TSTP Solution File: SWV339-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV339-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:12:04 EDT 2022
% Result : Unsatisfiable 138.88s 138.88s
% Output : Refutation 138.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV339-1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 15 11:29:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.68/1.97 ============================== Prover9 ===============================
% 1.68/1.97 Prover9 (32) version 2009-11A, November 2009.
% 1.68/1.97 Process 8904 was started by sandbox2 on n004.cluster.edu,
% 1.68/1.97 Wed Jun 15 11:29:55 2022
% 1.68/1.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8750_n004.cluster.edu".
% 1.68/1.97 ============================== end of head ===========================
% 1.68/1.97
% 1.68/1.97 ============================== INPUT =================================
% 1.68/1.97
% 1.68/1.97 % Reading from file /tmp/Prover9_8750_n004.cluster.edu
% 1.68/1.97
% 1.68/1.97 set(prolog_style_variables).
% 1.68/1.97 set(auto2).
% 1.68/1.97 % set(auto2) -> set(auto).
% 1.68/1.97 % set(auto) -> set(auto_inference).
% 1.68/1.97 % set(auto) -> set(auto_setup).
% 1.68/1.97 % set(auto_setup) -> set(predicate_elim).
% 1.68/1.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.68/1.97 % set(auto) -> set(auto_limits).
% 1.68/1.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.68/1.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.68/1.97 % set(auto) -> set(auto_denials).
% 1.68/1.97 % set(auto) -> set(auto_process).
% 1.68/1.97 % set(auto2) -> assign(new_constants, 1).
% 1.68/1.97 % set(auto2) -> assign(fold_denial_max, 3).
% 1.68/1.97 % set(auto2) -> assign(max_weight, "200.000").
% 1.68/1.97 % set(auto2) -> assign(max_hours, 1).
% 1.68/1.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.68/1.97 % set(auto2) -> assign(max_seconds, 0).
% 1.68/1.97 % set(auto2) -> assign(max_minutes, 5).
% 1.68/1.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.68/1.97 % set(auto2) -> set(sort_initial_sos).
% 1.68/1.97 % set(auto2) -> assign(sos_limit, -1).
% 1.68/1.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.68/1.97 % set(auto2) -> assign(max_megs, 400).
% 1.68/1.97 % set(auto2) -> assign(stats, some).
% 1.68/1.97 % set(auto2) -> clear(echo_input).
% 1.68/1.97 % set(auto2) -> set(quiet).
% 1.68/1.97 % set(auto2) -> clear(print_initial_clauses).
% 1.68/1.97 % set(auto2) -> clear(print_given).
% 1.68/1.97 assign(lrs_ticks,-1).
% 1.68/1.97 assign(sos_limit,10000).
% 1.68/1.97 assign(order,kbo).
% 1.68/1.97 set(lex_order_vars).
% 1.68/1.97 clear(print_given).
% 1.68/1.97
% 1.68/1.97 % formulas(sos). % not echoed (2950 formulas)
% 1.68/1.97
% 1.68/1.97 ============================== end of input ==========================
% 1.68/1.97
% 1.68/1.97 % From the command line: assign(max_seconds, 300).
% 1.68/1.97
% 1.68/1.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.68/1.97
% 1.68/1.97 % Formulas that are not ordinary clauses:
% 1.68/1.97
% 1.68/1.97 ============================== end of process non-clausal formulas ===
% 1.68/1.97
% 1.68/1.97 ============================== PROCESS INITIAL CLAUSES ===============
% 1.68/1.97
% 1.68/1.97 ============================== PREDICATE ELIMINATION =================
% 1.68/1.97 1 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom). [assumption].
% 1.68/1.97 2 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom). [assumption].
% 1.68/1.97 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1,a,2,a)].
% 1.68/1.97 3 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom). [assumption].
% 1.68/1.97 Derived: c_lessequals(A,A,tc_nat). [resolve(3,a,2,a)].
% 1.68/1.97 4 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom). [assumption].
% 1.68/1.97 Derived: c_lessequals(A,A,tc_set(B)). [resolve(4,a,2,a)].
% 1.68/1.97 5 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 1.68/1.97 Derived: -class_LOrder_Ojoin__semilorder(A) | c_lessequals(B,B,A). [resolve(5,b,2,a)].
% 1.68/1.97 6 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom). [assumption].
% 1.68/1.97 Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(6,b,2,a)].
% 1.68/1.97 7 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom). [assumption].
% 1.68/1.97 Derived: -class_LOrder_Omeet__semilorder(A) | c_lessequals(B,B,A). [resolve(7,b,2,a)].
% 1.68/1.97 8 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom). [assumption].
% 1.68/1.97 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(B,B,A). [resolve(8,b,2,a)].
% 1.68/1.97 9 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom). [assumption].
% 1.68/1.97 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(B,B,A). [resolve(9,b,2,a)].
% 1.68/1.98 10 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom). [assumption].
% 1.68/1.98 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(10,b,2,a)].
% 1.68/1.98 11 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom). [assumption].
% 1.68/1.98 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(11,b,2,a)].
% 1.68/1.98 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].
% 1.68/1.98 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(12,b,2,a)].
% 1.68/1.98 13 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom). [assumption].
% 1.68/1.98 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A). [resolve(13,b,2,a)].
% 1.68/1.98 14 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom). [assumption].
% 1.68/1.98 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(14,b,2,a)].
% 1.68/1.98 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].
% 1.68/1.98 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,B,A). [resolve(15,b,2,a)].
% 1.68/1.98 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].
% 1.68/1.98 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(16,b,2,a)].
% 1.68/1.98 17 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom). [assumption].
% 1.68/1.98 Derived: -class_Orderings_Olinorder(A) | c_lessequals(B,B,A). [resolve(17,b,2,a)].
% 1.68/1.98 18 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom). [assumption].
% 1.68/1.98 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(18,a,1,a)].
% 1.68/1.98 Derived: class_Orderings_Oord(tc_nat). [resolve(18,a,3,a)].
% 1.68/1.98 Derived: class_Orderings_Oord(tc_set(A)). [resolve(18,a,4,a)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_LOrder_Ojoin__semilorder(A). [resolve(18,a,5,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(18,a,6,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_LOrder_Omeet__semilorder(A). [resolve(18,a,7,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(18,a,8,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(18,a,9,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(18,a,10,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(18,a,11,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(18,a,12,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(18,a,13,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(18,a,14,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(18,a,15,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(18,a,16,b)].
% 1.68/1.98 Derived: class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(18,a,17,b)].
% 1.68/1.98 19 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(19,b,2,a)].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(20,b,2,a)].
% 1.76/2.04 21 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A). [resolve(21,b,2,a)].
% 1.76/2.04 22 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(22,b,2,a)].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,B,A). [resolve(23,b,2,a)].
% 1.76/2.04 24 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,B,A). [resolve(24,b,2,a)].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(25,b,2,a)].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(26,b,2,a)].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(27,b,2,a)].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A). [resolve(28,b,2,a)].
% 1.76/2.04 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].
% 1.76/2.04 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(29,b,2,a)].
% 1.76/2.04 30 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(30,b,2,a)].
% 1.76/2.04 31 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(31,b,2,a)].
% 1.76/2.04 32 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom). [assumption].
% 1.76/2.04 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(32,b,2,a)].
% 1.76/2.04 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(32,b,18,a)].
% 1.76/2.04 33 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl_0) # label(axiom). [assumption].
% 1.76/2.04 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(33,a,1,a)].
% 1.76/2.04 Derived: -c_less(A,A,tc_nat). [resolve(33,a,3,a)].
% 1.76/2.04 Derived: -c_less(A,A,tc_set(B)). [resolve(33,a,4,a)].
% 1.76/2.04 Derived: -c_less(A,A,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(33,a,5,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(33,a,6,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_LOrder_Omeet__semilorder(B). [resolve(33,a,7,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(33,a,8,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(33,a,9,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(33,a,10,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(33,a,11,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(33,a,12,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(33,a,13,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(33,a,14,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(33,a,15,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(33,a,16,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(33,a,17,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(33,a,19,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(33,a,20,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(33,a,21,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(33,a,22,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(33,a,23,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(33,a,24,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(33,a,25,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(33,a,26,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(33,a,27,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(33,a,28,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(33,a,29,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(33,a,30,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(33,a,31,b)].
% 1.76/2.06 Derived: -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(33,a,32,b)].
% 1.76/2.06 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].
% 1.76/2.06 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(34,a,1,a)].
% 1.76/2.06 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(34,a,3,a)].
% 1.76/2.06 Derived: -c_less(A,B,tc_set(C)) | c_SetInterval_OatLeastAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(34,a,4,a)].
% 1.76/2.06 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(34,a,5,b)].
% 1.76/2.06 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(34,a,6,b)].
% 1.76/2.06 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(34,a,7,b)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(34,a,17,b)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 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)].
% 1.76/2.06 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(34,a,32,b)].
% 1.76/2.06 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].
% 1.76/2.06 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(35,a,1,a)].
% 1.76/2.06 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(35,a,3,a)].
% 1.76/2.06 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_set(B)) = c_insert(A,c_emptyset,tc_set(B)). [resolve(35,a,4,a)].
% 1.76/2.06 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(35,a,5,b)].
% 1.76/2.06 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(35,a,6,b)].
% 1.76/2.06 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Omeet__semilorder(B). [resolve(35,a,7,b)].
% 1.76/2.06 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(35,a,8,b)].
% 1.76/2.06 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(35,a,17,b)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(35,a,32,b)].
% 1.76/2.07 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].
% 1.76/2.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(36,a,1,a)].
% 1.76/2.07 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(36,a,3,a)].
% 1.76/2.07 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OatLeastLessThan(B,A,tc_set(C)) = c_emptyset. [resolve(36,a,4,a)].
% 1.76/2.07 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(36,a,5,b)].
% 1.76/2.07 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(36,a,6,b)].
% 1.76/2.07 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(36,a,7,b)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(36,a,17,b)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(36,a,32,b)].
% 1.76/2.07 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].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.76/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.07 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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].
% 1.84/2.08 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(39,a,1,a)].
% 1.84/2.08 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(39,a,3,a)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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].
% 1.84/2.08 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(40,a,1,a)].
% 1.84/2.08 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(40,a,3,a)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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].
% 1.84/2.08 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(41,a,1,a)].
% 1.84/2.08 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(41,a,3,a)].
% 1.84/2.08 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OgreaterThanAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(41,a,4,a)].
% 1.84/2.08 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(41,a,5,b)].
% 1.84/2.08 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(41,a,6,b)].
% 1.84/2.08 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(41,a,7,b)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.08 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(41,a,17,b)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(41,a,32,b)].
% 1.84/2.09 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].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 1.84/2.09 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)].
% 2.17/2.43 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)].
% 2.17/2.43 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)].
% 2.17/2.43 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)].
% 2.17/2.43 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].
% 2.17/2.43 44 class_HOL_Oone(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_1) # label(axiom). [assumption].
% 2.17/2.43 45 class_HOL_Oone(tc_nat) # label(clsarity_nat_0) # label(axiom). [assumption].
