.23/20.34 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)].
% 20.23/20.34 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)].
% 20.23/20.34 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)].
% 20.23/20.34 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)].
% 20.23/20.34 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)].
% 20.23/20.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2414,a,2423,b)].
% 20.23/20.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2414,a,2424,b)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 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].
% 20.23/20.36 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)].
% 20.23/20.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2429,a,2416,a)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2429,a,2422,b)].
% 20.23/20.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2429,a,2423,b)].
% 20.23/20.36 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2429,a,2424,b)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 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].
% 20.23/20.36 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2430,a,2415,a)].
% 20.23/20.36 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(2430,a,2416,a)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.36 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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].
% 20.23/20.37 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)].
% 20.23/20.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2431,a,2416,a)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2431,a,2423,b)].
% 20.23/20.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2431,a,2424,b)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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)].
% 20.23/20.37 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].
% 20.23/20.39 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)].
% 20.23/20.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2432,a,2416,a)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2432,a,2422,b)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2432,a,2427,b)].
% 20.23/20.39 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)].
% 20.23/20.39 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].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 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)].
% 20.23/20.39 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2433,a,2422,b)].
% 20.23/20.39 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2433,a,2423,b)].
% 20.23/20.39 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2433,a,2424,b)].
% 20.23/20.39 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2433,a,2425,b)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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].
% 20.23/20.40 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)].
% 20.23/20.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2434,a,2416,a)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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].
% 20.23/20.40 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)].
% 20.23/20.40 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2435,a,2416,a)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.23/20.40 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2435,a,2427,b)].
% 20.32/20.42 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)].
% 20.32/20.42 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].
% 20.32/20.42 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)].
% 20.32/20.42 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2436,a,2416,a)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2436,a,2427,b)].
% 20.32/20.42 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)].
% 20.32/20.42 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].
% 20.32/20.42 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)].
% 20.32/20.42 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2437,a,2416,a)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.42 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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].
% 20.32/20.44 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)].
% 20.32/20.44 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2438,a,2416,a)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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].
% 20.32/20.44 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)].
% 20.32/20.44 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2439,a,2416,a)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.44 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.45 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)].
% 20.32/20.47 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].
% 20.32/20.47 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)].
% 20.32/20.47 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2441,a,2416,a)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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].
% 20.32/20.47 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)].
% 20.32/20.47 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2442,a,2416,a)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.47 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)].
% 20.32/20.48 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)].
% 20.32/20.48 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)].
% 20.32/20.48 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)].
% 20.32/20.48 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].
% 20.32/20.48 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2443,a,2415,a)].
% 20.32/20.48 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(2443,a,2416,a)].
% 20.32/20.48 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)].
% 20.32/20.48 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)].
% 20.32/20.48 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)].
% 20.32/20.48 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)].
% 20.32/20.48 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)].
% 20.32/20.48 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2443,a,2422,b)].
% 20.32/20.48 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2443,a,2423,b)].
% 20.32/20.48 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2443,a,2424,b)].
% 20.32/20.48 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2443,a,2425,b)].
% 20.32/20.48 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2443,a,2426,b)].
% 20.32/20.48 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2443,a,2427,b)].
% 20.32/20.48 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)].
% 20.32/20.48 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].
% 20.32/20.48 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)].
% 20.32/20.48 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2444,a,2416,a)].
% 20.32/20.48 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)].
% 20.32/20.48 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)].
% 20.32/20.48 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)].
% 20.32/20.48 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)].
% 20.32/20.48 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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].
% 20.42/20.50 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)].
% 20.42/20.50 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2445,a,2416,a)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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].
% 20.42/20.50 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)].
% 20.42/20.50 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2446,a,2416,a)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.42/20.50 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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].
% 20.63/20.73 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)].
% 20.63/20.73 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2447,a,2416,a)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 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)].
% 20.63/20.73 2448 class_Orderings_Oord(tc_IntDef_Oint). [resolve(18,a,1,a)].
% 20.63/20.73 2449 class_Orderings_Oord(tc_nat). [resolve(18,a,3,a)].
% 20.63/20.73 2450 class_Orderings_Oord(tc_set(A)). [resolve(18,a,4,a)].
% 20.63/20.73 2451 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(18,a,9,b)].
% 20.63/20.73 2452 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(18,a,10,b)].
% 20.63/20.73 2453 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(18,a,11,b)].
% 20.63/20.73 2454 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(18,a,13,b)].
% 20.63/20.73 2455 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(32,b,18,a)].
% 20.63/20.73 2456 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1079,b,1069,a)].
% 21.02/21.16 2457 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1089,b,1070,a)].
% 21.02/21.16 2458 class_Orderings_Oord(tc_nat). [resolve(1089,b,1071,a)].
% 21.02/21.16 2459 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1089,b,1081,b)].
% 21.02/21.16 2460 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1089,b,1082,b)].
% 21.02/21.16 2461 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1089,b,1083,b)].
% 21.02/21.16 2462 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1089,b,1084,b)].
% 21.02/21.16 2463 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1162,b,1132,a)].
% 21.02/21.16 2464 class_Orderings_Oord(tc_nat). [resolve(1162,b,1133,a)].
% 21.02/21.16 2465 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1162,b,1135,b)].
% 21.02/21.16 2466 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1162,b,1136,b)].
% 21.02/21.16 2467 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1162,b,1137,b)].
% 21.02/21.16 2468 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1162,b,1140,b)].
% 21.02/21.16 2469 class_Orderings_Oord(A) | -class_Wellfounded__Recursion_Owellorder(A). [resolve(1162,b,1147,b)].
% 21.02/21.16 2470 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1258,b,1175,a)].
% 21.02/21.16 2471 class_Orderings_Oord(tc_nat). [resolve(1258,b,1176,a)].
% 21.02/21.16 2472 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1258,b,1179,b)].
% 21.02/21.16 2473 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1258,b,1180,b)].
% 21.02/21.16 2474 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1258,b,1181,b)].
% 21.02/21.16 2475 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1258,b,1182,b)].
% 21.02/21.16 2476 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1296,b,1277,b)].
% 21.02/21.16 2477 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1296,b,1291,b)].
% 21.02/21.16 2478 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1387,b,1344,a)].
% 21.02/21.16 2479 class_Orderings_Oord(tc_nat). [resolve(1387,b,1345,a)].
% 21.02/21.16 2480 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1387,b,1347,b)].
% 21.02/21.16 2481 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1387,b,1348,b)].
% 21.02/21.16 2482 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1387,b,1349,b)].
% 21.02/21.16 2483 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1387,b,1351,b)].
% 21.02/21.16 2484 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1387,b,1354,b)].
% 21.02/21.16 2485 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1387,b,1356,b)].
% 21.02/21.16 2486 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1387,b,1357,b)].
% 21.02/21.16 2487 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1387,b,1358,b)].
% 21.02/21.16 2488 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1387,b,1359,b)].
% 21.02/21.16 2489 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1526,b,1401,a)].
% 21.02/21.16 2490 class_Orderings_Oord(tc_nat). [resolve(1526,b,1402,a)].
% 21.02/21.16 2491 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1647,b,1583,a)].
% 21.02/21.16 2492 class_Orderings_Oord(tc_nat). [resolve(1647,b,1584,a)].
% 21.02/21.16 2493 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1647,b,1585,b)].
% 21.02/21.16 2494 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1647,b,1587,b)].
% 21.02/21.16 2495 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1647,b,1588,b)].
% 21.02/21.16 2496 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1647,b,1589,b)].
% 21.02/21.16 2497 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1647,b,1590,b)].
% 21.02/21.16 2498 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1814,b,1649,a)].
% 21.02/21.16 2499 class_Orderings_Oord(tc_nat). [resolve(1814,b,1650,a)].
% 21.02/21.16 2500 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1814,b,1652,b)].
% 21.32/21.44 2501 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1814,b,1653,b)].
% 21.32/21.44 2502 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1814,b,1654,b)].
% 21.32/21.44 2503 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1814,b,1655,b)].
% 21.32/21.44 2504 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1852,b,1823,b)].
% 21.32/21.44 2505 class_Orderings_Oord(tc_IntDef_Oint). [resolve(2212,b,1957,a)].
% 21.32/21.44 2506 class_Orderings_Oord(tc_nat). [resolve(2212,b,1958,a)].
% 21.32/21.44 2507 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2413,b,2314,b)].
% 21.32/21.44 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].
% 21.32/21.44 2509 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom). [assumption].
% 21.32/21.44 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].
% 21.32/21.44 2511 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom). [assumption].
% 21.32/21.44 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].
% 21.32/21.44 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].
% 21.32/21.44 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].
% 21.32/21.44 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].
% 21.32/21.44 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].
% 21.32/21.44 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].
% 21.32/21.44 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(2517,a,2509,a)].
% 21.32/21.44 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2517,a,2513,b)].
% 21.32/21.44 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2517,a,2514,b)].
% 21.32/21.44 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2517,a,2515,b)].
% 21.32/21.44 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2517,a,2516,b)].
% 21.32/21.44 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].
% 21.32/21.44 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(2518,a,2509,a)].
% 21.32/21.44 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2518,a,2513,b)].
% 21.32/21.44 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2518,a,2514,b)].
% 21.32/21.44 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2518,a,2515,b)].
% 21.32/21.44 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2518,a,2516,b)].
% 21.32/21.44 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].
% 21.32/21.44 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)].
% 21.32/21.46 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)].
% 21.32/21.46 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)].
% 21.32/21.46 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)].
% 21.32/21.46 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)].
% 21.32/21.46 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].
% 21.32/21.46 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2520,a,2509,a)].
% 21.32/21.46 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2520,a,2513,b)].
% 21.32/21.46 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2520,a,2514,b)].
% 21.32/21.46 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2520,a,2515,b)].
% 21.32/21.46 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2520,a,2516,b)].
% 21.32/21.46 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].
% 21.32/21.46 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(2521,a,2509,a)].
% 21.32/21.46 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2521,a,2513,b)].
% 21.32/21.46 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2521,a,2514,b)].
% 21.32/21.46 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2521,a,2515,b)].
% 21.32/21.46 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2521,a,2516,b)].
% 21.32/21.46 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].
% 21.32/21.46 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2522,a,2509,a)].
% 21.32/21.46 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2522,a,2513,b)].
% 21.32/21.46 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2522,a,2514,b)].
% 21.32/21.46 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2522,a,2515,b)].
% 21.32/21.46 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2522,a,2516,b)].
% 21.32/21.46 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].
% 21.32/21.46 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)].
% 21.32/21.46 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)].
% 21.32/21.46 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)].
% 21.32/21.46 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)].
% 21.32/21.46 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)].
% 21.32/21.46 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].
% 21.32/21.46 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(2524,a,2509,a)].
% 21.32/21.46 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)].
% 21.32/21.46 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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].
% 21.39/21.47 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2525,a,2509,a)].
% 21.39/21.47 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2525,a,2513,b)].
% 21.39/21.47 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2525,a,2514,b)].
% 21.39/21.47 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2525,a,2515,b)].
% 21.39/21.47 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)].
% 21.39/21.47 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].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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].
% 21.39/21.47 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2527,a,2509,a)].
% 21.39/21.47 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2527,a,2513,b)].
% 21.39/21.47 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2527,a,2514,b)].
% 21.39/21.47 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2527,a,2515,b)].
% 21.39/21.47 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2527,a,2516,b)].
% 21.39/21.47 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].
% 21.39/21.47 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(2528,a,2509,a)].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.47 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)].
% 21.39/21.55 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)].
% 21.39/21.55 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].
% 21.39/21.55 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2530,a,2509,a)].
% 21.39/21.55 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2530,a,2513,b)].
% 21.39/21.55 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2530,a,2514,b)].
% 21.39/21.55 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2530,a,2515,b)].
% 21.39/21.55 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)].
% 21.39/21.55 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].
% 21.39/21.55 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(2531,a,2509,a)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 2532 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(B,B,A). [resolve(9,b,2,a)].
% 21.39/21.55 2533 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(33,a,9,b)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.39/21.55 2543 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(151,b,147,a)].
% 21.39/21.55 2544 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(151,b,148,a)].
% 21.39/21.55 2545 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(183,a,151,b)].
% 21.39/21.55 2546 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(184,a,151,b)].
% 21.39/21.55 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)].
% 21.39/21.55 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)].
% 21.64/21.73 2549 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(346,b,317,b)].
% 21.64/21.73 2550 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1087,a,1074,b)].
% 21.64/21.73 2551 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1118,a,1105,b)].
% 21.64/21.73 2552 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1161,b,1135,b)].
% 21.64/21.73 2553 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1163,b,1135,b)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 2565 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1342,a,1311,b)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 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)].
% 21.64/21.73 2574 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1384,b,1347,b)].
% 21.64/21.73 2575 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1386,b,1347,b)].
% 21.64/21.73 2576 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1388,b,1347,b)].
% 21.64/21.73 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2590,c,2509,a)].
% 21.79/21.90 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)].
% 21.79/21.90 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2591,b,2509,a)].
% 21.79/21.90 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)].
% 21.79/21.90 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2592,c,2509,a)].
% 21.79/21.90 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)].
% 21.79/21.90 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2593,b,2509,a)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 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)].
% 21.79/21.90 2596 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2241,a,2226,b)].
% 21.79/21.90 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2596,b,2509,a)].
% 21.84/21.94 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)].
% 21.84/21.94 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(2597,c,2509,a)].
% 21.84/21.94 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)].
% 21.84/21.94 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(2598,c,2509,a)].
% 21.84/21.94 2599 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2244,a,2226,b)].
% 21.84/21.94 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2599,b,2509,a)].
% 21.84/21.94 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)].
% 21.84/21.94 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(2600,c,2509,a)].
% 21.84/21.94 2601 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2246,a,2226,b)].
% 21.84/21.94 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2601,b,2509,a)].
% 21.84/21.94 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)].
% 21.84/21.94 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(2602,c,2509,a)].
% 21.84/21.94 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)].
% 21.84/21.94 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(2603,c,2509,a)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.84/21.94 2607 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2252,a,2226,b)].
% 21.84/21.94 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2607,b,2509,a)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.84/21.94 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2613,d,2509,a)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2620,d,2509,a)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 21.87/21.97 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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].
% 22.09/22.18 2629 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom). [assumption].
% 22.09/22.18 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].
% 22.09/22.18 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].
% 22.09/22.18 2632 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom). [assumption].
% 22.09/22.18 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].
% 22.09/22.18 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].
% 22.09/22.18 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].
% 22.09/22.18 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].
% 22.09/22.18 2637 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(11,b,2,a)].
% 22.09/22.18 2638 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(33,a,11,b)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.09/22.18 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)].
% 22.29/22.38 2648 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(153,b,147,a)].
% 22.29/22.38 2649 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(153,b,148,a)].
% 22.29/22.38 2650 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(183,a,153,b)].
% 22.29/22.38 2651 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(184,a,153,b)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 2654 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(346,b,319,b)].
% 22.29/22.38 2655 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1087,a,1076,b)].
% 22.29/22.38 2656 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1118,a,1107,b)].
% 22.29/22.38 2657 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1161,b,1137,b)].
% 22.29/22.38 2658 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1163,b,1137,b)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 2670 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1342,a,1313,b)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.29/22.38 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 2679 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1384,b,1349,b)].
% 22.47/22.56 2680 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1386,b,1349,b)].
% 22.47/22.56 2681 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1388,b,1349,b)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 2693 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2228,b,2220,a)].
% 22.47/22.56 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(2693,a,2629,a)].
% 22.47/22.56 2694 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2228,b,2222,a)].
% 22.47/22.56 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(2694,a,2629,a)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 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)].
% 22.47/22.56 2703 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2241,a,2228,b)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 2706 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2244,a,2228,b)].
% 22.53/22.63 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)].
% 22.53/22.63 2708 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2246,a,2228,b)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 2714 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2252,a,2228,b)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.53/22.63 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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].
% 22.76/22.84 2736 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom). [assumption].
% 22.76/22.84 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].
% 22.76/22.84 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].
% 22.76/22.84 2739 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom). [assumption].
% 22.76/22.84 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].
% 22.76/22.84 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].
% 22.76/22.84 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].
% 22.76/22.84 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].
% 22.76/22.84 2744 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(10,b,2,a)].
% 22.76/22.84 2745 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(33,a,10,b)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 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)].
% 22.76/22.84 2755 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(152,b,147,a)].
% 22.76/22.84 2756 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(152,b,148,a)].
% 22.92/23.01 2757 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(183,a,152,b)].
% 22.92/23.01 2758 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(184,a,152,b)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 2761 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(346,b,318,b)].
% 22.92/23.01 2762 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1087,a,1075,b)].
% 22.92/23.01 2763 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1118,a,1106,b)].
% 22.92/23.01 2764 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1161,b,1136,b)].
% 22.92/23.01 2765 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1163,b,1136,b)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 2777 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1342,a,1312,b)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 23.06/23.18 2786 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1384,b,1348,b)].
% 23.06/23.18 2787 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1386,b,1348,b)].
% 23.06/23.18 2788 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1388,b,1348,b)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 2800 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2227,b,2220,a)].
% 23.06/23.18 2801 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2227,b,2222,a)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 2810 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2241,a,2227,b)].
% 23.06/23.18 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)].
% 23.06/23.18 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)].
% 23.06/23.18 2813 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2244,a,2227,b)].
% 23.16/23.24 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)].
% 23.16/23.24 2815 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2246,a,2227,b)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 2821 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2252,a,2227,b)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.16/23.24 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)].
% 23.35/23.44 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)].
% 23.35/23.44 2842 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom). [assumption].
% 23.35/23.44 2843 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom). [assumption].
% 23.35/23.44 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].
% 23.35/23.44 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].
% 23.35/23.44 2846 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom). [assumption].
% 23.35/23.44 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].
% 23.35/23.44 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].
% 23.35/23.44 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].
% 23.35/23.44 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].
% 23.35/23.44 2851 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(19,b,2,a)].
% 23.35/23.44 2852 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(33,a,19,b)].
% 23.35/23.44 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)].
% 23.35/23.44 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)].
% 23.35/23.44 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)].
% 23.35/23.44 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)].
% 23.35/23.44 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)].
% 23.35/23.44 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)].
% 23.35/23.44 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)].
% 23.35/23.44 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)].
% 23.35/23.44 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)].
% 23.35/23.44 2862 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(71,a,85,b)].
% 23.35/23.44 2863 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(100,a,85,b)].
% 23.35/23.44 2864 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(102,a,85,b)].
% 23.35/23.44 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)].
% 23.35/23.44 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)].
% 23.35/23.46 2867 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(183,a,164,b)].
% 23.35/23.46 2868 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(184,a,164,b)].
% 23.35/23.46 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)].
% 23.35/23.46 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)].
% 23.35/23.46 2871 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(223,a,198,b)].
% 23.35/23.46 2872 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(224,a,198,b)].
% 23.35/23.46 2873 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(226,b,198,b)].
% 23.35/23.46 2874 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(227,b,198,b)].
% 23.35/23.46 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)].
% 23.35/23.46 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)].
% 23.35/23.46 2877 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(346,b,331,b)].
% 23.35/23.46 2878 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(380,a,361,b)].
% 23.35/23.46 2879 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(381,a,361,b)].
% 23.35/23.46 2880 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(386,b,361,b)].
% 23.35/23.46 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)].
% 23.35/23.46 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)].
% 23.35/23.46 2883 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(391,b,361,b)].
% 23.35/23.46 2884 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(410,a,400,b)].
% 23.35/23.46 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)].
% 23.35/23.46 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)].
% 23.35/23.46 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)].
% 23.35/23.46 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)].
% 23.35/23.46 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)].
% 23.35/23.46 2890 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(421,b,400,b)].
% 23.35/23.46 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)].
% 23.35/23.46 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)].
% 23.35/23.46 2893 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(433,b,400,b)].
% 23.35/23.46 2894 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(434,b,400,b)].
% 23.35/23.46 2895 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(439,b,400,b)].
% 23.52/23.61 2896 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(440,b,400,b)].
% 23.52/23.61 2897 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(441,b,400,b)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 2900 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(444,b,400,b)].
% 23.52/23.61 2901 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1087,a,1079,b)].
% 23.52/23.61 2902 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1118,a,1110,b)].
% 23.52/23.61 2903 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1161,b,1140,b)].
% 23.52/23.61 2904 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1163,b,1140,b)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 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)].
% 23.52/23.61 2922 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1385,b,1354,b)].
% 23.52/23.61 2923 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1386,b,1354,b)].
% 23.52/23.61 2924 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1388,b,1354,b)].
% 23.52/23.61 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 2936 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1631,b,1585,b)].
% 23.65/23.76 2937 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1632,b,1585,b)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 2947 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1642,b,1585,b)].
% 23.65/23.76 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)].
% 23.65/23.76 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)].
% 23.65/23.76 2950 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1645,b,1585,b)].
% 23.65/23.76 2951 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1646,b,1585,b)].
% 23.65/23.76 2952 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2229,b,2220,a)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 2961 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2241,a,2229,b)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 2964 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2244,a,2229,b)].
% 23.65/23.78 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)].
% 23.65/23.78 2966 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2246,a,2229,b)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 2972 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2252,a,2229,b)].
% 23.65/23.78 2973 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2297,b,2229,b)].
% 23.65/23.78 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2973,b,2843,a)].
% 23.65/23.78 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2973,b,2848,b)].
% 23.65/23.78 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2973,b,2849,b)].
% 23.65/23.78 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2973,b,2850,b)].
% 23.65/23.78 2974 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2356,b,2314,b)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.78 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 2980 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2367,b,2314,b)].
% 23.65/23.79 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2980,b,2843,a)].
% 23.65/23.79 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2980,b,2848,b)].
% 23.65/23.79 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2980,b,2849,b)].
% 23.65/23.79 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2980,b,2850,b)].
% 23.65/23.79 2981 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2368,b,2314,b)].
% 23.65/23.79 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2981,b,2843,a)].
% 23.65/23.79 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2981,b,2848,b)].
% 23.65/23.79 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2981,b,2849,b)].
% 23.65/23.79 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2981,b,2850,b)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 2990 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2382,b,2314,b)].
% 23.65/23.79 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(2990,b,2843,a)].
% 23.65/23.79 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2990,b,2848,b)].
% 23.65/23.79 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2990,b,2849,b)].
% 23.65/23.79 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2990,b,2850,b)].
% 23.65/23.79 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)].
% 23.65/23.79 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2991,c,2843,a)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2992,c,2843,a)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 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)].
% 23.65/23.79 2993 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2397,b,2314,b)].
% 23.65/23.79 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2993,b,2843,a)].
% 23.65/23.79 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2993,b,2848,b)].
% 23.65/23.79 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2993,b,2849,b)].
% 23.65/23.79 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2993,b,2850,b)].
% 23.65/23.79 2994 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2398,b,2314,b)].
% 23.65/23.80 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2994,b,2843,a)].
% 23.65/23.80 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2994,b,2848,b)].
% 23.65/23.80 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2994,b,2849,b)].
% 23.65/23.80 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2994,b,2850,b)].
% 23.65/23.80 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)].
% 23.65/23.80 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2995,c,2843,a)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2996,b,2843,a)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2997,c,2843,a)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3002,c,2843,a)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 3004 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2408,b,2314,b)].
% 23.65/23.80 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3004,b,2843,a)].
% 23.65/23.80 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3004,b,2848,b)].
% 23.65/23.80 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3004,b,2849,b)].
% 23.65/23.80 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3004,b,2850,b)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 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)].
% 23.65/23.80 3007 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2411,b,2314,b)].
% 23.65/23.80 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(3007,b,2843,a)].
% 23.65/23.80 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3007,b,2848,b)].
% 23.65/23.80 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3007,b,2849,b)].
% 23.65/23.80 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3007,b,2850,b)].
% 23.65/23.80 3008 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2412,b,2314,b)].
% 23.65/23.80 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(3008,b,2843,a)].
% 23.65/23.80 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3008,b,2848,b)].
% 23.65/23.80 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3008,b,2849,b)].
% 23.65/23.80 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3008,b,2850,b)].