% 2.17/2.43 46 -class_Numeral_Onumber__ring(A) | class_HOL_Oone(A) # label(clsrel_Numeral_Onumber__ring_20) # label(axiom). [assumption].
% 2.17/2.43 47 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_0) # label(axiom). [assumption].
% 2.17/2.43 48 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Omonoid__mult_0) # label(axiom). [assumption].
% 2.17/2.43 49 -class_Power_Orecpower(A) | class_HOL_Oone(A) # label(clsrel_Power_Orecpower_2) # label(axiom). [assumption].
% 2.17/2.43 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].
% 2.17/2.43 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].
% 2.17/2.43 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].
% 2.17/2.43 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].
% 2.17/2.43 54 -class_Ring__and__Field_Ofield(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ofield_13) # label(axiom). [assumption].
% 2.17/2.43 55 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oidom_13) # label(axiom). [assumption].
% 2.17/2.43 56 -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__field_16) # label(axiom). [assumption].
% 2.17/2.43 57 -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__idom_13) # label(axiom). [assumption].
% 2.17/2.43 58 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__semidom_7) # label(axiom). [assumption].
% 2.17/2.43 59 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oring__1_18) # label(axiom). [assumption].
% 2.17/2.43 60 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1_2) # label(axiom). [assumption].
% 2.17/2.43 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].
% 2.17/2.43 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)].
% 2.17/2.43 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)].
% 2.17/2.43 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)].
% 2.17/2.43 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)].
% 2.17/2.43 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)].
% 2.17/2.43 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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].
% 2.17/2.44 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].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.44 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)].
% 2.17/2.45 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(63,a,53,b)].
% 2.17/2.45 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(63,a,54,b)].
% 2.17/2.45 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(63,a,55,b)].
% 2.17/2.45 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(63,a,56,b)].
% 2.17/2.45 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(63,a,57,b)].
% 2.17/2.45 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(63,a,58,b)].
% 2.17/2.45 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_Oring__1(A). [resolve(63,a,59,b)].
% 2.17/2.45 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_Osemiring__1(A). [resolve(63,a,60,b)].
% 2.17/2.45 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_Osemiring__1__cancel(A). [resolve(63,a,61,b)].
% 2.17/2.45 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].
% 2.17/2.45 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(64,a,44,a)].
% 2.17/2.45 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(64,a,45,a)].
% 2.17/2.45 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(64,a,46,b)].
% 2.17/2.45 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_OrderedGroup_Ocomm__monoid__mult(A). [resolve(64,a,47,b)].
% 2.17/2.45 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_OrderedGroup_Omonoid__mult(A). [resolve(64,a,48,b)].
% 2.17/2.45 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(64,a,49,b)].
% 2.17/2.45 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_Oaxclass__0__neq__1(A). [resolve(64,a,50,b)].
% 2.17/2.45 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(64,a,51,b)].
% 2.17/2.45 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(64,a,52,b)].
% 2.17/2.45 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(64,a,53,b)].
% 2.17/2.45 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(64,a,54,b)].
% 2.17/2.45 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(64,a,55,b)].
% 2.17/2.45 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(64,a,56,b)].
% 2.17/2.45 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(64,a,57,b)].
% 2.17/2.45 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(64,a,58,b)].
% 2.17/2.45 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_Oring__1(A). [resolve(64,a,59,b)].
% 2.17/2.45 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_Osemiring__1(A). [resolve(64,a,60,b)].
% 2.17/2.45 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_Osemiring__1__cancel(A). [resolve(64,a,61,b)].
% 2.17/2.45 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].
% 2.17/2.45 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(65,a,44,a)].
% 2.17/2.45 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(65,a,45,a)].
% 2.17/2.45 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(65,a,46,b)].
% 2.17/2.45 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_OrderedGroup_Ocomm__monoid__mult(A). [resolve(65,a,47,b)].
% 2.17/2.45 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_OrderedGroup_Omonoid__mult(A). [resolve(65,a,48,b)].
% 2.17/2.45 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(65,a,49,b)].
% 2.17/2.45 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_Oaxclass__0__neq__1(A). [resolve(65,a,50,b)].
% 2.17/2.45 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(65,a,51,b)].
% 2.17/2.45 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(65,a,52,b)].
% 2.17/2.45 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(65,a,53,b)].
% 2.17/2.45 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(65,a,54,b)].
% 2.17/2.45 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(65,a,55,b)].
% 2.17/2.45 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(65,a,56,b)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.46 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)].
% 2.17/2.47 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].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.17/2.47 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 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)].
% 2.36/2.65 71 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_0) # label(axiom). [assumption].
% 2.36/2.65 72 class_Ring__and__Field_Osemiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_10) # label(axiom). [assumption].
% 2.36/2.65 73 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat_18) # label(axiom). [assumption].
% 2.36/2.65 74 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom). [assumption].
% 2.36/2.65 75 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Power_Orecpower_10) # label(axiom). [assumption].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 83 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ofield_20) # label(axiom). [assumption].
% 2.36/2.65 84 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom). [assumption].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 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].
% 2.36/2.65 98 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring_0) # label(axiom). [assumption].
% 2.36/2.65 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].
% 2.36/2.65 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(71,a,72,a)].
% 2.36/2.65 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(71,a,73,a)].
% 2.36/2.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(71,a,74,b)].
% 2.36/2.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(71,a,75,b)].
% 2.36/2.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(71,a,76,b)].
% 2.36/2.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(71,a,77,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(71,a,78,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(71,a,79,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(71,a,80,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(71,a,81,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(71,a,82,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(71,a,83,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(71,a,84,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(71,a,85,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(71,a,86,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(71,a,87,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(71,a,88,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(71,a,89,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(71,a,90,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(71,a,91,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(71,a,92,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(71,a,93,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(71,a,94,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(71,a,95,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(71,a,96,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(71,a,97,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(71,a,98,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(71,a,99,b)].
% 2.36/2.66 100 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_1) # label(axiom). [assumption].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(100,a,72,a)].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(100,a,73,a)].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(100,a,74,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(100,a,75,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(100,a,76,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(100,a,77,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(100,a,78,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(100,a,79,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(100,a,80,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(100,a,81,b)].
% 2.36/2.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(100,a,82,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(100,a,83,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(100,a,84,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(100,a,85,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(100,a,86,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(100,a,87,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(100,a,88,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(100,a,89,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(100,a,90,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(100,a,91,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(100,a,92,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(100,a,93,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(100,a,94,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(100,a,95,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(100,a,96,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(100,a,97,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(100,a,98,b)].
% 2.36/2.67 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(100,a,99,b)].
% 2.36/2.67 101 -class_Ring__and__Field_Osemiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring_2) # label(axiom). [assumption].
% 2.36/2.67 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(101,a,72,a)].
% 2.36/2.67 Derived: class_HOL_Oplus(tc_nat). [resolve(101,a,73,a)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(101,a,74,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(101,a,75,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(101,a,76,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(101,a,77,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(101,a,78,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(101,a,79,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(101,a,80,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(101,a,81,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(101,a,82,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(101,a,83,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(101,a,84,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(101,a,85,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(101,a,86,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(101,a,87,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(101,a,88,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(101,a,89,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(101,a,90,b)].
% 2.36/2.67 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(101,a,91,b)].
% 2.36/2.69 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(101,a,92,b)].
% 2.36/2.69 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(101,a,93,b)].
% 2.36/2.69 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(101,a,94,b)].
% 2.36/2.69 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(101,a,95,b)].
% 2.36/2.69 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(101,a,96,b)].
% 2.36/2.69 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(101,a,97,b)].
% 2.36/2.69 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(101,a,98,b)].
% 2.36/2.69 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(101,a,99,b)].
% 2.36/2.69 102 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring_3) # label(axiom). [assumption].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(102,a,72,a)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(102,a,73,a)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(102,a,74,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(102,a,75,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(102,a,76,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(102,a,77,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(102,a,78,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(102,a,79,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(102,a,80,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(102,a,81,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(102,a,82,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(102,a,83,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(102,a,84,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(102,a,85,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(102,a,86,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(102,a,87,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(102,a,88,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(102,a,89,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(102,a,90,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(102,a,91,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(102,a,92,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(102,a,93,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(102,a,94,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(102,a,95,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(102,a,96,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(102,a,97,b)].
% 2.36/2.69 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(102,a,98,b)].
% 2.47/2.73 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(102,a,99,b)].
% 2.47/2.73 103 -class_Ring__and__Field_Osemiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring_4) # label(axiom). [assumption].
% 2.47/2.73 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(103,a,72,a)].
% 2.47/2.73 Derived: class_HOL_Otimes(tc_nat). [resolve(103,a,73,a)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(103,a,74,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(103,a,75,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(103,a,76,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(103,a,77,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(103,a,78,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(103,a,79,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(103,a,80,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(103,a,81,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(103,a,82,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(103,a,83,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(103,a,84,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(103,a,85,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(103,a,86,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(103,a,87,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(103,a,88,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(103,a,89,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(103,a,90,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(103,a,91,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(103,a,92,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(103,a,93,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(103,a,94,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(103,a,95,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(103,a,96,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(103,a,97,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(103,a,98,b)].
% 2.47/2.73 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(103,a,99,b)].
% 2.47/2.73 104 -class_Ring__and__Field_Osemiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0_0) # label(axiom). [assumption].
% 2.47/2.73 105 -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].
% 2.47/2.73 106 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1_4) # label(axiom). [assumption].
% 2.47/2.73 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(106,b,101,a)].
% 2.47/2.73 107 -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].
% 2.47/2.73 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(107,b,102,a)].
% 2.47/2.73 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(107,b,103,a)].
% 2.47/2.73 108 -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].
% 2.47/2.73 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)].
% 2.47/2.73 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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = 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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = 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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 2.47/2.74 109 -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].
% 2.47/2.74 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)].
% 2.47/2.74 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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = 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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = 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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.74 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(109,b,91,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(109,b,92,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(109,b,93,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(109,b,94,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(109,b,95,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(109,b,96,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(109,b,97,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring(A). [resolve(109,b,98,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(109,b,99,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__0(A). [resolve(109,b,104,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(109,b,105,b)].
% 2.47/2.75 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(109,b,106,b)].
% 2.67/2.97 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 2.67/2.97 110 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_0) # label(axiom). [assumption].
% 2.67/2.97 111 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom). [assumption].
% 2.67/2.97 112 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom). [assumption].
% 2.67/2.97 113 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom). [assumption].
% 2.67/2.97 114 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom). [assumption].
% 2.67/2.97 115 -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].
% 2.67/2.97 116 -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].
% 2.67/2.97 117 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom). [assumption].
% 2.67/2.97 118 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom). [assumption].
% 2.67/2.97 119 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_3) # label(axiom). [assumption].
% 2.67/2.97 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(119,a,111,a)].
% 2.67/2.97 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(119,a,112,a)].
% 2.67/2.97 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(119,a,113,b)].
% 2.67/2.97 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Power_Orecpower(A). [resolve(119,a,114,b)].