% 23.65/23.80 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 3029 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2517,a,2513,b)].
% 23.76/23.85 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(3029,c,2843,a)].
% 23.76/23.85 3030 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2518,a,2513,b)].
% 23.76/23.85 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(3030,b,2843,a)].
% 23.76/23.85 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)].
% 23.76/23.85 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)].
% 23.76/23.85 3032 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2520,a,2513,b)].
% 23.76/23.85 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3032,c,2843,a)].
% 23.76/23.85 3033 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2521,a,2513,b)].
% 23.76/23.85 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(3033,b,2843,a)].
% 23.76/23.85 3034 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2522,a,2513,b)].
% 24.47/24.56 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3034,b,2843,a)].
% 24.47/24.56 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)].
% 24.47/24.56 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)].
% 24.47/24.56 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)].
% 24.47/24.56 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3036,c,2843,a)].
% 24.47/24.56 3037 c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2525,a,2513,b)].
% 24.47/24.56 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3037,b,2843,a)].
% 24.47/24.56 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)].
% 24.47/24.56 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)].
% 24.47/24.56 3039 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2527,a,2513,b)].
% 24.47/24.56 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3039,b,2843,a)].
% 24.47/24.56 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)].
% 24.47/24.56 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(3040,c,2843,a)].
% 24.47/24.56 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)].
% 24.47/24.56 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)].
% 24.47/24.56 3042 -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2530,a,2513,b)].
% 24.47/24.56 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3042,b,2843,a)].
% 24.47/24.56 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)].
% 24.47/24.56 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(3043,c,2843,a)].
% 24.47/24.56 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].
% 24.47/24.56 3045 class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_55) # label(axiom). [assumption].
% 24.47/24.56 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].
% 24.47/24.56 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].
% 24.47/24.56 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].
% 24.47/24.56 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].
% 24.47/24.56 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].
% 24.47/24.56 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].
% 24.47/24.56 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].
% 24.47/24.56 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)].
% 24.47/24.57 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)].
% 24.47/24.57 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)].
% 24.47/24.57 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].
% 24.47/24.57 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)].
% 24.47/24.57 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)].
% 24.47/24.57 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)].
% 24.47/24.57 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].
% 24.47/24.57 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)].
% 24.47/24.57 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)].
% 24.47/24.57 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)].
% 24.47/24.57 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].
% 24.47/24.57 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)].
% 24.47/24.57 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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)].
% 24.47/24.58 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].
% 24.47/24.59 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)].
% 24.47/24.59 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)].
% 24.47/24.59 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)].
% 24.47/24.59 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].
% 24.47/24.59 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)].
% 24.47/24.59 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)].
% 24.47/24.59 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)].
% 24.47/24.59 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].
% 24.47/24.59 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)].
% 24.47/24.59 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)].
% 24.47/24.59 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)].
% 24.47/24.59 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].
% 24.47/24.59 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)].
% 24.47/24.59 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)].
% 24.54/24.60 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)].
% 24.54/24.60 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].
% 24.54/24.60 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)].
% 24.54/24.60 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)].
% 24.54/24.60 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)].
% 24.54/24.60 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].
% 24.54/24.60 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)].
% 24.54/24.60 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)].
% 24.54/24.60 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)].
% 24.54/24.60 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].
% 24.54/24.60 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)].
% 24.54/24.60 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)].
% 24.54/24.60 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)].
% 24.54/24.61 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].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.54/24.61 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)].
% 24.61/24.68 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].
% 24.61/24.68 Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0. [resolve(3076,a,3045,a)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 3077 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,B,A). [resolve(23,b,2,a)].
% 24.61/24.68 3078 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(33,a,23,b)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 3088 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(71,a,89,b)].
% 24.61/24.68 3089 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(100,a,89,b)].
% 24.61/24.68 3090 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(102,a,89,b)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 3093 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(183,a,168,b)].
% 24.61/24.68 3094 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(184,a,168,b)].
% 24.61/24.68 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)].
% 24.61/24.68 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)].
% 24.61/24.68 3097 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(223,a,202,b)].
% 24.61/24.77 3098 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(224,a,202,b)].
% 24.61/24.77 3099 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(226,b,202,b)].
% 24.61/24.77 3100 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(227,b,202,b)].
% 24.61/24.77 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)].
% 24.61/24.77 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)].
% 24.61/24.77 3103 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(346,b,335,b)].
% 24.61/24.77 3104 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(380,a,365,b)].
% 24.61/24.77 3105 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(381,a,365,b)].
% 24.61/24.77 3106 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(386,b,365,b)].
% 24.61/24.77 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)].
% 24.61/24.77 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)].
% 24.61/24.77 3109 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(391,b,365,b)].
% 24.61/24.77 3110 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(410,a,403,b)].
% 24.61/24.77 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)].
% 24.61/24.77 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)].
% 24.61/24.77 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)].
% 24.61/24.77 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)].
% 24.61/24.77 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)].
% 24.61/24.77 3116 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(421,b,403,b)].
% 24.61/24.77 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)].
% 24.61/24.77 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)].
% 24.61/24.77 3119 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(433,b,403,b)].
% 24.61/24.77 3120 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(434,b,403,b)].
% 24.61/24.77 3121 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(439,b,403,b)].
% 24.61/24.77 3122 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(440,b,403,b)].
% 24.61/24.77 3123 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(441,b,403,b)].
% 24.61/24.77 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)].
% 24.61/24.77 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)].
% 24.61/24.77 3126 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(444,b,403,b)].
% 24.61/24.77 3127 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1087,a,1083,b)].
% 24.74/24.80 3128 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1118,a,1114,b)].
% 24.74/24.80 3129 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1161,b,1144,b)].
% 24.74/24.80 3130 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1163,b,1144,b)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.74/24.80 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.83 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)].
% 24.77/24.85 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)].
% 24.77/24.85 3174 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1219,a,1181,b)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 3179 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1224,a,1181,b)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.77/24.85 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 3206 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1385,b,1358,b)].
% 24.85/24.91 3207 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1386,b,1358,b)].
% 24.85/24.91 3208 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1388,b,1358,b)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 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)].
% 24.85/24.91 3220 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1498,b,1408,b)].
% 24.85/24.91 3221 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1499,b,1408,b)].
% 24.85/24.91 3222 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1523,b,1408,b)].
% 24.85/24.91 3223 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1631,b,1589,b)].
% 24.85/24.93 3224 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1632,b,1589,b)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 3234 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1642,b,1589,b)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 3237 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1645,b,1589,b)].
% 24.85/24.93 3238 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1646,b,1589,b)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.93 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.94 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.95 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.85/24.96 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)].
% 24.92/24.97 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)].
% 24.92/24.97 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)].
% 24.92/24.97 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)].
% 24.92/24.97 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)].
% 24.92/24.97 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)].
% 24.92/24.97 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)].
% 24.92/24.97 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 3273 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1740,b,1654,b)].
% 24.92/24.98 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3273,b,3046,b)].
% 24.92/24.98 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3273,b,3047,b)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 3278 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1745,b,1654,b)].
% 24.92/24.98 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3278,b,3046,b)].
% 24.92/24.98 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3278,b,3047,b)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.98 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/24.99 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 3305 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1773,b,1654,b)].
% 24.92/25.01 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)].
% 24.92/25.01 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)].
% 24.92/25.01 3308 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1788,b,1654,b)].
% 24.92/25.01 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3308,b,3046,b)].
% 24.92/25.01 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3308,b,3047,b)].
% 24.92/25.01 3309 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1789,b,1654,b)].
% 24.92/25.01 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3309,b,3046,b)].
% 24.92/25.01 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3309,b,3047,b)].
% 24.92/25.01 3310 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1790,b,1654,b)].
% 24.92/25.01 3311 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1796,b,1654,b)].
% 24.92/25.06 3312 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1797,b,1654,b)].
% 24.92/25.06 3313 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1798,b,1654,b)].
% 24.92/25.06 3314 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1799,b,1654,b)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 3324 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1809,b,1654,b)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 3327 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1812,b,1654,b)].
% 24.92/25.06 3328 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1813,b,1654,b)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.06 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 3337 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2241,a,2232,b)].
% 24.92/25.07 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3337,b,3046,b)].
% 24.92/25.07 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3337,b,3047,b)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 3340 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2244,a,2232,b)].
% 24.92/25.07 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3340,b,3046,b)].
% 24.92/25.07 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3340,b,3047,b)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.07 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)].
% 24.92/25.08 3342 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2246,a,2232,b)].
% 24.92/25.08 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3342,b,3046,b)].
% 24.92/25.08 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3342,b,3047,b)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 24.92/25.08 3348 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2252,a,2232,b)].
% 24.92/25.08 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3348,b,3046,b)].
% 24.92/25.08 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3348,b,3047,b)].
% 24.92/25.08 3349 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2321,a,2317,b)].
% 24.92/25.08 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3349,b,3046,b)].
% 24.92/25.08 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3349,b,3047,b)].
% 24.92/25.08 3350 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2356,b,2317,b)].
% 24.92/25.08 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3350,b,3046,b)].
% 24.92/25.08 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3350,b,3047,b)].
% 24.92/25.08 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)].
% 24.92/25.08 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.04/25.10 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.12 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 3376 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2517,a,2516,b)].
% 25.07/25.13 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3376,c,3046,b)].
% 25.07/25.13 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3376,c,3047,b)].
% 25.07/25.13 3377 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2518,a,2516,b)].
% 25.07/25.13 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3377,b,3046,b)].
% 25.07/25.13 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3377,b,3047,b)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 3379 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2520,a,2516,b)].
% 25.07/25.13 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3379,c,3046,b)].
% 25.07/25.13 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3379,c,3047,b)].
% 25.07/25.13 3380 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2521,a,2516,b)].
% 25.07/25.13 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3380,b,3046,b)].
% 25.07/25.13 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3380,b,3047,b)].
% 25.07/25.13 3381 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2522,a,2516,b)].
% 25.07/25.13 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3381,b,3046,b)].
% 25.07/25.13 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3381,b,3047,b)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.07/25.13 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)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3384,b,3046,b)].
% 25.09/25.15 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3384,b,3047,b)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 3386 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2527,a,2516,b)].
% 25.09/25.15 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3386,b,3046,b)].
% 25.09/25.15 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3386,b,3047,b)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3389,b,3046,b)].
% 25.09/25.15 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3389,b,3047,b)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 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)].
% 25.09/25.15 3391 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2973,b,2850,b)].
% 25.09/25.15 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(3391,b,3045,a)].
% 25.09/25.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3391,b,3046,b)].
% 25.09/25.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3391,b,3047,b)].
% 25.09/25.15 3392 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2980,b,2850,b)].
% 25.09/25.15 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(3392,b,3045,a)].
% 25.09/25.15 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3392,b,3046,b)].
% 25.09/25.15 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3392,b,3047,b)].
% 25.09/25.15 3393 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2981,b,2850,b)].
% 25.09/25.15 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(3393,b,3045,a)].
% 25.09/25.15 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3393,b,3046,b)].
% 25.09/25.16 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3393,b,3047,b)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 3402 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2990,b,2850,b)].
% 25.09/25.16 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(3402,b,3045,a)].
% 25.09/25.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3402,b,3046,b)].
% 25.09/25.16 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3402,b,3047,b)].
% 25.09/25.16 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)].
% 25.09/25.16 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(3403,c,3045,a)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(3404,c,3045,a)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 3405 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2993,b,2850,b)].
% 25.09/25.16 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(3405,b,3045,a)].
% 25.09/25.16 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3405,b,3046,b)].
% 25.09/25.16 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3405,b,3047,b)].
% 25.09/25.16 3406 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2994,b,2850,b)].
% 25.09/25.16 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(3406,b,3045,a)].
% 25.09/25.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3406,b,3046,b)].
% 25.09/25.16 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3406,b,3047,b)].
% 25.09/25.16 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)].
% 25.09/25.16 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3407,c,3045,a)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(3408,b,3045,a)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.16 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)].
% 25.09/25.17 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3409,c,3045,a)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3414,c,3045,a)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.09/25.17 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)].
% 25.30/25.37 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)].
% 25.30/25.37 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)].
% 25.30/25.37 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)].
% 25.30/25.37 3416 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3004,b,2850,b)].
% 25.30/25.37 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3416,b,3045,a)].
% 25.30/25.37 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3416,b,3046,b)].
% 25.30/25.37 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3416,b,3047,b)].
% 25.30/25.37 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)].
% 25.30/25.37 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)].
% 25.30/25.37 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)].
% 25.30/25.37 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)].
% 25.30/25.37 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)].
% 25.30/25.37 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)].
% 25.30/25.37 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)].
% 25.30/25.37 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)].
% 25.30/25.37 3419 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3007,b,2850,b)].
% 25.30/25.37 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(3419,b,3045,a)].
% 25.30/25.37 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3419,b,3046,b)].
% 25.30/25.37 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3419,b,3047,b)].
% 25.30/25.37 3420 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3008,b,2850,b)].
% 25.30/25.37 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(3420,b,3045,a)].
% 25.30/25.37 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3420,b,3046,b)].
% 25.30/25.37 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3420,b,3047,b)].
% 25.30/25.37 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].
% 25.32/25.39 3422 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom). [assumption].
% 25.32/25.39 3423 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom). [assumption].
% 25.32/25.39 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].
% 25.32/25.39 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].
% 25.32/25.39 3426 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom). [assumption].
% 25.32/25.39 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].
% 25.32/25.39 3428 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom). [assumption].
% 25.32/25.39 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].
% 25.32/25.39 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(3429,a,3422,a)].
% 25.32/25.39 Derived: c_0 != c_NatArith_Oof__nat(A,tc_nat) | c_0 = A. [resolve(3429,a,3423,a)].
% 25.32/25.39 Derived: c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3429,a,3424,b)].
% 25.32/25.39 Derived: c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3429,a,3425,b)].
% 25.32/25.39 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].
% 25.32/25.39 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(3430,a,3422,a)].
% 25.32/25.39 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_nat). [resolve(3430,a,3423,a)].
% 25.32/25.39 Derived: c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3430,a,3424,b)].
% 25.32/25.39 Derived: c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3430,a,3425,b)].
% 25.32/25.39 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].
% 25.32/25.39 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3431,a,3422,a)].
% 25.32/25.39 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(3431,a,3423,a)].
% 25.32/25.39 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3431,a,3424,b)].
% 25.32/25.39 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3431,a,3425,b)].
% 25.32/25.39 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].
% 25.32/25.39 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)].
% 25.32/25.39 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)].
% 25.32/25.39 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)].
% 25.32/25.39 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)].
% 25.32/25.39 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].
% 25.32/25.39 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)].
% 25.32/25.39 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)].
% 25.32/25.41 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)].
% 25.32/25.41 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)].
% 25.32/25.41 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].
% 25.32/25.41 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3434,a,3422,a)].
% 25.32/25.41 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_0 | A = c_0. [resolve(3434,a,3423,a)].
% 25.32/25.41 Derived: c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3434,a,3424,b)].
% 25.32/25.41 Derived: c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3434,a,3425,b)].
% 25.32/25.41 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].
% 25.32/25.41 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(3435,a,3422,a)].
% 25.32/25.41 Derived: c_NatArith_Oof__nat(c_0,tc_nat) = c_0. [resolve(3435,a,3423,a)].
% 25.32/25.41 Derived: c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3435,a,3424,b)].
% 25.32/25.41 Derived: c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3435,a,3425,b)].
% 25.32/25.41 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].
% 25.32/25.41 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(3436,a,3422,a)].
% 25.32/25.41 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_NatArith_Oof__nat(B,tc_nat) | A = B. [resolve(3436,a,3423,a)].
% 25.32/25.41 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)].
% 25.32/25.41 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)].
% 25.32/25.41 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].
% 25.32/25.41 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3437,a,3422,a)].
% 25.32/25.41 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat) | A = c_0. [resolve(3437,a,3423,a)].
% 25.32/25.41 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)].
% 25.32/25.41 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)].
% 25.32/25.41 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].
% 25.32/25.41 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3438,a,3422,a)].
% 25.32/25.41 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_nat),c_0,tc_nat). [resolve(3438,a,3423,a)].
% 25.32/25.41 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)].
% 25.32/25.41 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)].
% 25.32/25.41 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].
% 25.32/25.41 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)].
% 25.32/25.41 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)].
% 25.32/25.41 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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].
% 25.37/25.44 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3441,a,3422,a)].
% 25.37/25.44 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3441,a,3424,b)].
% 25.37/25.44 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3441,a,3425,b)].
% 25.37/25.44 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].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.37/25.44 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)].
% 25.39/25.45 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)].
% 25.39/25.45 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].
% 25.39/25.45 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)].
% 25.39/25.45 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)].
% 25.39/25.45 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)].
% 25.39/25.45 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)].
% 25.39/25.45 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].
% 25.39/25.45 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)].
% 25.39/25.45 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)].
% 25.39/25.45 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)].
% 25.39/25.45 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)].
% 25.39/25.45 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].
% 25.39/25.45 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)].
% 25.39/25.45 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)].
% 25.39/25.45 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)].
% 25.39/25.45 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)].
% 25.39/25.45 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].
% 25.39/25.45 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)].
% 25.39/25.45 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)].
% 25.39/25.50 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)].
% 25.39/25.50 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)].
% 25.39/25.50 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].
% 25.39/25.50 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(3449,a,3422,a)].
% 25.39/25.50 Derived: -c_lessequals(c_1,c_0,tc_nat). [resolve(3449,a,3423,a)].
% 25.39/25.50 Derived: -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3449,a,3424,b)].
% 25.39/25.50 Derived: -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3449,a,3425,b)].
% 25.39/25.50 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].
% 25.39/25.50 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(3450,a,3422,a)].
% 25.39/25.50 Derived: -c_less(c_1,c_0,tc_nat). [resolve(3450,a,3423,a)].
% 25.39/25.50 Derived: -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3450,a,3424,b)].
% 25.39/25.50 Derived: -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3450,a,3425,b)].
% 25.39/25.50 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].
% 25.39/25.50 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(3451,a,3422,a)].
% 25.39/25.50 Derived: c_less(c_0,c_1,tc_nat). [resolve(3451,a,3423,a)].
% 25.39/25.50 Derived: c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3451,a,3424,b)].
% 25.39/25.50 Derived: c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3451,a,3425,b)].
% 25.39/25.50 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].
% 25.39/25.50 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(3452,a,3422,a)].
% 25.39/25.50 Derived: c_lessequals(c_0,c_1,tc_nat). [resolve(3452,a,3423,a)].
% 25.39/25.50 Derived: c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3452,a,3424,b)].
% 25.39/25.50 Derived: c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3452,a,3425,b)].
% 25.39/25.50 3453 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,B,A). [resolve(24,b,2,a)].
% 25.39/25.50 3454 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(33,a,24,b)].
% 25.39/25.50 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)].
% 25.39/25.50 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)].
% 25.39/25.50 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)].
% 25.39/25.50 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)].
% 25.39/25.50 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)].
% 25.39/25.50 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)].
% 25.39/25.50 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)].
% 25.39/25.50 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)].
% 25.39/25.50 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)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 3473 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(71,a,90,b)].
% 25.39/25.52 3474 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(100,a,90,b)].
% 25.39/25.52 3475 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(102,a,90,b)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 3478 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(183,a,169,b)].
% 25.39/25.52 3479 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(184,a,169,b)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 3482 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(223,a,203,b)].
% 25.39/25.52 3483 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(224,a,203,b)].
% 25.39/25.52 3484 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(226,b,203,b)].
% 25.39/25.52 3485 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(227,b,203,b)].
% 25.39/25.52 3486 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(249,b,228,a)].
% 25.39/25.52 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)].
% 25.39/25.52 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)].
% 25.39/25.52 3489 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(346,b,336,b)].
% 25.49/25.57 3490 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(380,a,366,b)].
% 25.49/25.57 3491 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(381,a,366,b)].
% 25.49/25.57 3492 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(386,b,366,b)].
% 25.49/25.57 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)].
% 25.49/25.57 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)].
% 25.49/25.57 3495 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(391,b,366,b)].
% 25.49/25.57 3496 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(598,a,594,b)].
% 25.49/25.57 3497 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(599,a,594,b)].
% 25.49/25.57 3498 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(633,b,623,b)].
% 25.49/25.57 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)].
% 25.49/25.57 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)].
% 25.49/25.57 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)].
% 25.49/25.57 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)].
% 25.49/25.57 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)].
% 25.49/25.57 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)].
% 25.49/25.57 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)].
% 25.49/25.57 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)].
% 25.49/25.57 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)].
% 25.49/25.57 3508 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(681,b,658,b)].
% 25.49/25.57 3509 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(682,b,658,b)].
% 25.49/25.57 3510 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(738,b,699,b)].
% 25.49/25.57 3511 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(739,b,699,b)].
% 25.49/25.57 3512 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(779,b,753,b)].
% 25.49/25.57 3513 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(780,b,753,b)].
% 25.49/25.57 3514 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(869,a,868,b)].
% 25.49/25.57 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(3514,b,3423,a)].
% 25.49/25.57 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3514,b,3424,b)].
% 25.49/25.57 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3514,b,3425,b)].
% 25.49/25.57 3515 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(870,a,868,b)].
% 25.49/25.57 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(3515,b,3423,a)].
% 25.49/25.57 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3515,b,3424,b)].
% 25.49/25.57 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3515,b,3425,b)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(3518,b,3423,a)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 3520 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__semidom(A). [resolve(875,a,868,b)].
% 25.54/25.59 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(3520,b,3423,a)].
% 25.54/25.59 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(3520,b,3424,b)].
% 25.54/25.59 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3520,b,3425,b)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.59 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)].
% 25.54/25.63 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),C) = c_times(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3522,b,3425,b)].
% 25.54/25.63 3523 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(878,a,868,b)].
% 25.54/25.63 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(3523,b,3423,a)].
% 25.54/25.63 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3523,b,3424,b)].
% 25.54/25.63 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3523,b,3425,b)].
% 25.54/25.63 3524 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1087,a,1084,b)].
% 25.54/25.63 3525 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1118,a,1115,b)].
% 25.54/25.63 3526 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1161,b,1145,b)].
% 25.54/25.63 3527 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1163,b,1145,b)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.63 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.54/25.66 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 3571 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1219,a,1182,b)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 3576 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1224,a,1182,b)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.65/25.69 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 3603 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1385,b,1359,b)].
% 25.69/25.74 3604 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1386,b,1359,b)].
% 25.69/25.74 3605 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1388,b,1359,b)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 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)].
% 25.69/25.74 3617 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1498,b,1409,b)].
% 25.69/25.74 3618 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1499,b,1409,b)].
% 25.70/25.76 3619 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1523,b,1409,b)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 3622 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1579,b,1547,b)].
% 25.70/25.76 3623 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1580,b,1547,b)].
% 25.70/25.76 3624 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1631,b,1590,b)].
% 25.70/25.76 3625 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1632,b,1590,b)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 3635 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1642,b,1590,b)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 3638 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1645,b,1590,b)].
% 25.70/25.76 3639 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1646,b,1590,b)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.76 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.70/25.78 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 3674 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1740,b,1655,b)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 3679 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1745,b,1655,b)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.81 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 3706 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1773,b,1655,b)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.78/25.83 3709 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1788,b,1655,b)].
% 25.78/25.83 3710 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1789,b,1655,b)].
% 25.78/25.83 3711 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1790,b,1655,b)].
% 25.78/25.83 3712 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1796,b,1655,b)].
% 25.78/25.83 3713 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1797,b,1655,b)].
% 25.78/25.83 3714 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1798,b,1655,b)].
% 25.78/25.83 3715 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1799,b,1655,b)].
% 25.78/25.83 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)].
% 25.78/25.83 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)].
% 25.83/25.90 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)].
% 25.83/25.90 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)].
% 25.83/25.90 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)].
% 25.83/25.90 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)].
% 25.83/25.90 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)].
% 25.83/25.90 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)].
% 25.83/25.90 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)].
% 25.83/25.90 3725 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1809,b,1655,b)].
% 25.83/25.90 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)].