% 2.67/2.97 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(119,a,115,b)].
% 2.67/2.97 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(119,a,116,b)].
% 2.67/2.97 120 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom). [assumption].
% 2.67/2.97 121 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom). [assumption].
% 2.67/2.97 122 -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].
% 2.67/2.97 123 -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].
% 2.67/2.97 124 -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].
% 2.67/2.97 125 -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].
% 2.67/2.97 126 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom). [assumption].
% 2.67/2.97 127 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom). [assumption].
% 2.67/2.97 128 -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].
% 2.86/3.12 129 -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].
% 2.86/3.12 130 -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].
% 2.86/3.12 131 -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].
% 2.86/3.12 132 -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].
% 2.86/3.12 133 -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].
% 2.86/3.12 134 -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].
% 2.86/3.12 135 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(71,a,78,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(135,b,111,a)].
% 2.86/3.12 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(135,b,112,a)].
% 2.86/3.12 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(135,b,113,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(135,b,114,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(135,b,115,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(135,b,116,b)].
% 2.86/3.12 136 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(100,a,78,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(136,b,111,a)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(136,b,112,a)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(136,b,113,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(136,b,114,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(136,b,115,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(136,b,116,b)].
% 2.86/3.12 137 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(101,a,78,b)].
% 2.86/3.12 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(137,b,111,a)].
% 2.86/3.12 Derived: class_HOL_Oplus(tc_nat). [resolve(137,b,112,a)].
% 2.86/3.12 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(137,b,113,b)].
% 2.86/3.12 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(137,b,114,b)].
% 2.86/3.12 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(137,b,115,b)].
% 2.86/3.12 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(137,b,116,b)].
% 2.86/3.12 138 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(102,a,78,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(138,b,111,a)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(138,b,112,a)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(138,b,113,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(138,b,114,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(138,b,115,b)].
% 2.86/3.12 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(138,b,116,b)].
% 2.86/3.12 139 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(103,a,78,b)].
% 2.95/3.20 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(139,b,111,a)].
% 2.95/3.20 Derived: class_HOL_Otimes(tc_nat). [resolve(139,b,112,a)].
% 2.95/3.20 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(139,b,113,b)].
% 2.95/3.20 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(139,b,114,b)].
% 2.95/3.20 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(139,b,115,b)].
% 2.95/3.20 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(139,b,116,b)].
% 2.95/3.20 140 -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)].
% 2.95/3.20 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(140,c,111,a)].
% 2.95/3.20 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(140,c,112,a)].
% 2.95/3.20 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(140,c,113,b)].
% 2.95/3.20 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(140,c,114,b)].
% 2.95/3.20 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(140,c,115,b)].
% 2.95/3.20 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(140,c,116,b)].
% 2.95/3.20 141 -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)].
% 2.95/3.20 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(141,c,111,a)].
% 2.95/3.20 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(141,c,112,a)].
% 2.95/3.20 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_Numeral_Onumber__ring(A). [resolve(141,c,113,b)].
% 2.95/3.20 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_Power_Orecpower(A). [resolve(141,c,114,b)].
% 2.95/3.20 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_Ocomm__ring(A). [resolve(141,c,115,b)].
% 2.95/3.20 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_Ocomm__ring__1(A). [resolve(141,c,116,b)].
% 2.95/3.20 142 -class_OrderedGroup_Ocomm__monoid__add(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_0) # label(axiom). [assumption].
% 2.97/3.21 143 class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_12) # label(axiom). [assumption].
% 2.97/3.21 144 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat_20) # label(axiom). [assumption].
% 2.97/3.21 145 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom). [assumption].
% 2.97/3.21 146 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Oab__group__add_1) # label(axiom). [assumption].
% 2.97/3.21 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(142,a,143,a)].
% 2.97/3.21 Derived: class_HOL_Ozero(tc_nat). [resolve(142,a,144,a)].
% 2.97/3.21 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(142,a,145,b)].
% 2.97/3.21 Derived: class_HOL_Ozero(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(142,a,146,b)].
% 2.97/3.21 147 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom). [assumption].
% 2.97/3.21 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(147,a,146,b)].
% 2.97/3.21 148 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_2) # label(axiom). [assumption].
% 2.97/3.21 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(148,a,146,b)].
% 2.97/3.21 149 -class_OrderedGroup_Ocomm__monoid__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_3) # label(axiom). [assumption].
% 2.97/3.21 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(149,a,146,b)].
% 2.97/3.21 150 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom). [assumption].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(150,b,147,a)].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(150,b,148,a)].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A). [resolve(150,b,149,a)].
% 2.97/3.21 151 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_4) # label(axiom). [assumption].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(151,b,147,a)].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(151,b,148,a)].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(151,b,149,a)].
% 2.97/3.21 152 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_3) # label(axiom). [assumption].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(152,b,147,a)].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(152,b,148,a)].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A). [resolve(152,b,149,a)].
% 2.97/3.21 153 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_3) # label(axiom). [assumption].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(153,b,147,a)].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(153,b,148,a)].
% 2.97/3.21 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A). [resolve(153,b,149,a)].
% 2.97/3.21 154 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_2) # label(axiom). [assumption].
% 2.97/3.22 155 -class_Power_Orecpower(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Power_Orecpower_12) # label(axiom). [assumption].
% 2.97/3.22 Derived: -class_Power_Orecpower(A) | class_HOL_Ozero(A). [resolve(155,b,142,a)].
% 2.97/3.22 156 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_7) # label(axiom). [assumption].
% 2.97/3.22 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(156,b,142,a)].
% 2.97/3.22 157 -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].
% 2.97/3.22 158 -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].
% 2.97/3.22 159 -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].
% 2.97/3.22 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(159,b,142,a)].
% 2.97/3.22 160 -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].
% 2.97/3.22 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A). [resolve(160,b,142,a)].
% 2.97/3.22 161 -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].
% 2.97/3.22 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Ozero(A). [resolve(161,b,142,a)].
% 2.97/3.22 162 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ofield_23) # label(axiom). [assumption].
% 2.97/3.22 163 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom). [assumption].
% 2.97/3.22 164 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_17) # label(axiom). [assumption].
% 2.97/3.22 165 -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].
% 2.97/3.22 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Ozero(A). [resolve(165,b,142,a)].
% 2.97/3.22 166 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__field_25) # label(axiom). [assumption].
% 2.97/3.22 167 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_23) # label(axiom). [assumption].
% 2.97/3.22 168 -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].
% 2.97/3.22 169 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_17) # label(axiom). [assumption].
% 2.97/3.22 170 -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].
% 2.97/3.22 171 -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].
% 2.97/3.22 172 -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].
% 2.97/3.22 173 -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].
% 2.97/3.22 174 -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].
% 2.97/3.28 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Ozero(A). [resolve(174,b,142,a)].
% 2.97/3.28 175 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_10) # label(axiom). [assumption].
% 2.97/3.28 176 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_4) # label(axiom). [assumption].
% 2.97/3.28 177 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom). [assumption].
% 2.97/3.28 178 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring__1_10) # label(axiom). [assumption].
% 2.97/3.28 179 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_6) # label(axiom). [assumption].
% 2.97/3.28 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(179,b,147,a)].
% 2.97/3.28 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(179,b,148,a)].
% 2.97/3.28 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A). [resolve(179,b,149,a)].
% 2.97/3.28 180 -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].
% 2.97/3.28 181 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_7) # label(axiom). [assumption].
% 2.97/3.28 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(181,b,142,a)].
% 2.97/3.28 182 -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].
% 2.97/3.28 183 -class_OrderedGroup_Ocomm__monoid__add(A) | c_plus(B,c_0,A) = B # label(cls_OrderedGroup_Oadd__0__right_0) # label(axiom). [assumption].
% 2.97/3.28 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(183,a,143,a)].
% 2.97/3.28 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(183,a,144,a)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(183,a,145,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Oab__group__add(B). [resolve(183,a,146,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(183,a,150,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(183,a,151,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(183,a,152,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(183,a,153,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(183,a,154,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(183,a,155,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(183,a,156,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(183,a,157,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(183,a,158,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(183,a,159,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(183,a,160,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(183,a,161,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(183,a,162,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(183,a,163,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(183,a,164,b)].
% 2.97/3.28 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(183,a,165,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(183,a,166,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(183,a,167,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(183,a,168,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(183,a,169,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(183,a,170,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(183,a,171,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(183,a,172,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(183,a,173,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(183,a,174,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(183,a,175,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(183,a,176,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(183,a,177,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(183,a,178,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(183,a,179,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(183,a,180,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(183,a,181,b)].
% 2.97/3.29 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(183,a,182,b)].
% 2.97/3.29 184 -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].
% 2.97/3.29 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(184,a,143,a)].
% 2.97/3.29 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(184,a,144,a)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(184,a,145,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Oab__group__add(B). [resolve(184,a,146,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(184,a,150,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(184,a,151,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(184,a,152,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(184,a,153,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(184,a,154,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(184,a,155,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(184,a,156,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(184,a,157,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(184,a,158,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(184,a,159,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(184,a,160,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(184,a,161,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(184,a,162,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(184,a,163,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(184,a,164,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(184,a,165,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(184,a,166,b)].
% 2.97/3.29 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(184,a,167,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(184,a,168,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(184,a,169,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(184,a,170,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(184,a,171,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(184,a,172,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(184,a,173,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(184,a,174,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(184,a,175,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(184,a,176,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(184,a,177,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(184,a,178,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(184,a,179,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(184,a,180,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(184,a,181,b)].
% 3.25/3.50 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(184,a,182,b)].
% 3.25/3.50 185 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_1) # label(axiom). [assumption].
% 3.25/3.50 186 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom). [assumption].
% 3.25/3.50 187 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom). [assumption].
% 3.25/3.50 188 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom). [assumption].
% 3.25/3.50 189 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom). [assumption].
% 3.25/3.50 190 -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].
% 3.25/3.50 191 -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].
% 3.25/3.50 192 -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].
% 3.25/3.50 193 -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].
% 3.25/3.50 194 -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].
% 3.25/3.50 195 -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].
% 3.25/3.50 196 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom). [assumption].
% 3.25/3.50 197 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom). [assumption].
% 3.25/3.50 198 -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].
% 3.25/3.50 199 -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].
% 3.25/3.50 200 -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].
% 3.29/3.55 201 -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].
% 3.29/3.55 202 -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].
% 3.29/3.55 203 -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].
% 3.29/3.55 204 -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].
% 3.29/3.55 205 -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].
% 3.29/3.55 206 -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].
% 3.29/3.55 207 -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].
% 3.29/3.55 208 -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].
% 3.29/3.55 209 -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].
% 3.29/3.55 210 -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].
% 3.29/3.55 211 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom). [assumption].
% 3.29/3.55 212 -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].
% 3.29/3.55 213 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom). [assumption].
% 3.29/3.55 214 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom). [assumption].
% 3.29/3.55 215 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom). [assumption].
% 3.29/3.55 216 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom). [assumption].