% 25.83/25.90 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)].
% 25.83/25.90 3728 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1812,b,1655,b)].
% 25.83/25.90 3729 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1813,b,1655,b)].
% 25.83/25.90 3730 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1955,b,1877,b)].
% 25.83/25.90 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3730,b,3424,b)].
% 25.83/25.90 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3730,b,3425,b)].
% 25.83/25.90 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)].
% 25.83/25.90 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3731,c,3423,a)].
% 25.83/25.90 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)].
% 25.83/25.90 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3732,c,3423,a)].
% 25.83/25.90 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)].
% 25.83/25.90 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)].
% 25.83/25.90 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)].
% 25.83/25.90 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3734,c,3423,a)].
% 25.83/25.90 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)].
% 25.83/25.90 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3735,c,3423,a)].
% 25.83/25.90 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)].
% 25.83/25.90 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)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3737,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(3738,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(3739,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(3740,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3741,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3742,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 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)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3744,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3745,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 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)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3747,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(3748,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(3749,c,3423,a)].
% 26.08/26.17 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)].
% 26.08/26.17 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(3750,c,3423,a)].
% 26.08/26.17 3751 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom). [assumption].
% 26.08/26.17 3752 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom). [assumption].
% 26.08/26.17 3753 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom). [assumption].
% 26.15/26.24 3754 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom). [assumption].
% 26.15/26.24 3755 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom). [assumption].
% 26.15/26.24 3756 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom). [assumption].
% 26.15/26.24 3757 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom). [assumption].
% 26.15/26.24 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].
% 26.15/26.24 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].
% 26.15/26.24 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)].
% 26.15/26.24 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)].
% 26.15/26.24 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)].
% 26.15/26.24 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)].
% 26.15/26.24 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)].
% 26.15/26.24 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)].
% 26.15/26.24 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)].
% 26.15/26.24 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)].
% 26.15/26.24 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)].
% 26.15/26.24 3769 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(71,a,84,b)].
% 26.15/26.24 3770 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(100,a,84,b)].
% 26.15/26.24 3771 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(102,a,84,b)].
% 26.15/26.24 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)].
% 26.15/26.24 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)].
% 26.15/26.24 3774 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(183,a,163,b)].
% 26.15/26.24 3775 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(184,a,163,b)].
% 26.15/26.24 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)].
% 26.15/26.24 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)].
% 26.15/26.24 3778 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(223,a,197,b)].
% 26.15/26.26 3779 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(224,a,197,b)].
% 26.15/26.26 3780 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(226,b,197,b)].
% 26.15/26.26 3781 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(227,b,197,b)].
% 26.15/26.26 3782 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(307,a,291,b)].
% 26.15/26.26 3783 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(308,a,291,b)].
% 26.15/26.26 3784 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(346,b,330,b)].
% 26.15/26.26 3785 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(380,a,360,b)].
% 26.15/26.26 3786 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(381,a,360,b)].
% 26.15/26.26 3787 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(386,b,360,b)].
% 26.15/26.26 3788 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(389,c,360,b)].
% 26.15/26.26 3789 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(390,c,360,b)].
% 26.15/26.26 3790 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(391,b,360,b)].
% 26.15/26.26 3791 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(410,a,399,b)].
% 26.15/26.26 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3791,b,3753,b)].
% 26.15/26.26 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)].
% 26.15/26.26 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)].
% 26.15/26.26 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)].
% 26.15/26.26 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)].
% 26.15/26.26 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)].
% 26.15/26.26 3797 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(421,b,399,b)].
% 26.15/26.26 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)].
% 26.15/26.26 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)].
% 26.15/26.26 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)].
% 26.15/26.26 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)].
% 26.15/26.26 3800 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(433,b,399,b)].
% 26.15/26.26 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3800,b,3753,b)].
% 26.15/26.26 3801 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(434,b,399,b)].
% 26.15/26.26 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3801,b,3753,b)].
% 26.15/26.26 3802 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(439,b,399,b)].
% 26.15/26.26 3803 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(440,b,399,b)].
% 26.15/26.26 3804 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(441,b,399,b)].
% 26.15/26.26 3805 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(442,c,399,b)].
% 26.24/26.29 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3805,c,3753,b)].
% 26.24/26.29 3806 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(443,c,399,b)].
% 26.24/26.29 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3806,c,3753,b)].
% 26.24/26.29 3807 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(444,b,399,b)].
% 26.24/26.29 3808 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(511,b,501,b)].
% 26.24/26.29 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3808,b,3753,b)].
% 26.24/26.29 3809 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(598,a,591,b)].
% 26.24/26.29 3810 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(599,a,591,b)].
% 26.24/26.29 3811 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(633,b,620,b)].
% 26.24/26.29 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)].
% 26.24/26.29 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)].
% 26.24/26.29 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)].
% 26.24/26.29 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)].
% 26.24/26.29 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)].
% 26.24/26.29 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)].
% 26.24/26.29 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)].
% 26.24/26.29 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)].
% 26.24/26.29 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)].
% 26.24/26.29 3821 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(681,b,655,b)].
% 26.24/26.29 3822 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(682,b,655,b)].
% 26.24/26.29 3823 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(738,b,696,b)].
% 26.24/26.29 3824 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(739,b,696,b)].
% 26.24/26.29 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)].
% 26.24/26.29 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_Ofield(A). [resolve(3825,c,3753,b)].
% 26.24/26.29 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)].
% 26.24/26.29 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_Ofield(A). [resolve(3826,c,3753,b)].
% 26.24/26.29 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)].
% 26.24/26.29 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 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)].
% 26.24/26.30 3839 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(846,b,789,b)].
% 26.24/26.30 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3839,b,3753,b)].
% 26.24/26.30 3840 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(847,b,789,b)].
% 26.29/26.32 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3840,b,3753,b)].
% 26.29/26.32 3841 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(848,b,789,b)].
% 26.29/26.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3841,b,3753,b)].
% 26.29/26.32 3842 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(850,b,789,b)].
% 26.29/26.32 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3842,b,3753,b)].
% 26.29/26.32 3843 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(851,b,789,b)].
% 26.29/26.32 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3843,b,3753,b)].
% 26.29/26.32 3844 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(869,a,865,b)].
% 26.29/26.32 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3844,b,3753,b)].
% 26.29/26.32 3845 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(870,a,865,b)].
% 26.29/26.32 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3845,b,3753,b)].
% 26.29/26.32 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)].
% 26.29/26.32 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)].
% 26.29/26.32 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)].
% 26.29/26.32 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)].
% 26.29/26.32 3848 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oidom(B). [resolve(873,a,865,b)].
% 26.29/26.32 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3848,b,3753,b)].
% 26.29/26.32 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)].
% 26.29/26.32 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)].
% 26.29/26.32 3850 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(875,a,865,b)].
% 26.29/26.32 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3850,b,3753,b)].
% 26.29/26.32 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)].
% 26.29/26.32 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)].
% 26.29/26.32 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)].
% 26.29/26.32 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)].
% 26.29/26.32 3853 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(878,a,865,b)].
% 26.29/26.32 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3853,b,3753,b)].
% 26.29/26.32 3854 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(945,a,942,b)].
% 26.29/26.32 Derived: c_in(c_0,c_IntDef_OInts,tc_IntDef_Oint). [resolve(3854,b,3752,a)].
% 26.29/26.32 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3854,b,3753,b)].
% 26.29/26.32 3855 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(946,a,942,b)].
% 26.29/26.32 Derived: c_in(c_1,c_IntDef_OInts,tc_IntDef_Oint). [resolve(3855,b,3752,a)].
% 26.29/26.32 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3855,b,3753,b)].
% 26.29/26.32 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)].
% 26.29/26.32 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 3860 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(951,a,942,b)].
% 26.31/26.33 Derived: c_IntDef_Oof__int(c_1,tc_IntDef_Oint) = c_1. [resolve(3860,b,3752,a)].
% 26.31/26.33 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3860,b,3753,b)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.33 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.31/26.34 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)].
% 26.71/26.79 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)].
% 26.71/26.79 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)].
% 26.71/26.79 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)].
% 26.71/26.79 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)].
% 26.71/26.79 3873 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1067,b,942,b)].
% 26.71/26.79 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3873,b,3753,b)].
% 26.71/26.79 3874 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1068,b,942,b)].
% 26.71/26.79 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3874,b,3753,b)].
% 26.71/26.79 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].
% 26.71/26.79 3876 class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_58) # label(axiom). [assumption].
% 26.71/26.79 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].
% 26.71/26.79 3878 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_21) # label(axiom). [assumption].
% 26.71/26.79 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].
% 26.71/26.79 3880 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_28) # label(axiom). [assumption].
% 26.71/26.79 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].
% 26.71/26.79 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].
% 26.71/26.79 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].
% 26.71/26.79 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)].
% 26.71/26.79 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)].
% 26.71/26.79 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].
% 26.71/26.79 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)].
% 26.71/26.79 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)].
% 26.71/26.79 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].
% 26.71/26.79 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)].
% 26.71/26.79 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)].
% 26.71/26.79 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].
% 26.71/26.79 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)].
% 26.71/26.79 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)].
% 26.71/26.79 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].
% 26.71/26.79 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)].
% 26.71/26.79 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)].
% 26.71/26.79 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].
% 26.71/26.79 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)].
% 26.71/26.79 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)].
% 26.71/26.79 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].
% 26.71/26.79 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)].
% 26.71/26.79 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)].
% 26.71/26.80 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].
% 26.71/26.80 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)].
% 26.71/26.80 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)].
% 26.71/26.80 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].
% 26.71/26.80 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)].
% 26.71/26.80 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)].
% 26.71/26.80 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].
% 26.71/26.80 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)].
% 26.71/26.80 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)].
% 26.71/26.80 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].
% 26.71/26.80 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)].
% 26.71/26.80 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)].
% 26.71/26.80 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].
% 26.78/26.81 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)].
% 26.78/26.81 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)].
% 26.78/26.81 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].
% 26.78/26.81 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)].
% 26.78/26.81 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)].
% 26.78/26.81 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].
% 26.78/26.81 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)].
% 26.78/26.81 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)].
% 26.78/26.81 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].
% 26.78/26.81 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)].
% 26.78/26.81 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)].
% 26.78/26.81 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].
% 26.78/26.81 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)].
% 26.78/26.81 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)].
% 26.78/26.82 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].
% 26.78/26.82 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)].
% 26.78/26.82 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)].
% 26.78/26.82 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].
% 26.78/26.82 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)].
% 26.78/26.82 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)].
% 26.78/26.82 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].
% 26.78/26.82 Derived: c_0 != c_IntDef_Oof__int(A,tc_IntDef_Oint) | c_0 = A. [resolve(3901,a,3876,a)].
% 26.78/26.82 Derived: c_0 != c_IntDef_Oof__int(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3901,a,3877,b)].
% 26.78/26.82 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].
% 26.78/26.82 Derived: c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint). [resolve(3902,a,3876,a)].
% 26.78/26.82 Derived: c_0 = c_IntDef_Oof__int(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3902,a,3877,b)].
% 26.78/26.82 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].
% 26.78/26.82 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)].
% 26.78/26.82 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)].
% 26.78/26.82 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].
% 26.78/26.82 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)].
% 26.78/26.82 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)].
% 26.78/26.82 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].
% 26.78/26.83 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)].
% 26.78/26.83 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)].
% 26.78/26.83 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].
% 26.78/26.83 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)].
% 26.78/26.83 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)].
% 26.78/26.83 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].
% 26.78/26.83 Derived: c_IntDef_Oof__int(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3907,a,3876,a)].
% 26.78/26.83 Derived: c_IntDef_Oof__int(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3907,a,3877,b)].
% 26.78/26.83 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].
% 26.78/26.83 Derived: c_IntDef_Oof__int(c_0,tc_IntDef_Oint) = c_0. [resolve(3908,a,3876,a)].
% 26.78/26.83 Derived: c_IntDef_Oof__int(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3908,a,3877,b)].
% 26.78/26.83 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].
% 26.78/26.83 Derived: c_IntDef_Oof__int(A,tc_IntDef_Oint) != c_IntDef_Oof__int(B,tc_IntDef_Oint) | A = B. [resolve(3909,a,3876,a)].