% 3.29/3.55 217 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom). [assumption].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(217,a,191,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(217,a,192,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(217,a,196,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(217,a,197,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(217,a,198,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(217,a,200,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(217,a,201,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(217,a,202,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(217,a,203,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(217,a,204,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(217,a,205,b)].
% 3.29/3.55 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(217,a,206,b)].
% 3.45/3.70 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(217,a,207,b)].
% 3.45/3.70 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(217,a,209,b)].
% 3.45/3.70 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(217,a,210,b)].
% 3.45/3.70 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(217,a,211,b)].
% 3.45/3.70 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(217,a,212,b)].
% 3.45/3.70 218 -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].
% 3.45/3.70 219 -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].
% 3.45/3.70 220 -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].
% 3.45/3.70 221 -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)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(221,c,192,b)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(221,c,193,b)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(221,c,194,b)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(221,c,195,b)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(221,c,196,b)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(221,c,197,b)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(221,c,198,b)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(221,c,199,b)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(221,c,200,b)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(221,c,201,b)].
% 3.45/3.70 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(221,c,202,b)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.45/3.71 222 -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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.71 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 3.45/3.72 223 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(179,b,147,a)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(223,a,186,a)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(223,a,187,a)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(223,a,188,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(223,a,189,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(223,a,190,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(223,a,191,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(223,a,192,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(223,a,193,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(223,a,194,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(223,a,195,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(223,a,196,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(223,a,197,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(223,a,198,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(223,a,199,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(223,a,200,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(223,a,201,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(223,a,202,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(223,a,203,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(223,a,204,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(223,a,205,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(223,a,206,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(223,a,207,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(223,a,208,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(223,a,209,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(223,a,210,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(223,a,211,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(223,a,212,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(223,a,218,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(223,a,219,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(223,a,220,b)].
% 3.45/3.72 224 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(179,b,148,a)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(224,a,186,a)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(224,a,187,a)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(224,a,188,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(224,a,189,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(224,a,190,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(224,a,191,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(224,a,192,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(224,a,193,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(224,a,194,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(224,a,195,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(224,a,196,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(224,a,197,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(224,a,198,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(224,a,199,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(224,a,200,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(224,a,201,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(224,a,202,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(224,a,203,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(224,a,204,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(224,a,205,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(224,a,206,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(224,a,207,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(224,a,208,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(224,a,209,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(224,a,210,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(224,a,211,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(224,a,212,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(224,a,218,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(224,a,219,b)].
% 3.45/3.72 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(224,a,220,b)].
% 3.45/3.72 225 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A). [resolve(179,b,149,a)].
% 3.45/3.72 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(225,a,186,a)].
% 3.45/3.72 Derived: class_HOL_Oplus(tc_nat). [resolve(225,a,187,a)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(225,a,188,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(225,a,189,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(225,a,190,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(225,a,191,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(225,a,192,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(225,a,193,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(225,a,194,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(225,a,195,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(225,a,196,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(225,a,197,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(225,a,198,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(225,a,199,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(225,a,200,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(225,a,201,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(225,a,202,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(225,a,203,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(225,a,204,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(225,a,205,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(225,a,206,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(225,a,207,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(225,a,208,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(225,a,209,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(225,a,210,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(225,a,211,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(225,a,212,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(225,a,218,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(225,a,219,b)].
% 3.45/3.72 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(225,a,220,b)].
% 3.45/3.72 226 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(183,a,179,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(226,b,186,a)].
% 3.45/3.72 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(226,b,187,a)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(226,b,188,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(226,b,189,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(226,b,190,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(226,b,191,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(226,b,192,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(226,b,193,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(226,b,194,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(226,b,195,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(226,b,196,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(226,b,197,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(226,b,198,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(226,b,199,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(226,b,200,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(226,b,201,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(226,b,202,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(226,b,203,b)].
% 3.45/3.72 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(226,b,204,b)].
% 3.56/3.81 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(226,b,205,b)].
% 3.56/3.81 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(226,b,206,b)].
% 3.56/3.81 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(226,b,207,b)].
% 3.56/3.81 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(226,b,208,b)].
% 3.56/3.81 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(226,b,209,b)].
% 3.56/3.81 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(226,b,210,b)].
% 3.56/3.81 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(226,b,211,b)].
% 3.56/3.81 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(226,b,212,b)].
% 3.56/3.81 227 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0(B). [resolve(184,a,179,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(227,b,186,a)].
% 3.56/3.81 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(227,b,187,a)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(227,b,188,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(227,b,189,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(227,b,190,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(227,b,191,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(227,b,192,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(227,b,193,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(227,b,194,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(227,b,195,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(227,b,196,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(227,b,197,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(227,b,198,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(227,b,199,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(227,b,200,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(227,b,201,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(227,b,202,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(227,b,203,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(227,b,204,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(227,b,205,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(227,b,206,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(227,b,207,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(227,b,208,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(227,b,209,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(227,b,210,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(227,b,211,b)].
% 3.56/3.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(227,b,212,b)].
% 3.56/3.81 228 -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].
% 3.56/3.81 229 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom). [assumption].
% 3.56/3.81 230 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom). [assumption].
% 3.75/3.99 231 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom). [assumption].
% 3.75/3.99 232 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom). [assumption].
% 3.75/3.99 233 -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].
% 3.75/3.99 234 -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].
% 3.75/3.99 235 -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].
% 3.75/3.99 236 -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].
% 3.75/3.99 237 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_5) # label(axiom). [assumption].
% 3.75/3.99 238 -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].
% 3.75/3.99 239 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_7) # label(axiom). [assumption].
% 3.75/3.99 240 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_9) # label(axiom). [assumption].
% 3.75/3.99 241 -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].
% 3.75/3.99 242 -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].
% 3.75/3.99 243 -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].
% 3.75/3.99 244 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ofield_15) # label(axiom). [assumption].
% 3.75/3.99 245 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oidom_15) # label(axiom). [assumption].
% 3.75/3.99 246 -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].
% 3.75/3.99 247 -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].
% 3.75/3.99 248 -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].
% 3.75/3.99 249 -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].
% 3.75/3.99 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(249,b,228,a)].
% 3.75/3.99 250 -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].
% 3.75/3.99 251 -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].
% 3.75/3.99 252 -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].
% 3.75/3.99 253 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(71,a,79,b)].
% 3.75/4.03 254 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(100,a,79,b)].
% 3.75/4.03 255 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(101,a,79,b)].
% 3.75/4.03 256 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(102,a,79,b)].
% 3.75/4.03 257 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(103,a,79,b)].
% 3.75/4.03 258 -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)].
% 3.75/4.03 259 -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)].
% 3.75/4.03 260 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(183,a,158,b)].
% 3.75/4.03 261 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(184,a,158,b)].
% 3.75/4.03 262 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(217,a,192,b)].
% 3.75/4.03 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(262,b,229,a)].
% 3.75/4.03 Derived: class_HOL_Ozero(tc_nat). [resolve(262,b,230,a)].
% 3.75/4.03 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(262,b,231,b)].
% 3.75/4.03 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(262,b,232,b)].
% 3.75/4.03 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(262,b,233,b)].
% 3.75/4.03 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(262,b,234,b)].
% 3.75/4.03 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(262,b,241,b)].
% 3.75/4.03 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(262,b,242,b)].
% 3.75/4.03 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(262,b,243,b)].
% 3.75/4.03 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(262,b,246,b)].
% 3.75/4.03 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(262,b,252,b)].
% 3.75/4.03 263 -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)].
% 3.75/4.03 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)].
% 3.75/4.03 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)].
% 3.75/4.03 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = 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)].
% 3.75/4.03 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = 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)].
% 3.75/4.03 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.75/4.03 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 3.75/4.05 264 -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)].
% 3.75/4.05 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(264,c,229,a)].
% 3.75/4.05 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)].
% 3.75/4.05 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_Numeral_Onumber__ring(A). [resolve(264,c,231,b)].
% 3.75/4.05 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_Power_Orecpower(A). [resolve(264,c,232,b)].
% 3.75/4.05 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_Ocomm__ring(A). [resolve(264,c,233,b)].
% 3.75/4.05 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_Ocomm__ring__1(A). [resolve(264,c,234,b)].
% 3.75/4.05 265 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(223,a,192,b)].
% 3.75/4.05 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(265,b,229,a)].
% 3.75/4.05 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(265,b,230,a)].
% 3.75/4.05 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(265,b,231,b)].
% 3.75/4.05 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(265,b,232,b)].
% 3.75/4.05 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(265,b,233,b)].
% 3.75/4.05 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(265,b,234,b)].
% 3.75/4.05 266 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(224,a,192,b)].
% 3.75/4.05 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(266,b,229,a)].
% 3.75/4.05 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(266,b,230,a)].
% 3.75/4.05 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(266,b,231,b)].
% 3.75/4.05 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(266,b,232,b)].
% 3.75/4.05 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(266,b,233,b)].
% 3.75/4.05 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(266,b,234,b)].
% 3.75/4.05 267 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(225,a,192,b)].
% 3.75/4.05 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(267,b,229,a)].
% 3.75/4.05 Derived: class_HOL_Oplus(tc_nat). [resolve(267,b,230,a)].
% 3.75/4.05 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(267,b,231,b)].
% 3.75/4.05 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(267,b,232,b)].
% 3.75/4.05 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(267,b,233,b)].
% 3.75/4.05 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(267,b,234,b)].
% 3.75/4.05 268 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(226,b,192,b)].
% 3.75/4.05 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(268,b,229,a)].
% 3.75/4.05 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(268,b,230,a)].
% 3.75/4.05 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(268,b,231,b)].
% 3.88/4.12 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(268,b,232,b)].
% 3.88/4.12 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(268,b,233,b)].
% 3.88/4.12 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(268,b,234,b)].
% 3.88/4.12 269 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(227,b,192,b)].
% 3.88/4.12 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(269,b,229,a)].
% 3.88/4.12 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(269,b,230,a)].
% 3.88/4.12 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(269,b,231,b)].
% 3.88/4.12 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(269,b,232,b)].
% 3.88/4.12 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(269,b,233,b)].
% 3.88/4.12 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(269,b,234,b)].
% 3.88/4.12 270 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom). [assumption].
% 3.88/4.12 271 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom). [assumption].
% 3.88/4.12 272 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom). [assumption].
% 3.88/4.12 273 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom). [assumption].
% 3.88/4.12 274 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom). [assumption].
% 3.88/4.12 275 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 3.88/4.12 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(270,a,275,b)].
% 3.88/4.12 276 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom). [assumption].
% 3.88/4.12 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(276,a,275,b)].
% 3.88/4.12 277 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom). [assumption].
% 3.88/4.12 278 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_11) # label(axiom). [assumption].
% 3.88/4.12 279 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_12) # label(axiom). [assumption].
% 3.88/4.12 280 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_12) # label(axiom). [assumption].
% 3.88/4.12 281 -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].
% 3.88/4.12 282 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_6) # label(axiom). [assumption].
% 3.88/4.12 283 -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].
% 3.88/4.12 284 -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].
% 3.88/4.12 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(284,b,270,a)].