% 26.78/26.83 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)].
% 26.78/26.83 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].
% 26.78/26.83 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)].
% 26.78/26.83 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)].
% 26.78/26.83 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].
% 26.78/26.83 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)].
% 26.78/26.83 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)].
% 26.78/26.83 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].
% 26.78/26.83 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)].
% 26.78/26.83 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)].
% 26.78/26.83 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].
% 26.78/26.83 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)].
% 26.78/26.83 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)].
% 26.78/26.85 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].
% 26.78/26.85 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)].
% 26.78/26.85 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)].
% 26.78/26.85 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].
% 26.78/26.85 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)].
% 26.78/26.85 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)].
% 26.78/26.85 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].
% 26.78/26.85 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)].
% 26.78/26.85 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)].
% 26.78/26.85 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].
% 26.78/26.85 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)].
% 26.78/26.85 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)].
% 26.78/26.85 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].
% 26.78/26.85 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)].
% 26.78/26.85 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)].
% 26.78/26.85 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].
% 26.78/26.85 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)].
% 26.78/26.85 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)].
% 26.78/26.85 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].
% 26.78/26.85 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)].
% 26.78/26.85 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)].
% 26.78/26.86 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].
% 26.78/26.86 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)].
% 26.78/26.86 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)].
% 26.78/26.86 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].
% 26.78/26.86 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)].
% 26.78/26.86 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)].
% 26.78/26.86 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].
% 26.78/26.86 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)].
% 26.78/26.86 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)].
% 26.78/26.86 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].
% 26.78/26.86 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)].
% 26.78/26.86 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)].
% 26.78/26.86 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].
% 26.78/26.86 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)].
% 26.78/26.86 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)].
% 26.78/26.87 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].
% 26.78/26.87 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)].
% 26.78/26.87 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)].
% 26.78/26.87 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].
% 26.78/26.87 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)].
% 26.78/26.87 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)].
% 26.78/26.87 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].
% 26.78/26.87 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)].
% 26.78/26.87 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)].
% 26.78/26.87 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].
% 26.78/26.87 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)].
% 26.78/26.87 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)].
% 26.78/26.87 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].
% 26.78/26.87 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)].
% 26.78/26.87 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)].
% 26.78/26.87 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].
% 26.78/26.87 Derived: -c_IntDef_Oneg(c_0,tc_IntDef_Oint). [resolve(3931,a,3876,a)].
% 26.78/26.88 Derived: -c_IntDef_Oneg(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3931,a,3877,b)].
% 26.78/26.88 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].
% 26.78/26.88 Derived: -c_IntDef_Oneg(c_1,tc_IntDef_Oint). [resolve(3932,a,3876,a)].
% 26.78/26.88 Derived: -c_IntDef_Oneg(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3932,a,3877,b)].
% 26.78/26.88 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].
% 26.78/26.88 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)].
% 26.78/26.88 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)].
% 26.78/26.88 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].
% 26.86/26.88 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)].
% 26.86/26.88 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)].
% 26.86/26.88 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].
% 26.86/26.88 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)].
% 26.86/26.88 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)].
% 26.86/26.88 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].
% 26.86/26.88 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)].
% 26.86/26.88 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)].
% 26.86/26.88 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].
% 26.86/26.88 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)].
% 26.86/26.88 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)].
% 26.86/26.88 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].
% 26.86/26.89 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)].
% 26.86/26.89 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)].
% 26.86/26.89 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].
% 26.86/26.89 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)].
% 26.86/26.89 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)].
% 26.86/26.89 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].
% 26.86/26.89 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)].
% 26.86/26.89 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)].
% 26.86/26.89 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].
% 26.86/26.89 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)].
% 26.86/26.89 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)].
% 26.86/26.89 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].
% 26.86/26.89 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)].
% 26.86/26.89 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)].
% 26.87/26.89 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].
% 26.87/26.89 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)].
% 26.87/26.89 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)].
% 26.87/26.89 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].
% 26.87/26.89 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)].
% 26.87/26.89 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)].
% 26.87/26.89 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].
% 26.87/26.89 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)].
% 26.87/26.89 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)].
% 26.87/26.89 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].
% 26.87/26.89 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)].
% 26.87/26.89 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)].
% 26.87/26.89 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].
% 26.87/26.89 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)].
% 26.87/26.89 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)].
% 26.87/26.89 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].
% 26.87/26.90 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)].
% 26.87/26.90 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)].
% 26.87/26.90 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].
% 26.87/26.90 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)].
% 26.87/26.90 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)].
% 26.87/26.90 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].
% 26.87/26.90 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)].
% 26.87/26.90 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)].
% 26.87/26.90 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].
% 26.87/26.90 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)].
% 26.87/26.90 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)].
% 26.87/26.90 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].
% 26.87/26.90 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)].
% 26.87/26.90 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)].
% 26.87/26.90 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].
% 26.89/26.91 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)].
% 26.89/26.91 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)].
% 26.89/26.91 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].
% 26.89/26.91 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)].
% 26.89/26.91 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)].
% 26.89/26.91 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].
% 26.89/26.91 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)].
% 26.89/26.91 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)].
% 26.89/26.91 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].
% 26.89/26.91 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)].
% 26.89/26.91 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)].
% 26.89/26.91 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].
% 26.89/26.91 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)].
% 26.89/26.91 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)].
% 26.89/26.91 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].
% 26.89/26.91 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)].
% 26.89/26.91 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)].
% 26.89/26.91 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].
% 26.89/26.91 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)].
% 26.89/26.91 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)].
% 26.89/26.91 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].
% 26.90/26.93 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)].
% 26.90/26.93 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)].
% 26.90/26.93 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].
% 26.90/26.93 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)].
% 26.90/26.93 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)].
% 26.90/26.93 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].
% 26.90/26.93 Derived: c_HOL_Oabs(c_1,tc_IntDef_Oint) = c_1. [resolve(3962,a,3876,a)].
% 26.90/26.93 Derived: c_HOL_Oabs(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(3962,a,3877,b)].
% 26.90/26.93 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].
% 26.90/26.93 Derived: A != c_times(A,B,tc_IntDef_Oint) | A = c_0 | B = c_1. [resolve(3963,a,3876,a)].
% 26.90/26.93 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)].
% 26.90/26.93 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].
% 26.90/26.93 Derived: c_0 = c_times(c_0,A,tc_IntDef_Oint). [resolve(3964,a,3876,a)].
% 26.90/26.93 Derived: c_0 = c_times(c_0,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3964,a,3877,b)].
% 26.90/26.93 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].
% 26.90/26.93 Derived: A = c_times(A,c_1,tc_IntDef_Oint). [resolve(3965,a,3876,a)].
% 26.90/26.93 Derived: A = c_times(A,c_1,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3965,a,3877,b)].
% 26.90/26.93 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].
% 26.90/26.93 Derived: c_times(A,B,tc_IntDef_Oint) != A | A = c_0 | B = c_1. [resolve(3966,a,3876,a)].
% 26.90/26.93 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)].
% 26.90/26.93 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].
% 26.90/26.93 Derived: A != c_times(B,A,tc_IntDef_Oint) | A = c_0 | B = c_1. [resolve(3967,a,3876,a)].
% 26.90/26.93 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)].
% 26.90/26.93 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].
% 26.90/26.93 Derived: c_0 = c_times(A,c_0,tc_IntDef_Oint). [resolve(3968,a,3876,a)].
% 26.90/26.93 Derived: c_0 = c_times(A,c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3968,a,3877,b)].
% 26.90/26.93 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].
% 26.90/26.93 Derived: A = c_times(c_1,A,tc_IntDef_Oint). [resolve(3969,a,3876,a)].
% 26.90/26.93 Derived: A = c_times(c_1,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3969,a,3877,b)].
% 26.90/26.93 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].
% 26.90/26.93 Derived: c_times(A,B,tc_IntDef_Oint) != B | B = c_0 | A = c_1. [resolve(3970,a,3876,a)].
% 26.90/26.93 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)].
% 26.90/26.96 3971 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(22,b,2,a)].
% 26.90/26.96 3972 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(33,a,22,b)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.96 3991 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(71,a,88,b)].
% 26.90/26.96 3992 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(100,a,88,b)].
% 26.90/26.96 3993 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(102,a,88,b)].
% 26.90/26.96 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)].
% 26.90/26.96 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)].
% 26.90/26.98 3996 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(183,a,167,b)].
% 26.90/26.98 3997 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(184,a,167,b)].
% 26.90/26.98 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)].
% 26.90/26.98 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)].
% 26.90/26.98 4000 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(223,a,201,b)].
% 26.90/26.98 4001 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(224,a,201,b)].
% 26.90/26.98 4002 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(226,b,201,b)].
% 26.90/26.98 4003 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(227,b,201,b)].
% 26.90/26.98 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)].
% 26.90/26.98 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)].
% 26.90/26.98 4006 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(346,b,334,b)].
% 26.90/26.98 4007 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(380,a,364,b)].
% 26.90/26.98 4008 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(381,a,364,b)].
% 26.90/26.98 4009 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(386,b,364,b)].
% 26.90/26.98 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)].
% 26.90/26.98 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)].
% 26.90/26.98 4012 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(391,b,364,b)].
% 26.90/26.98 4013 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(410,a,402,b)].
% 26.90/26.98 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)].
% 26.90/26.98 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)].
% 26.90/26.98 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)].
% 26.90/26.98 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)].
% 26.90/26.98 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)].
% 26.90/26.98 4019 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(421,b,402,b)].
% 26.90/26.98 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)].
% 26.90/26.98 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)].
% 26.90/26.98 4022 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(433,b,402,b)].
% 26.90/26.98 4023 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(434,b,402,b)].
% 26.90/26.98 4024 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(439,b,402,b)].
% 26.90/26.98 4025 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(440,b,402,b)].
% 27.00/27.01 4026 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(441,b,402,b)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 4029 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(444,b,402,b)].
% 27.00/27.01 4030 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(511,b,503,b)].
% 27.00/27.01 4031 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(598,a,593,b)].
% 27.00/27.01 4032 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(599,a,593,b)].
% 27.00/27.01 4033 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(633,b,622,b)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 4043 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(681,b,657,b)].
% 27.00/27.01 4044 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(682,b,657,b)].
% 27.00/27.01 4045 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(738,b,698,b)].
% 27.00/27.01 4046 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(739,b,698,b)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.01 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 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)].
% 27.00/27.02 4061 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(846,b,791,b)].
% 27.00/27.02 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4061,b,3877,b)].
% 27.00/27.02 4062 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(847,b,791,b)].
% 27.00/27.02 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4062,b,3877,b)].
% 27.00/27.02 4063 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(848,b,791,b)].
% 27.00/27.02 4064 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(850,b,791,b)].
% 27.00/27.02 4065 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(851,b,791,b)].
% 27.00/27.02 4066 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(869,a,867,b)].
% 27.00/27.02 4067 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(870,a,867,b)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 4072 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(875,a,867,b)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 4075 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(878,a,867,b)].
% 27.00/27.04 4076 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(945,a,944,b)].
% 27.00/27.04 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4076,b,3877,b)].
% 27.00/27.04 4077 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(946,a,944,b)].
% 27.00/27.04 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4077,b,3877,b)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 4082 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(951,a,944,b)].
% 27.00/27.04 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(4082,b,3877,b)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.04 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 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)].
% 27.00/27.06 4095 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1067,b,944,b)].
% 27.00/27.06 4096 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1068,b,944,b)].
% 27.00/27.08 4097 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1087,a,1082,b)].
% 27.00/27.08 4098 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1118,a,1113,b)].
% 27.00/27.08 4099 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1161,b,1143,b)].
% 27.00/27.08 4100 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1163,b,1143,b)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.00/27.08 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.10 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)].
% 27.09/27.12 4144 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1219,a,1180,b)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 4149 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1224,a,1180,b)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.12 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 4176 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1385,b,1357,b)].
% 27.09/27.16 4177 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1386,b,1357,b)].
% 27.09/27.16 4178 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1388,b,1357,b)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 4190 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1498,b,1407,b)].