% 3.88/4.12 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(284,b,276,a)].
% 3.90/4.17 285 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom). [assumption].
% 3.90/4.17 286 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_15) # label(axiom). [assumption].
% 3.90/4.17 287 -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].
% 3.90/4.17 288 -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].
% 3.90/4.17 289 -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].
% 3.90/4.17 290 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom). [assumption].
% 3.90/4.17 291 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom). [assumption].
% 3.90/4.17 292 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_21) # label(axiom). [assumption].
% 3.90/4.17 293 -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].
% 3.90/4.17 294 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_28) # label(axiom). [assumption].
% 3.90/4.17 295 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_27) # label(axiom). [assumption].
% 3.90/4.17 296 -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].
% 3.90/4.17 297 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_21) # label(axiom). [assumption].
% 3.90/4.17 298 -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].
% 3.90/4.17 299 -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].
% 3.90/4.17 300 -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].
% 3.90/4.17 301 -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].
% 3.90/4.17 302 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_5) # label(axiom). [assumption].
% 3.90/4.17 303 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom). [assumption].
% 3.90/4.17 304 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_5) # label(axiom). [assumption].
% 3.90/4.17 305 -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].
% 3.90/4.17 306 -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].
% 3.90/4.17 307 -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].
% 3.90/4.18 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(307,a,271,a)].
% 3.90/4.18 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(307,a,272,a)].
% 3.90/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(307,a,273,b)].
% 3.90/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(307,a,274,b)].
% 3.90/4.18 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)].
% 3.90/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(307,a,277,b)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(307,a,285,b)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(307,a,290,b)].
% 3.90/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(307,a,291,b)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.18 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(307,a,303,b)].
% 3.90/4.18 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)].
% 3.90/4.18 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)].
% 3.90/4.19 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)].
% 3.90/4.19 308 -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].
% 3.90/4.19 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(308,a,271,a)].
% 3.90/4.19 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(308,a,272,a)].
% 3.90/4.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(308,a,273,b)].
% 3.90/4.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(308,a,274,b)].
% 3.90/4.19 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)].
% 3.90/4.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(308,a,277,b)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(308,a,285,b)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(308,a,290,b)].
% 3.90/4.19 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(308,a,291,b)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 3.90/4.19 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)].
% 4.18/4.43 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(308,a,303,b)].
% 4.18/4.43 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)].
% 4.18/4.43 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)].
% 4.18/4.43 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)].
% 4.18/4.43 309 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) # label(axiom). [assumption].
% 4.18/4.43 310 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom). [assumption].
% 4.18/4.43 311 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom). [assumption].
% 4.18/4.43 312 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom). [assumption].
% 4.18/4.43 313 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom). [assumption].
% 4.18/4.43 314 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 4.18/4.43 315 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 4.18/4.43 316 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom). [assumption].
% 4.18/4.43 317 -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].
% 4.18/4.43 318 -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].
% 4.18/4.43 319 -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].
% 4.18/4.43 320 -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].
% 4.18/4.43 321 -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].
% 4.18/4.43 322 -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].
% 4.18/4.43 323 -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].
% 4.18/4.43 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(323,b,309,a)].
% 4.18/4.43 324 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom). [assumption].
% 4.18/4.43 325 -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].
% 4.18/4.43 326 -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].
% 4.18/4.43 327 -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].
% 4.36/4.64 328 -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].
% 4.36/4.64 329 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom). [assumption].
% 4.36/4.64 330 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom). [assumption].
% 4.36/4.64 331 -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].
% 4.36/4.64 332 -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].
% 4.36/4.64 333 -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].
% 4.36/4.64 334 -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].
% 4.36/4.64 335 -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].
% 4.36/4.64 336 -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].
% 4.36/4.64 337 -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].
% 4.36/4.64 338 -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].
% 4.36/4.64 339 -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].
% 4.36/4.64 340 -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].
% 4.36/4.64 341 -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].
% 4.36/4.64 342 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom). [assumption].
% 4.36/4.64 343 -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].
% 4.36/4.64 344 -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].
% 4.36/4.64 345 -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].
% 4.36/4.64 346 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(270,a,275,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(346,b,310,a)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(346,b,311,a)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(346,b,312,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(346,b,313,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(346,b,316,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(346,b,317,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(346,b,318,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(346,b,319,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(346,b,320,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(346,b,321,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(346,b,322,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(346,b,324,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(346,b,325,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(346,b,326,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(346,b,327,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(346,b,328,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(346,b,329,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(346,b,330,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(346,b,331,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(346,b,332,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(346,b,333,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(346,b,334,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(346,b,335,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(346,b,336,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(346,b,337,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(346,b,338,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(346,b,339,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(346,b,340,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(346,b,341,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(346,b,342,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(346,b,343,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(346,b,344,b)].
% 4.36/4.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(346,b,345,b)].
% 4.36/4.64 347 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(276,a,275,b)].
% 4.36/4.64 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(347,b,310,a)].
% 4.36/4.64 Derived: class_HOL_Oplus(tc_nat). [resolve(347,b,311,a)].
% 4.36/4.64 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(347,b,312,b)].
% 4.36/4.64 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(347,b,313,b)].
% 4.36/4.64 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(347,b,316,b)].
% 4.36/4.64 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(347,b,317,b)].
% 4.36/4.64 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(347,b,318,b)].
% 4.36/4.64 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(347,b,319,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(347,b,320,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(347,b,321,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(347,b,322,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(347,b,324,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(347,b,325,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(347,b,326,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(347,b,327,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(347,b,328,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(347,b,329,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(347,b,330,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(347,b,331,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(347,b,332,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(347,b,333,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(347,b,334,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(347,b,335,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(347,b,336,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(347,b,337,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(347,b,338,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(347,b,339,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(347,b,340,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(347,b,341,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(347,b,342,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(347,b,343,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(347,b,344,b)].
% 4.50/4.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(347,b,345,b)].
% 4.50/4.73 348 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Ocancel__ab__semigroup__add(C). [resolve(307,a,275,b)].
% 4.50/4.73 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(348,c,310,a)].
% 4.50/4.73 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(348,c,311,a)].
% 4.50/4.73 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(348,c,312,b)].
% 4.50/4.73 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(348,c,313,b)].
% 4.50/4.73 349 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Ocancel__ab__semigroup__add(C). [resolve(308,a,275,b)].
% 4.50/4.73 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(349,c,310,a)].
% 4.50/4.73 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(349,c,311,a)].
% 4.50/4.73 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(349,c,312,b)].
% 4.50/4.73 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(349,c,313,b)].
% 4.50/4.73 350 -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].
% 4.50/4.73 351 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom). [assumption].
% 4.50/4.73 352 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom). [assumption].
% 4.51/4.74 353 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom). [assumption].
% 4.51/4.74 354 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom). [assumption].
% 4.51/4.74 355 -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].
% 4.51/4.74 356 -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].
% 4.51/4.74 357 -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].
% 4.51/4.74 358 -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].
% 4.51/4.74 359 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_18) # label(axiom). [assumption].
% 4.51/4.74 360 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_18) # label(axiom). [assumption].
% 4.51/4.74 361 -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].
% 4.51/4.74 362 -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].
% 4.51/4.74 363 -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].
% 4.51/4.74 364 -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].
% 4.51/4.74 365 -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].
% 4.51/4.74 366 -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].
% 4.51/4.74 367 -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].
% 4.51/4.74 368 -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].
% 4.51/4.74 369 -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].
% 4.51/4.74 370 -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].
% 4.51/4.74 371 -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].
% 4.51/4.74 372 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring_12) # label(axiom). [assumption].
% 4.51/4.74 373 -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].
% 4.51/4.74 374 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_3) # label(axiom). [assumption].
% 4.51/4.74 375 -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].
% 4.59/4.83 376 -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].
% 4.59/4.83 377 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_7) # label(axiom). [assumption].
% 4.59/4.83 378 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_8) # label(axiom). [assumption].
% 4.59/4.83 379 -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].
% 4.59/4.83 380 -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].
% 4.59/4.83 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(380,a,351,a)].
% 4.59/4.83 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(380,a,352,a)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(380,a,353,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(380,a,354,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(380,a,355,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(380,a,356,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(380,a,357,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(380,a,358,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(380,a,359,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(380,a,360,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(380,a,361,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(380,a,362,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(380,a,363,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(380,a,364,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(380,a,365,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(380,a,366,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(380,a,367,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(380,a,368,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(380,a,369,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(380,a,370,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(380,a,371,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(380,a,372,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(380,a,373,b)].
% 4.59/4.83 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(380,a,379,b)].
% 4.59/4.83 381 -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].
% 4.59/4.83 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(381,a,351,a)].
% 4.59/4.83 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(381,a,352,a)].
% 4.59/4.83 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(381,a,353,b)].
% 4.59/4.83 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(381,a,354,b)].
% 4.59/4.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(381,a,355,b)].
% 4.59/4.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(381,a,356,b)].
% 4.59/4.83 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(381,a,357,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(381,a,358,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(381,a,359,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(381,a,360,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(381,a,361,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(381,a,362,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(381,a,363,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(381,a,364,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(381,a,365,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(381,a,366,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(381,a,367,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(381,a,368,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(381,a,369,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(381,a,370,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(381,a,371,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(381,a,372,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(381,a,373,b)].
% 4.65/4.95 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(381,a,379,b)].
% 4.65/4.95 382 -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)].
% 4.65/4.95 383 -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)].
% 4.65/4.95 384 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(183,a,180,b)].
% 4.65/4.95 385 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__0__cancel(B). [resolve(184,a,180,b)].
% 4.65/4.95 386 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(223,a,218,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(386,b,357,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(386,b,358,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(386,b,359,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(386,b,360,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(386,b,361,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(386,b,362,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(386,b,363,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(386,b,364,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(386,b,365,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(386,b,366,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(386,b,367,b)].
% 4.65/4.95 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(386,b,368,b)].
% 4.74/4.97 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(386,b,369,b)].
% 4.74/4.97 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(386,b,370,b)].
% 4.74/4.97 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(386,b,371,b)].
% 4.74/4.97 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(386,b,372,b)].
% 4.74/4.97 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(386,b,373,b)].
% 4.74/4.97 387 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(224,a,218,b)].
% 4.74/4.97 388 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(225,a,218,b)].
% 4.74/4.97 389 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)].
% 4.74/4.97 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(389,c,354,b)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(389,c,359,b)].
% 4.74/4.97 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(389,c,360,b)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(389,c,372,b)].
% 4.74/4.97 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)].
% 4.74/4.97 390 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)].
% 4.74/4.97 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(390,c,354,b)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.97 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)].
% 4.74/4.98 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(390,c,359,b)].
% 4.74/4.98 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(390,c,360,b)].
% 4.74/4.98 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)].
% 4.74/4.98 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)].
% 4.74/4.98 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)].
% 4.74/4.98 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)].
% 4.74/4.98 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)].
% 4.74/4.98 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)].
% 4.74/4.98 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)].
% 4.74/4.98 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)].
% 4.74/4.98 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)].