% 27.09/27.16 4191 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1499,b,1407,b)].
% 27.09/27.16 4192 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1523,b,1407,b)].
% 27.09/27.16 4193 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1631,b,1588,b)].
% 27.09/27.16 4194 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1632,b,1588,b)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.16 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 4204 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1642,b,1588,b)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 4207 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1645,b,1588,b)].
% 27.09/27.18 4208 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1646,b,1588,b)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.09/27.18 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 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)].
% 27.19/27.19 4243 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1740,b,1653,b)].
% 27.19/27.19 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 4248 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1745,b,1653,b)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.19/27.20 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 4275 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1773,b,1653,b)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 4278 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1788,b,1653,b)].
% 27.22/27.22 4279 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1789,b,1653,b)].
% 27.22/27.22 4280 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1790,b,1653,b)].
% 27.22/27.22 4281 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1796,b,1653,b)].
% 27.22/27.22 4282 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1797,b,1653,b)].
% 27.22/27.22 4283 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1798,b,1653,b)].
% 27.22/27.22 4284 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1799,b,1653,b)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 4294 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1809,b,1653,b)].
% 27.22/27.22 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)].
% 27.22/27.22 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)].
% 27.22/27.22 4297 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1812,b,1653,b)].
% 27.22/27.27 4298 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1813,b,1653,b)].
% 27.22/27.27 4299 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1955,b,1876,b)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 4308 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2241,a,2231,b)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 4311 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2244,a,2231,b)].
% 27.22/27.27 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)].
% 27.22/27.27 4313 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2246,a,2231,b)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 4319 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2252,a,2231,b)].
% 27.22/27.27 4320 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2321,a,2316,b)].
% 27.22/27.27 4321 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2356,b,2316,b)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.27 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 4342 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2517,a,2515,b)].
% 27.22/27.31 4343 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2518,a,2515,b)].
% 27.22/27.31 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)].
% 27.22/27.31 4345 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2520,a,2515,b)].
% 27.22/27.31 4346 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2521,a,2515,b)].
% 27.22/27.31 4347 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2522,a,2515,b)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 4350 c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2525,a,2515,b)].
% 27.22/27.31 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)].
% 27.22/27.31 4352 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2527,a,2515,b)].
% 27.22/27.31 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)].
% 27.22/27.31 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)].
% 27.22/27.31 4355 -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2530,a,2515,b)].
% 27.22/27.31 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)].
% 27.22/27.31 4357 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2973,b,2849,b)].
% 27.22/27.31 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 Derived: c_times(A,c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4362,b,3876,a)].
% 27.22/27.32 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)].
% 27.22/27.32 4363 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2980,b,2849,b)].
% 27.22/27.32 4364 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2981,b,2849,b)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 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)].
% 27.22/27.32 4373 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2990,b,2849,b)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 4376 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2993,b,2849,b)].
% 27.32/27.33 4377 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2994,b,2849,b)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 4387 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3004,b,2849,b)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 4390 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3007,b,2849,b)].
% 27.32/27.33 4391 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3008,b,2849,b)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.33 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.34 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.35 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0. [resolve(4416,d,3876,a)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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(4417,e,3877,b)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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(4418,d,3877,b)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.36 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(4426,b,3876,a)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.37 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(4436,b,3876,a)].
% 27.32/27.37 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)].
% 27.32/27.37 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.38 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 4451 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3273,b,3047,b)].
% 27.32/27.39 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(4451,b,3876,a)].
% 27.32/27.39 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4451,b,3877,b)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 4456 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3278,b,3047,b)].
% 27.32/27.39 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(4456,b,3876,a)].
% 27.32/27.39 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4456,b,3877,b)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(4462,c,3876,a)].
% 27.32/27.39 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)].
% 27.32/27.39 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)].
% 27.32/27.39 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(4463,c,3876,a)].
% 27.32/27.39 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)].
% 27.32/27.40 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)].
% 27.32/27.40 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(4464,c,3876,a)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(4472,c,3876,a)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 4475 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3308,b,3047,b)].
% 27.32/27.40 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(4475,b,3876,a)].
% 27.32/27.40 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4475,b,3877,b)].
% 27.32/27.40 4476 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3309,b,3047,b)].
% 27.32/27.40 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(4476,b,3876,a)].
% 27.32/27.40 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4476,b,3877,b)].
% 27.32/27.40 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)].
% 27.32/27.40 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(4477,c,3876,a)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.32/27.40 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4478,c,3876,a)].
% 27.32/27.40 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)].
% 27.32/27.40 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)].
% 27.42/27.41 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4479,c,3876,a)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.41 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(4480,b,3876,a)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.41 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4481,c,3876,a)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.41 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(4482,b,3876,a)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.41 4485 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3337,b,3047,b)].
% 27.42/27.41 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(4485,b,3876,a)].
% 27.42/27.41 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4485,b,3877,b)].
% 27.42/27.41 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)].
% 27.42/27.41 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(4486,c,3876,a)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.41 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(4487,c,3876,a)].
% 27.42/27.41 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)].
% 27.42/27.41 4488 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3340,b,3047,b)].
% 27.42/27.41 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4488,b,3876,a)].
% 27.42/27.41 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4488,b,3877,b)].
% 27.42/27.41 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)].
% 27.42/27.41 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)].
% 27.42/27.42 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)].
% 27.42/27.42 4490 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3342,b,3047,b)].
% 27.42/27.42 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(4490,b,3876,a)].
% 27.42/27.42 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4490,b,3877,b)].
% 27.42/27.42 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)].
% 27.42/27.42 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(4491,c,3876,a)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(4492,c,3876,a)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 4496 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3348,b,3047,b)].
% 27.42/27.42 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4496,b,3876,a)].
% 27.42/27.42 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4496,b,3877,b)].
% 27.42/27.42 4497 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3349,b,3047,b)].
% 27.42/27.42 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(4497,b,3876,a)].
% 27.42/27.42 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4497,b,3877,b)].
% 27.42/27.42 4498 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3350,b,3047,b)].
% 27.42/27.42 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(4498,b,3876,a)].
% 27.42/27.42 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4498,b,3877,b)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4501,d,3877,b)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4504,d,3877,b)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.42 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.43 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 4519 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3376,c,3047,b)].
% 27.42/27.44 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(4519,c,3876,a)].
% 27.42/27.44 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4519,c,3877,b)].
% 27.42/27.44 4520 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3377,b,3047,b)].
% 27.42/27.44 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(4520,b,3876,a)].
% 27.42/27.44 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4520,b,3877,b)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 4522 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3379,c,3047,b)].
% 27.42/27.44 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4522,c,3876,a)].
% 27.42/27.44 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4522,c,3877,b)].
% 27.42/27.44 4523 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3380,b,3047,b)].
% 27.42/27.44 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(4523,b,3876,a)].
% 27.42/27.44 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4523,b,3877,b)].
% 27.42/27.44 4524 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3381,b,3047,b)].
% 27.42/27.44 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4524,b,3876,a)].
% 27.42/27.44 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4524,b,3877,b)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(4526,c,3876,a)].
% 27.42/27.44 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)].
% 27.42/27.44 4527 c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3384,b,3047,b)].
% 27.42/27.44 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4527,b,3876,a)].
% 27.42/27.44 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4527,b,3877,b)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 4529 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3386,b,3047,b)].
% 27.42/27.44 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4529,b,3876,a)].
% 27.42/27.44 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4529,b,3877,b)].
% 27.42/27.44 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)].
% 27.42/27.44 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(4530,c,3876,a)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 4532 -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3389,b,3047,b)].
% 27.42/27.44 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4532,b,3876,a)].
% 27.42/27.44 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4532,b,3877,b)].
% 27.42/27.44 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)].
% 27.42/27.44 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(4533,c,3876,a)].
% 27.42/27.44 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)].
% 27.42/27.44 4534 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3391,b,3047,b)].
% 27.42/27.44 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(4534,b,3876,a)].
% 27.42/27.44 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4534,b,3877,b)].
% 27.42/27.44 4535 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3392,b,3047,b)].
% 27.42/27.44 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(4535,b,3876,a)].
% 27.42/27.44 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4535,b,3877,b)].
% 27.42/27.44 4536 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3393,b,3047,b)].
% 27.42/27.44 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(4536,b,3876,a)].
% 27.42/27.44 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4536,b,3877,b)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.44 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 4545 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3402,b,3047,b)].
% 27.42/27.45 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(4545,b,3876,a)].
% 27.42/27.45 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4545,b,3877,b)].
% 27.42/27.45 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)].
% 27.42/27.45 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(4546,c,3876,a)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(4547,c,3876,a)].
% 27.42/27.45 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)].
% 27.42/27.45 4548 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3405,b,3047,b)].
% 27.42/27.45 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(4548,b,3876,a)].
% 27.42/27.45 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4548,b,3877,b)].
% 27.42/27.45 4549 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3406,b,3047,b)].
% 27.42/27.45 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(4549,b,3876,a)].
% 27.42/27.45 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4549,b,3877,b)].
% 27.42/27.45 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)].
% 27.42/27.45 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(4550,c,3876,a)].
% 27.42/27.45 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)].
% 27.42/27.45 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)].
% 27.42/27.45 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(4551,b,3876,a)].
% 27.42/27.45 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)].
% 27.42/27.46 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)].
% 27.42/27.46 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(4552,c,3876,a)].
% 27.42/27.46 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)].
% 27.42/27.46 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)].
% 27.42/27.46 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)].
% 27.42/27.46 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)].
% 27.42/27.46 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)].
% 27.42/27.46 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)].
% 27.42/27.46 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)].
% 27.42/27.46 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)].
% 27.42/27.46 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)].
% 27.42/27.46 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4555,c,3877,b)].
% 27.42/27.46 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)].
% 27.42/27.46 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(4556,c,3876,a)].
% 27.42/27.46 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(4556,c,3877,b)].
% 27.42/27.46 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)].
% 27.42/27.46 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(4557,c,3876,a)].
% 27.42/27.46 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)].
% 27.42/27.46 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)].
% 27.42/27.46 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(4558,b,3876,a)].
% 27.42/27.46 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4558,b,3877,b)].
% 27.42/27.46 4559 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3416,b,3047,b)].
% 27.42/27.46 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(4559,b,3876,a)].
% 27.42/27.46 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4559,b,3877,b)].
% 27.42/27.46 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)].
% 27.42/27.47 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4560,c,3876,a)].
% 27.42/27.47 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)].
% 27.42/27.47 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)].
% 27.42/27.47 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)].
% 27.42/27.47 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)].
% 27.42/27.47 4562 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3419,b,3047,b)].
% 27.42/27.47 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(4562,b,3876,a)].
% 27.42/27.47 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4562,b,3877,b)].
% 27.42/27.47 4563 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3420,b,3047,b)].
% 27.42/27.47 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(4563,b,3876,a)].
% 27.42/27.47 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4563,b,3877,b)].
% 27.42/27.47 4564 c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3429,a,3425,b)].
% 27.42/27.47 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(4564,c,3876,a)].
% 27.42/27.47 Derived: c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4564,c,3877,b)].
% 27.42/27.47 4565 c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3430,a,3425,b)].
% 27.42/27.47 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(4565,b,3876,a)].
% 27.42/27.47 Derived: c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4565,b,3877,b)].
% 27.42/27.47 4566 c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3431,a,3425,b)].
% 27.42/27.47 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4566,b,3876,a)].
% 27.42/27.47 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4566,b,3877,b)].
% 27.42/27.47 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)].
% 27.42/27.47 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,A,tc_nat). [resolve(4567,c,3876,a)].
% 27.42/27.47 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)].
% 27.42/27.47 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)].
% 27.42/27.47 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4568,c,3876,a)].
% 27.42/27.47 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)].
% 27.42/27.47 4569 c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3434,a,3425,b)].
% 27.42/27.47 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4569,c,3876,a)].
% 27.42/27.48 Derived: c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4569,c,3877,b)].
% 27.42/27.48 4570 c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3435,a,3425,b)].
% 27.42/27.48 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(4570,b,3876,a)].
% 27.42/27.48 Derived: c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4570,b,3877,b)].
% 27.42/27.48 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)].
% 27.42/27.48 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(4571,c,3876,a)].
% 27.42/27.48 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)].
% 27.42/27.48 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)].
% 27.42/27.48 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(4572,c,3876,a)].
% 27.42/27.48 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)].
% 27.42/27.48 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)].
% 27.42/27.48 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4573,b,3876,a)].
% 27.42/27.48 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)].
% 27.42/27.48 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)].
% 27.42/27.48 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_nat). [resolve(4574,c,3876,a)].
% 27.42/27.48 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)].
% 27.42/27.48 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)].
% 27.42/27.48 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4575,c,3876,a)].
% 27.42/27.48 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)].
% 27.42/27.48 4576 -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3441,a,3425,b)].
% 27.42/27.48 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4576,b,3876,a)].
% 27.42/27.48 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4576,b,3877,b)].
% 27.42/27.48 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)].
% 27.42/27.48 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_nat). [resolve(4577,c,3876,a)].
% 27.42/27.48 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)].
% 27.42/27.48 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)].
% 27.42/27.48 Derived: -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4578,c,3876,a)].
% 27.42/27.48 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)].
% 27.42/27.48 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 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)].
% 27.42/27.49 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(A,B,tc_nat) | -c_less(c_1,C,tc_IntDef_Oint) | c_less(c_Nat_Opower(C,A,tc_IntDef_Oint),c_Nat_Opower(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4583,e,3876,a)].
% 27.42/27.49 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)].
% 27.42/27.49 4584 -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3449,a,3425,b)].
% 27.42/27.49 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(4584,b,3876,a)].
% 27.42/27.49 Derived: -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4584,b,3877,b)].
% 27.42/27.49 4585 -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3450,a,3425,b)].
% 27.42/27.49 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(4585,b,3876,a)].
% 27.42/27.49 Derived: -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4585,b,3877,b)].
% 27.42/27.49 4586 c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3451,a,3425,b)].
% 27.42/27.49 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(4586,b,3876,a)].
% 27.42/27.49 Derived: c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4586,b,3877,b)].
% 27.42/27.49 4587 c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3452,a,3425,b)].
% 27.42/27.49 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(4587,b,3876,a)].
% 27.42/27.49 Derived: c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4587,b,3877,b)].
% 27.42/27.49 4588 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3514,b,3425,b)].
% 27.42/27.50 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(4588,b,3876,a)].
% 27.42/27.50 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4588,b,3877,b)].
% 27.42/27.50 4589 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3515,b,3425,b)].
% 27.42/27.50 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(4589,b,3876,a)].
% 27.42/27.50 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4589,b,3877,b)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(4592,b,3876,a)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 4594 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3520,b,3425,b)].
% 27.42/27.50 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(4594,b,3876,a)].
% 27.42/27.50 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(4594,b,3877,b)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 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)].
% 27.42/27.50 4597 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3523,b,3425,b)].
% 27.42/27.50 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(4597,b,3876,a)].
% 27.42/27.50 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4597,b,3877,b)].
% 31.41/31.47 4598 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3730,b,3425,b)].
% 31.41/31.47 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(4598,b,3876,a)].
% 31.41/31.47 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4598,b,3877,b)].
% 31.41/31.47 4599 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(32,b,2,a)].
% 31.41/31.47 4600 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom). [assumption].
% 31.41/31.47 4601 -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(33,a,32,b)].
% 31.41/31.47 4602 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(34,a,32,b)].
% 31.41/31.47 4603 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(35,a,32,b)].
% 31.41/31.47 4604 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(36,a,32,b)].
% 31.41/31.47 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)].
% 31.41/31.47 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)].
% 31.41/31.47 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)].
% 31.41/31.47 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)].
% 31.41/31.47 4609 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(41,a,32,b)].
% 31.41/31.47 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)].
% 31.41/31.47 4611 c_LOrder_Omeet(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1087,a,1086,b)].
% 31.41/31.47 4612 c_LOrder_Ojoin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1118,a,1117,b)].
% 31.41/31.47 4613 c_lessequals(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1161,b,1147,b)].
% 31.41/31.47 4614 -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1163,b,1147,b)].
% 31.41/31.47 4615 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1164,c,1147,b)].
% 31.41/31.47 4616 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1165,b,1147,b)].
% 31.41/31.47 4617 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1166,c,1147,b)].
% 31.41/31.47 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)].
% 31.41/31.47 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)].
% 31.41/31.47 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)].
% 31.41/31.47 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)].
% 31.41/31.47 4622 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1171,c,1147,b)].
% 31.41/31.47 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)].
% 31.41/31.47 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 4633 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1194,a,1184,b)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 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)].
% 31.41/31.48 4643 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1204,a,1184,b)].
% 31.41/31.48 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 4658 c_Orderings_Omin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1219,a,1184,b)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 4663 c_Orderings_Omax(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1224,a,1184,b)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 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)].
% 31.51/31.49 4669 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1230,a,1184,b)].
% 31.51/31.49 4670 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1231,a,1184,b)].
% 31.51/31.49 4671 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1232,a,1184,b)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 4679 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1240,a,1184,b)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 31.54/31.59 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)].
% 32.30/32.35 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)].
% 32.30/32.35 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)].
% 32.30/32.35 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)].
% 32.30/32.35 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)].
% 32.30/32.35 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)].
% 32.30/32.35 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)].
% 32.30/32.35 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)].
% 32.30/32.35 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].
% 32.30/32.35 4703 -class_Ring__and__Field_Ofield(A) | class_HOL_Oinverse(A) # label(clsrel_Ring__and__Field_Ofield_30) # label(axiom). [assumption].
% 32.30/32.35 4704 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ofield_4) # label(axiom). [assumption].
% 32.30/32.35 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].
% 32.30/32.35 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)].
% 32.30/32.35 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].
% 32.30/32.35 Derived: c_divide(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4706,a,4702,b)].
% 32.30/32.35 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].
% 32.30/32.35 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)].
% 32.30/32.35 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].
% 32.30/32.35 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)].
% 32.30/32.35 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].
% 32.30/32.35 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)].
% 32.30/32.35 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].
% 32.30/32.35 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)].
% 32.30/32.35 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].
% 32.30/32.35 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)].
% 32.30/32.35 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].
% 32.30/32.35 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)].
% 32.30/32.35 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].
% 32.39/32.38 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)].
% 32.39/32.38 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].
% 32.39/32.38 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)].
% 32.39/32.38 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].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 4727 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(183,a,162,b)].
% 32.39/32.38 4728 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(184,a,162,b)].
% 32.39/32.38 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)].
% 32.39/32.38 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)].
% 32.39/32.38 4731 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(226,b,196,b)].
% 32.39/32.38 4732 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(227,b,196,b)].
% 32.39/32.38 4733 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(307,a,290,b)].
% 32.39/32.38 4734 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(308,a,290,b)].
% 32.39/32.38 4735 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(380,a,359,b)].
% 32.39/32.38 4736 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(381,a,359,b)].
% 32.39/32.39 4737 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(389,c,359,b)].
% 32.39/32.39 4738 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(390,c,359,b)].
% 32.39/32.39 4739 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(410,a,398,b)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 4747 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(433,b,398,b)].
% 32.39/32.39 4748 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(434,b,398,b)].
% 32.39/32.39 4749 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(439,b,398,b)].
% 32.39/32.39 4750 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(440,b,398,b)].
% 32.39/32.39 4751 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(442,c,398,b)].
% 32.39/32.39 4752 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(443,c,398,b)].
% 32.39/32.39 4753 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(598,a,590,b)].
% 32.39/32.39 4754 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(599,a,590,b)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 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)].
% 32.39/32.39 4764 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(681,b,654,b)].
% 32.39/32.41 4765 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(682,b,654,b)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 4780 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(846,b,788,b)].
% 32.39/32.41 4781 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(847,b,788,b)].
% 32.39/32.41 4782 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(850,b,788,b)].
% 32.39/32.41 4783 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(851,b,788,b)].
% 32.39/32.41 4784 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(869,a,864,b)].
% 32.39/32.41 4785 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(870,a,864,b)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.39/32.41 4788 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(873,a,864,b)].
% 32.39/32.41 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)].
% 32.39/32.41 4790 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(875,a,864,b)].
% 32.39/32.41 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)].
% 32.39/32.41 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)].
% 32.60/32.59 4793 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(878,a,864,b)].
% 32.60/32.59 4794 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(945,a,941,b)].
% 32.60/32.59 4795 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(946,a,941,b)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 4800 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(951,a,941,b)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 4813 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3791,b,3753,b)].
% 32.60/32.59 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)].
% 32.60/32.59 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)].
% 32.60/32.59 4816 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3800,b,3753,b)].
% 32.60/32.59 4817 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3801,b,3753,b)].
% 32.60/32.60 4818 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3805,c,3753,b)].
% 32.60/32.60 4819 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3806,c,3753,b)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 4834 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3839,b,3753,b)].
% 32.60/32.60 4835 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3840,b,3753,b)].
% 32.60/32.60 4836 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3842,b,3753,b)].
% 32.60/32.60 4837 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3843,b,3753,b)].
% 32.60/32.60 4838 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3844,b,3753,b)].
% 32.60/32.60 4839 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3845,b,3753,b)].
% 32.60/32.60 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)].
% 32.60/32.60 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)].
% 32.60/32.60 4842 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3848,b,3753,b)].
% 32.60/32.60 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)].
% 32.60/32.60 4844 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3850,b,3753,b)].
% 32.60/32.60 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)].
% 34.02/34.02 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)].
% 34.02/34.02 4847 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3853,b,3753,b)].
% 34.02/34.02 4848 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3854,b,3753,b)].
% 34.02/34.02 4849 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3855,b,3753,b)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 4854 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3860,b,3753,b)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02 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)].
% 34.02/34.02
% 34.02/34.02 ============================== end predicate elimination =============
% 34.02/34.02
% 34.02/34.02 Auto_denials: (non-Horn, no changes).
% 34.02/34.02
% 34.02/34.02 Term ordering decisions:
% 34.02/34.02 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. 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_Numeral_OMin=1. c_Message_Oagent_OSpy=1. tc_Event_Oevent=1. tc_List_Onibble=1. c_Relation_OId=1. tc_Message_Oagent=1. c_Event_Obad=1. c_IntDef_Ointrel=1. c_Message_OsymKeys=1. c_Datatype_Ooption_ONone=1. c_Yahalom_Oyahalom=1. v_evsf=1. c_IntDef_OInteg=1. c_Wellfounded__Relations_Oless__than=1. v_K=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. tc_Extraction_Osumbool=1. tc_Numeral_Obit=1. tc_Product__Type_Ounit=1. tc_Public_Okeymode=1. v_X=1. c_Message_Oagent_OServer=1. tc_List_Ochar=1. tc_bool=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_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_SetInterval_OgreaterThan=1. c_IntDef_Oof__int=1. c_Numeral_Obin__add=1. c_List_Oset=1. c_Message_Omsg_OMPair=1. c_List_Orev=1. c_Event_Oknows=1. c_Message_Omsg_OCrypt=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_Finite__Set_Ocard=1. c_Inter=1. c_List_Oremdups=1. c_List_Oupt=1. c_List_Olast=1. c_List_Oconcat=1. c_List_Olistrel=1. c_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_Event_Oevent_OGets=1. c_Event_Oevent_ONotes=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_Numeral_Obin__minus=1. c_IntDef_Oint=1. c_Message_Omsg_OKey=1. c_Message_OkeysFor=1. c_IntDef_Onat=1. c_Message_Omsg_OHash=1. c_Message_OinvKey=1. c_GCD_Ogcd=1. c_Event_Oused=1. c_IntDiv_OnegDivAlg=1. c_IntDiv_OposDivAlg=1. c_Public_OshrK=1. c_Message_Omsg_ONonce=1. c_Message_Omsg_OAgent=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. c_IntDef_ORep__Integ=1. c_plus=1. c_times=1. c_insert=1. c_minus=1. c_SetInterval_OatLeastLessThan=1. c_Nat_Opower=1. c_List_Olist_OCons=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_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_Event_Oevent_OSays=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__Universe_ONumb=1. c_Equiv__Relations_Oquotient=1. c_List_Oitrev=1. cCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------