% 4.74/4.98 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)].
% 4.74/4.98 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)].
% 4.74/4.98 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(390,c,372,b)].
% 4.74/4.98 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)].
% 4.74/4.98 391 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(346,b,344,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(391,b,351,a)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(391,b,352,a)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(391,b,353,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(391,b,354,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(391,b,355,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(391,b,356,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(391,b,357,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(391,b,358,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(391,b,359,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(391,b,360,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(391,b,361,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(391,b,362,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(391,b,363,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(391,b,364,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(391,b,365,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(391,b,366,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(391,b,367,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(391,b,368,b)].
% 4.74/4.98 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(391,b,369,b)].
% 4.81/5.07 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(391,b,370,b)].
% 4.81/5.07 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(391,b,371,b)].
% 4.81/5.07 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(391,b,372,b)].
% 4.81/5.07 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(391,b,373,b)].
% 4.81/5.07 392 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(347,b,344,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(392,b,351,a)].
% 4.81/5.07 Derived: class_HOL_Oplus(tc_nat). [resolve(392,b,352,a)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(392,b,353,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(392,b,354,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(392,b,355,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(392,b,356,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(392,b,357,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(392,b,358,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(392,b,359,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(392,b,360,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(392,b,361,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(392,b,362,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(392,b,363,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(392,b,364,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(392,b,365,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(392,b,366,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(392,b,367,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(392,b,368,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(392,b,369,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(392,b,370,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(392,b,371,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(392,b,372,b)].
% 4.81/5.07 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(392,b,373,b)].
% 4.81/5.07 393 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_1) # label(axiom). [assumption].
% 4.81/5.07 394 class_Ring__and__Field_Oring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_19) # label(axiom). [assumption].
% 4.81/5.07 395 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom). [assumption].
% 4.81/5.07 396 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_16) # label(axiom). [assumption].
% 4.81/5.07 397 -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].
% 4.81/5.07 398 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ofield_3) # label(axiom). [assumption].
% 4.81/5.07 399 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom). [assumption].
% 4.81/5.07 400 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Olordered__ring_1) # label(axiom). [assumption].
% 4.81/5.07 401 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__field_6) # label(axiom). [assumption].
% 4.90/5.12 402 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__idom_3) # label(axiom). [assumption].
% 4.90/5.12 403 -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].
% 4.90/5.12 404 -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].
% 4.90/5.12 405 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__ring_0) # label(axiom). [assumption].
% 4.90/5.12 406 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring_2) # label(axiom). [assumption].
% 4.90/5.12 407 -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring_3) # label(axiom). [assumption].
% 4.90/5.12 408 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring_4) # label(axiom). [assumption].
% 4.90/5.12 409 -class_Ring__and__Field_Oring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring_5) # label(axiom). [assumption].
% 4.90/5.12 410 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring_6) # label(axiom). [assumption].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(410,a,394,a)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(410,a,395,b)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(410,a,396,b)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(410,a,397,b)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(410,a,398,b)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(410,a,399,b)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(410,a,400,b)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(410,a,401,b)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(410,a,402,b)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(410,a,403,b)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(410,a,404,b)].
% 4.90/5.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(410,a,405,b)].
% 4.90/5.12 411 -class_Ring__and__Field_Oring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring_9) # label(axiom). [assumption].
% 4.90/5.12 412 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oring__1_0) # label(axiom). [assumption].
% 4.90/5.12 413 -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].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 414 -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].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.12 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 415 -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].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.90/5.16 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)].
% 4.98/5.24 416 -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].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 417 -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].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 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)].
% 4.98/5.24 418 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(71,a,98,b)].
% 4.98/5.24 419 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(100,a,98,b)].
% 5.07/5.28 420 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(101,a,98,b)].
% 5.07/5.28 421 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(102,a,98,b)].
% 5.07/5.28 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(421,b,398,b)].
% 5.07/5.28 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(421,b,399,b)].
% 5.07/5.28 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(421,b,400,b)].
% 5.07/5.28 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(421,b,401,b)].
% 5.07/5.28 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(421,b,402,b)].
% 5.07/5.28 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(421,b,403,b)].
% 5.07/5.28 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(421,b,404,b)].
% 5.07/5.28 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(421,b,405,b)].
% 5.07/5.28 422 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(103,a,98,b)].
% 5.07/5.28 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(422,b,398,b)].
% 5.07/5.28 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(422,b,399,b)].
% 5.07/5.28 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(422,b,400,b)].
% 5.07/5.28 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(422,b,401,b)].
% 5.07/5.28 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(422,b,402,b)].
% 5.07/5.28 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(422,b,403,b)].
% 5.07/5.28 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(422,b,404,b)].
% 5.07/5.28 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(422,b,405,b)].
% 5.07/5.28 423 -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)].
% 5.07/5.28 424 -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)].
% 5.07/5.28 425 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(183,a,177,b)].
% 5.07/5.28 426 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(184,a,177,b)].
% 5.07/5.28 427 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(217,a,211,b)].
% 5.07/5.28 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(427,b,398,b)].
% 5.07/5.28 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(427,b,399,b)].
% 5.07/5.28 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(427,b,400,b)].
% 5.07/5.28 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(427,b,401,b)].
% 5.07/5.28 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(427,b,402,b)].
% 5.07/5.28 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(427,b,403,b)].
% 5.07/5.28 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(427,b,404,b)].
% 5.07/5.28 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(427,b,405,b)].
% 5.07/5.28 428 -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)].
% 5.07/5.28 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(428,c,398,b)].
% 5.07/5.28 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oidom(A). [resolve(428,c,399,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(428,c,400,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(428,c,401,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(428,c,402,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(428,c,403,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(428,c,404,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(428,c,405,b)].
% 5.07/5.29 429 -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)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(429,c,398,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(429,c,399,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(429,c,400,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(429,c,401,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(429,c,402,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(429,c,403,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(429,c,404,b)].
% 5.07/5.29 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(429,c,405,b)].
% 5.07/5.29 430 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(223,a,211,b)].
% 5.07/5.29 431 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(224,a,211,b)].
% 5.11/5.33 432 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(225,a,211,b)].
% 5.11/5.33 433 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(226,b,211,b)].
% 5.11/5.33 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(433,b,398,b)].
% 5.11/5.33 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(433,b,399,b)].
% 5.11/5.33 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(433,b,400,b)].
% 5.11/5.33 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(433,b,401,b)].
% 5.11/5.33 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(433,b,402,b)].
% 5.11/5.33 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(433,b,403,b)].
% 5.11/5.33 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(433,b,404,b)].
% 5.11/5.33 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(433,b,405,b)].
% 5.11/5.33 434 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(227,b,211,b)].
% 5.11/5.33 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(434,b,398,b)].
% 5.11/5.33 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(434,b,399,b)].
% 5.11/5.33 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(434,b,400,b)].
% 5.11/5.33 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(434,b,401,b)].
% 5.11/5.33 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(434,b,402,b)].
% 5.11/5.33 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(434,b,403,b)].
% 5.11/5.33 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(434,b,404,b)].
% 5.11/5.33 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(434,b,405,b)].
% 5.11/5.33 435 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(307,a,303,b)].
% 5.11/5.33 436 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(308,a,303,b)].
% 5.11/5.33 437 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(346,b,342,b)].
% 5.11/5.33 438 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(347,b,342,b)].
% 5.11/5.33 439 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(380,a,372,b)].
% 5.11/5.33 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(439,b,394,a)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(439,b,395,b)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(439,b,396,b)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(439,b,397,b)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(439,b,398,b)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(439,b,399,b)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(439,b,400,b)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(439,b,401,b)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(439,b,402,b)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(439,b,403,b)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(439,b,404,b)].
% 5.11/5.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(439,b,405,b)].
% 5.11/5.33 440 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring(B). [resolve(381,a,372,b)].
% 5.11/5.33 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(440,b,394,a)].
% 5.11/5.33 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(440,b,395,b)].
% 5.11/5.33 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(440,b,396,b)].
% 5.11/5.33 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(440,b,397,b)].
% 5.11/5.33 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(440,b,398,b)].
% 5.11/5.34 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(440,b,399,b)].
% 5.11/5.34 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(440,b,400,b)].
% 5.11/5.34 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(440,b,401,b)].
% 5.11/5.34 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(440,b,402,b)].
% 5.11/5.34 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(440,b,403,b)].
% 5.11/5.34 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(440,b,404,b)].
% 5.11/5.34 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(440,b,405,b)].
% 5.11/5.34 441 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(386,b,372,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(441,b,394,a)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(441,b,395,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(441,b,396,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(441,b,397,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(441,b,398,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(441,b,399,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(441,b,400,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(441,b,401,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(441,b,402,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(441,b,403,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(441,b,404,b)].
% 5.11/5.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(441,b,405,b)].
% 5.11/5.34 442 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(389,c,372,b)].
% 5.11/5.34 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(442,c,394,a)].
% 5.11/5.34 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(442,c,395,b)].
% 5.11/5.34 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)].
% 5.11/5.34 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)].
% 5.11/5.34 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(442,c,398,b)].
% 5.11/5.34 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(442,c,399,b)].
% 5.11/5.34 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)].
% 5.11/5.34 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)].
% 5.11/5.34 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)].
% 5.11/5.34 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)].
% 5.11/5.34 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)].
% 5.11/5.34 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)].
% 5.11/5.34 443 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(390,c,372,b)].
% 5.11/5.34 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(443,c,394,a)].
% 5.11/5.34 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(443,c,395,b)].
% 5.11/5.34 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)].
% 5.50/5.73 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)].
% 5.50/5.73 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(443,c,398,b)].
% 5.50/5.73 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(443,c,399,b)].
% 5.50/5.73 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)].
% 5.50/5.73 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)].
% 5.50/5.73 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)].
% 5.50/5.73 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)].
% 5.50/5.73 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)].
% 5.50/5.73 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)].
% 5.50/5.73 444 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(391,b,372,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(444,b,394,a)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(444,b,395,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(444,b,396,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(444,b,397,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(444,b,398,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(444,b,399,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(444,b,400,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(444,b,401,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(444,b,402,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(444,b,403,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(444,b,404,b)].
% 5.50/5.73 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(444,b,405,b)].
% 5.50/5.73 445 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(392,b,372,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(445,b,394,a)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(445,b,395,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(445,b,396,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(445,b,397,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(445,b,398,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(445,b,399,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(445,b,400,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(445,b,401,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(445,b,402,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(445,b,403,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(445,b,404,b)].
% 5.50/5.73 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(445,b,405,b)].
% 5.50/5.73 446 -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].
% 5.50/5.73 447 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom). [assumption].
% 5.59/5.89 448 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom). [assumption].
% 5.59/5.89 449 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom). [assumption].
% 5.59/5.89 450 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom). [assumption].
% 5.59/5.89 451 -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].
% 5.59/5.89 452 -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].
% 5.59/5.89 453 -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].
% 5.59/5.89 454 -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].
% 5.59/5.89 455 -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].
% 5.59/5.89 456 -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].
% 5.59/5.89 457 -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].
% 5.59/5.89 458 -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].
% 5.59/5.89 459 -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].
% 5.59/5.89 460 -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].
% 5.59/5.89 461 -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].
% 5.59/5.89 462 -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].
% 5.59/5.89 463 -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].
% 5.59/5.89 464 -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].
% 5.59/5.89 465 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(71,a,80,b)].
% 5.59/5.89 466 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(100,a,80,b)].
% 5.59/5.89 467 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(102,a,80,b)].
% 5.59/5.89 468 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(103,a,80,b)].
% 5.59/5.89 469 -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)].
% 5.59/5.89 470 -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)].
% 5.59/5.89 471 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(159,b,142,a)].
% 5.69/5.94 472 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(183,a,159,b)].
% 5.69/5.94 473 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(184,a,159,b)].
% 5.69/5.94 474 -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)].
% 5.69/5.94 475 -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)].
% 5.69/5.94 476 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(223,a,193,b)].
% 5.69/5.94 477 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(224,a,193,b)].
% 5.69/5.94 478 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(226,b,193,b)].
% 5.69/5.94 479 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(227,b,193,b)].
% 5.69/5.94 480 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(262,b,241,b)].
% 5.69/5.94 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(480,b,447,a)].
% 5.69/5.94 Derived: class_HOL_Ozero(tc_nat). [resolve(480,b,448,a)].
% 5.69/5.94 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(480,b,449,b)].
% 5.69/5.94 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(480,b,450,b)].
% 5.69/5.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(480,b,451,b)].
% 5.69/5.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(480,b,452,b)].
% 5.69/5.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(480,b,463,b)].
% 5.69/5.94 481 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)].
% 5.69/5.94 482 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)].
% 5.69/5.94 483 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(346,b,327,b)].
% 5.69/5.94 484 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(380,a,357,b)].
% 5.69/5.94 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(484,b,448,a)].
% 5.69/5.94 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(484,b,450,b)].
% 5.69/5.94 485 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(381,a,357,b)].
% 5.69/5.94 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(485,b,448,a)].
% 5.69/5.94 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(485,b,450,b)].
% 5.69/5.94 486 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(386,b,357,b)].
% 5.69/5.94 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(486,b,448,a)].
% 5.69/5.94 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(486,b,450,b)].
% 5.69/5.94 487 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)].
% 5.69/5.94 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(487,c,448,a)].
% 5.69/5.94 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(487,c,450,b)].
% 5.69/5.94 488 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)].
% 5.69/5.94 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(488,c,448,a)].
% 5.69/5.94 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(488,c,450,b)].
% 5.69/5.94 489 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(391,b,357,b)].
% 5.69/5.94 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(489,b,448,a)].
% 5.69/5.94 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(489,b,450,b)].
% 5.89/6.17 490 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom). [assumption].
% 5.89/6.17 491 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom). [assumption].
% 5.89/6.17 492 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom). [assumption].
% 5.89/6.17 493 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_12) # label(axiom). [assumption].
% 5.89/6.17 494 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_2) # label(axiom). [assumption].
% 5.89/6.17 495 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom). [assumption].
% 5.89/6.17 496 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom). [assumption].
% 5.89/6.17 497 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_8) # label(axiom). [assumption].
% 5.89/6.17 498 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom). [assumption].
% 5.89/6.17 499 -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].
% 5.89/6.17 500 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom). [assumption].
% 5.89/6.17 501 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom). [assumption].
% 5.89/6.17 502 -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].
% 5.89/6.17 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(502,b,494,a)].
% 5.89/6.17 503 -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].
% 5.89/6.17 504 -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].
% 5.89/6.17 505 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(71,a,76,b)].
% 5.89/6.17 506 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(100,a,76,b)].
% 5.89/6.17 507 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(102,a,76,b)].
% 5.89/6.17 508 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(103,a,76,b)].
% 5.89/6.17 509 -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)].
% 5.89/6.17 510 -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)].
% 5.89/6.17 511 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(119,a,115,b)].
% 5.89/6.17 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(511,b,491,a)].
% 5.89/6.17 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(511,b,492,b)].
% 5.89/6.17 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(511,b,500,b)].
% 5.89/6.17 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(511,b,501,b)].
% 5.89/6.17 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(511,b,503,b)].
% 5.89/6.17 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(511,b,504,b)].
% 5.98/6.21 512 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(135,b,115,b)].
% 5.98/6.21 513 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(136,b,115,b)].
% 5.98/6.21 514 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(138,b,115,b)].
% 5.98/6.21 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(514,b,491,a)].
% 5.98/6.21 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(514,b,492,b)].
% 5.98/6.21 515 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(139,b,115,b)].
% 5.98/6.21 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(515,b,491,a)].
% 5.98/6.21 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(515,b,492,b)].
% 5.98/6.21 516 -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)].
% 5.98/6.21 517 -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)].
% 5.98/6.21 518 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(156,b,142,a)].
% 5.98/6.21 519 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(183,a,156,b)].
% 5.98/6.21 520 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(184,a,156,b)].
% 5.98/6.21 521 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(223,a,190,b)].
% 5.98/6.21 522 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(224,a,190,b)].
% 5.98/6.21 523 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(226,b,190,b)].
% 5.98/6.21 524 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(227,b,190,b)].
% 5.98/6.21 525 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(262,b,233,b)].
% 5.98/6.21 526 -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)].
% 5.98/6.21 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)].
% 5.98/6.21 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = 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)].
% 5.98/6.21 527 -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)].
% 5.98/6.21 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)].
% 5.98/6.21 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = 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)].
% 5.98/6.21 528 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(265,b,233,b)].
% 5.98/6.21 529 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(266,b,233,b)].
% 5.98/6.21 530 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(268,b,233,b)].
% 5.98/6.21 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(530,b,491,a)].
% 5.98/6.24 Derived: c_plus(A,c_0,B) = A | -class_Numeral_Onumber__ring(B). [resolve(530,b,492,b)].
% 5.98/6.24 531 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(269,b,233,b)].
% 5.98/6.24 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(531,b,491,a)].
% 5.98/6.24 Derived: c_plus(c_0,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(531,b,492,b)].
% 5.98/6.24 532 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(307,a,286,b)].
% 5.98/6.24 533 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(308,a,286,b)].
% 5.98/6.24 534 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(346,b,325,b)].
% 5.98/6.24 535 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(380,a,355,b)].
% 5.98/6.24 536 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(381,a,355,b)].
% 5.98/6.24 537 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(389,c,355,b)].
% 5.98/6.24 538 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(390,c,355,b)].
% 5.98/6.24 539 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(391,b,355,b)].
% 5.98/6.24 540 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(410,a,396,b)].
% 5.98/6.24 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(540,b,491,a)].
% 5.98/6.24 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Numeral_Onumber__ring(A). [resolve(540,b,492,b)].
% 5.98/6.24 541 -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)].
% 5.98/6.24 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)].
% 5.98/6.24 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)].
% 5.98/6.24 542 -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)].
% 5.98/6.24 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)].
% 5.98/6.24 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)].
% 5.98/6.24 543 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)].
% 5.98/6.24 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)].
% 5.98/6.24 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)].
% 5.98/6.24 544 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)].
% 5.98/6.24 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)].
% 5.98/6.24 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)].
% 5.98/6.24 545 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)].
% 5.98/6.24 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)].
% 6.09/6.33 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)].
% 6.09/6.33 546 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(439,b,396,b)].
% 6.09/6.33 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(546,b,491,a)].
% 6.09/6.33 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(546,b,492,b)].
% 6.09/6.33 547 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(440,b,396,b)].
% 6.09/6.33 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(547,b,491,a)].
% 6.09/6.33 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(547,b,492,b)].
% 6.09/6.33 548 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(441,b,396,b)].
% 6.09/6.33 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(548,b,491,a)].
% 6.09/6.33 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(548,b,492,b)].
% 6.09/6.33 549 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(442,c,396,b)].
% 6.09/6.33 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(549,c,491,a)].
% 6.09/6.33 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Numeral_Onumber__ring(C). [resolve(549,c,492,b)].
% 6.09/6.33 550 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(443,c,396,b)].
% 6.09/6.33 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(550,c,491,a)].
% 6.09/6.33 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Numeral_Onumber__ring(C). [resolve(550,c,492,b)].
% 6.09/6.33 551 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(444,b,396,b)].
% 6.09/6.33 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(551,b,491,a)].
% 6.09/6.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(551,b,492,b)].
% 6.09/6.33 552 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(480,b,451,b)].
% 6.09/6.33 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(552,b,491,a)].
% 6.09/6.33 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(552,b,492,b)].
% 6.09/6.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(552,b,500,b)].
% 6.09/6.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(552,b,501,b)].
% 6.09/6.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(552,b,502,b)].
% 6.09/6.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(552,b,503,b)].
% 6.09/6.33 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(552,b,504,b)].
% 6.09/6.33 553 -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].
% 6.09/6.33 554 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom). [assumption].
% 6.09/6.33 555 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom). [assumption].
% 6.09/6.33 556 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom). [assumption].
% 6.09/6.33 557 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom). [assumption].
% 6.09/6.33 558 -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].
% 6.09/6.33 559 -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].
% 6.09/6.33 560 -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].
% 6.09/6.33 561 -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].
% 6.19/6.45 562 -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].
% 6.19/6.45 563 -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].
% 6.19/6.45 564 -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].
% 6.19/6.45 565 -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].
% 6.19/6.45 566 -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].
% 6.19/6.45 567 -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].
% 6.19/6.45 568 -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].
% 6.19/6.45 569 -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].
% 6.19/6.45 Derived: c_0 != c_1. [resolve(569,a,554,a)].
% 6.19/6.45 570 -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].
% 6.19/6.45 Derived: c_1 != c_0. [resolve(570,a,554,a)].
% 6.19/6.45 571 -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)].
% 6.19/6.45 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)].
% 6.19/6.45 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)].
% 6.19/6.45 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)].
% 6.19/6.45 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)].
% 6.19/6.45 572 -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)].
% 6.19/6.45 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(572,d,554,a)].
% 6.19/6.45 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(572,d,555,a)].
% 6.19/6.45 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(572,d,556,b)].
% 6.19/6.45 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(572,d,557,b)].
% 6.19/6.45 573 -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)].
% 6.19/6.45 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(573,d,554,a)].
% 6.19/6.45 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(573,d,555,a)].
% 6.19/6.45 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(573,d,556,b)].
% 6.19/6.46 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)].
% 6.19/6.46 574 -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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 575 -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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 576 -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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 577 -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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 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)].
% 6.19/6.46 578 -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)].
% 6.40/6.62 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)].
% 6.40/6.62 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)].
% 6.40/6.62 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)].
% 6.40/6.62 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)].
% 6.40/6.62 579 -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)].
% 6.40/6.62 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)].
% 6.40/6.62 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)].
% 6.40/6.62 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)].
% 6.40/6.62 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)].
% 6.40/6.62 580 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom). [assumption].
% 6.40/6.62 581 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom). [assumption].
% 6.40/6.62 582 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom). [assumption].
% 6.40/6.62 583 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom). [assumption].
% 6.40/6.62 584 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom). [assumption].
% 6.40/6.62 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(580,a,584,b)].
% 6.40/6.62 585 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom). [assumption].
% 6.40/6.62 Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(585,a,584,b)].
% 6.40/6.62 586 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom). [assumption].
% 6.40/6.62 587 -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].
% 6.40/6.62 588 -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].
% 6.40/6.62 589 -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].
% 6.40/6.62 590 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom). [assumption].
% 6.40/6.62 591 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom). [assumption].
% 6.40/6.62 592 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom). [assumption].
% 6.40/6.62 593 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom). [assumption].
% 6.50/6.75 594 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom). [assumption].
% 6.50/6.75 595 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom). [assumption].
% 6.50/6.75 596 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom). [assumption].
% 6.50/6.75 597 -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].
% 6.50/6.75 598 -class_OrderedGroup_Omonoid__mult(A) | c_times(c_1,B,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) # label(axiom). [assumption].
% 6.50/6.75 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(598,a,581,a)].
% 6.50/6.75 Derived: c_times(c_1,A,tc_nat) = A. [resolve(598,a,582,a)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(598,a,583,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(598,a,584,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(598,a,586,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(598,a,587,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(598,a,588,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(598,a,589,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(598,a,590,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(598,a,591,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(598,a,592,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(598,a,593,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(598,a,594,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(598,a,595,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(598,a,596,b)].
% 6.50/6.75 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(598,a,597,b)].
% 6.50/6.75 599 -class_OrderedGroup_Omonoid__mult(A) | c_times(B,c_1,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) # label(axiom). [assumption].
% 6.50/6.75 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(599,a,581,a)].
% 6.50/6.75 Derived: c_times(A,c_1,tc_nat) = A. [resolve(599,a,582,a)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(599,a,583,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(599,a,584,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(599,a,586,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(599,a,587,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(599,a,588,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(599,a,589,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(599,a,590,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(599,a,591,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(599,a,592,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(599,a,593,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(599,a,594,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(599,a,595,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(599,a,596,b)].
% 6.50/6.75 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(599,a,597,b)].
% 6.50/6.75 600 -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)].
% 6.68/6.93 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)].
% 6.68/6.93 601 -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)].
% 6.68/6.93 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)].
% 6.68/6.93 602 -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)].
% 6.68/6.93 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)].
% 6.68/6.93 603 -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)].
% 6.68/6.93 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)].
% 6.68/6.93 604 -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)].
% 6.68/6.93 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)].
% 6.68/6.93 605 -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)].
% 6.68/6.93 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)].
% 6.68/6.93 606 -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)].
% 6.68/6.93 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)].
% 6.68/6.93 607 -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)].
% 6.68/6.93 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)].
% 6.68/6.93 608 -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)].
% 6.68/6.93 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)].
% 6.68/6.93 609 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom). [assumption].
% 6.68/6.93 610 class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_24) # label(axiom). [assumption].
% 6.68/6.93 611 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat_24) # label(axiom). [assumption].
% 6.68/6.93 612 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom). [assumption].
% 6.68/6.93 613 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_2) # label(axiom). [assumption].
% 6.68/6.93 614 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_3) # label(axiom). [assumption].
% 6.90/7.15 615 -class_Power_Orecpower(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Power_Orecpower_16) # label(axiom). [assumption].
% 6.90/7.15 616 -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].
% 6.90/7.15 617 -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].
% 6.90/7.15 618 -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].
% 6.90/7.15 619 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_8) # label(axiom). [assumption].
% 6.90/7.15 620 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom). [assumption].
% 6.90/7.15 621 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_11) # label(axiom). [assumption].
% 6.90/7.15 622 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_8) # label(axiom). [assumption].
% 6.90/7.15 623 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_2) # label(axiom). [assumption].
% 6.90/7.15 624 -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)].
% 6.90/7.15 625 -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)].
% 6.90/7.15 626 -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)].
% 6.90/7.15 627 -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)].
% 6.90/7.15 628 -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)].
% 6.90/7.15 629 -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)].
% 6.90/7.15 630 -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)].
% 6.90/7.15 631 -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)].
% 6.90/7.15 632 -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)].
% 6.90/7.15 633 class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(580,a,584,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(633,b,610,a)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(633,b,611,a)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(633,b,612,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(633,b,615,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(633,b,616,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(633,b,617,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(633,b,618,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(633,b,619,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(633,b,620,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(633,b,621,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(633,b,622,b)].
% 6.90/7.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(633,b,623,b)].
% 6.90/7.15 634 class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(585,a,584,b)].
% 6.90/7.15 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(634,b,610,a)].
% 6.90/7.15 Derived: class_HOL_Otimes(tc_nat). [resolve(634,b,611,a)].
% 6.90/7.15 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(634,b,612,b)].
% 6.90/7.15 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(634,b,615,b)].
% 6.90/7.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(634,b,616,b)].
% 6.90/7.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(634,b,617,b)].
% 6.90/7.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(634,b,618,b)].
% 6.90/7.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(634,b,619,b)].
% 6.90/7.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(634,b,620,b)].
% 6.90/7.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(634,b,621,b)].
% 6.90/7.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(634,b,622,b)].
% 6.90/7.15 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(634,b,623,b)].
% 6.90/7.15 635 c_times(c_1,A,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(598,a,584,b)].
% 6.90/7.15 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(635,b,610,a)].
% 6.90/7.15 Derived: c_times(c_1,A,tc_nat) = A. [resolve(635,b,611,a)].
% 6.90/7.15 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(635,b,612,b)].
% 6.90/7.15 636 c_times(A,c_1,B) = A | -class_OrderedGroup_Ocomm__monoid__mult(B). [resolve(599,a,584,b)].
% 6.90/7.15 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(636,b,610,a)].
% 6.90/7.15 Derived: c_times(A,c_1,tc_nat) = A. [resolve(636,b,611,a)].
% 6.90/7.15 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(636,b,612,b)].
% 6.90/7.15 637 -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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 638 -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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 639 -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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.15 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 640 -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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 641 -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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 642 -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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 643 -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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 644 -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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.90/7.16 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 645 -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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 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)].
% 6.99/7.24 646 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom). [assumption].
% 7.08/7.38 647 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom). [assumption].
% 7.08/7.38 648 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom). [assumption].
% 7.08/7.38 649 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom). [assumption].
% 7.08/7.38 650 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom). [assumption].
% 7.08/7.38 651 -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].
% 7.08/7.38 652 -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].
% 7.08/7.38 653 -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].
% 7.08/7.38 654 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom). [assumption].
% 7.08/7.38 655 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom). [assumption].
% 7.08/7.38 656 -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].
% 7.08/7.38 657 -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].
% 7.08/7.38 658 -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].
% 7.08/7.38 659 -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].
% 7.08/7.38 660 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom). [assumption].
% 7.08/7.38 661 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom). [assumption].
% 7.08/7.38 662 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_8) # label(axiom). [assumption].
% 7.08/7.38 663 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom). [assumption].
% 7.08/7.38 664 -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].
% 7.08/7.38 665 -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)].
% 7.08/7.38 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)].
% 7.08/7.38 666 -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)].
% 7.08/7.38 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)].
% 7.08/7.38 667 -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)].
% 7.08/7.38 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)].
% 7.08/7.38 668 -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)].
% 7.22/7.50 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)].
% 7.22/7.50 669 -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)].
% 7.22/7.50 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)].
% 7.22/7.50 670 -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)].
% 7.22/7.50 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)].
% 7.22/7.50 671 -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)].
% 7.22/7.50 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)].
% 7.22/7.50 672 -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)].
% 7.22/7.50 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)].
% 7.22/7.50 673 -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)].
% 7.22/7.50 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)].
% 7.22/7.50 674 -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)].
% 7.22/7.50 675 -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)].
% 7.22/7.50 676 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(181,b,142,a)].
% 7.22/7.50 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(676,a,664,b)].
% 7.22/7.50 677 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(183,a,181,b)].
% 7.22/7.50 678 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(184,a,181,b)].
% 7.22/7.50 679 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(223,a,219,b)].
% 7.22/7.50 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(679,b,652,b)].
% 7.22/7.50 680 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(224,a,219,b)].
% 7.22/7.50 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(680,b,652,b)].
% 7.22/7.50 681 c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(598,a,596,b)].
% 7.22/7.50 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(681,b,650,b)].
% 7.22/7.50 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(681,b,651,b)].
% 7.22/7.50 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(681,b,652,b)].
% 7.22/7.50 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(681,b,653,b)].
% 7.22/7.50 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(681,b,654,b)].
% 7.38/7.61 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(681,b,655,b)].
% 7.38/7.61 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(681,b,656,b)].
% 7.38/7.61 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(681,b,657,b)].
% 7.38/7.61 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(681,b,658,b)].
% 7.38/7.61 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(681,b,659,b)].
% 7.38/7.61 682 c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1(B). [resolve(599,a,596,b)].
% 7.38/7.61 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(682,b,650,b)].
% 7.38/7.61 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(682,b,651,b)].
% 7.38/7.61 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(682,b,652,b)].
% 7.38/7.61 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(682,b,653,b)].
% 7.38/7.61 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(682,b,654,b)].
% 7.38/7.61 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(682,b,655,b)].
% 7.38/7.61 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(682,b,656,b)].
% 7.38/7.61 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(682,b,657,b)].
% 7.38/7.61 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(682,b,658,b)].
% 7.38/7.61 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(682,b,659,b)].
% 7.38/7.61 683 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_1) # label(axiom). [assumption].
% 7.38/7.61 684 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom). [assumption].
% 7.38/7.61 685 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom). [assumption].
% 7.38/7.61 686 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom). [assumption].
% 7.38/7.61 687 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom). [assumption].
% 7.38/7.61 688 -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].
% 7.38/7.61 689 -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].
% 7.38/7.61 690 -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].
% 7.38/7.61 691 -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].
% 7.38/7.61 692 -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].
% 7.38/7.61 693 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_9) # label(axiom). [assumption].
% 7.38/7.61 694 -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].
% 7.38/7.61 695 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ofield_7) # label(axiom). [assumption].
% 7.38/7.61 696 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oidom_7) # label(axiom). [assumption].
% 7.38/7.61 697 -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].
% 7.38/7.61 698 -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].
% 7.52/7.76 699 -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].
% 7.52/7.76 700 -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)].
% 7.52/7.76 701 -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)].
% 7.52/7.76 702 -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)].
% 7.52/7.76 703 -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)].
% 7.52/7.76 704 -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)].
% 7.52/7.76 705 -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)].
% 7.52/7.76 706 -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)].
% 7.52/7.76 707 -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)].
% 7.52/7.76 708 -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)].
% 7.52/7.76 709 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(71,a,81,b)].
% 7.52/7.76 710 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(100,a,81,b)].
% 7.52/7.76 711 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(102,a,81,b)].
% 7.52/7.76 712 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(103,a,81,b)].
% 7.52/7.76 713 -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)].
% 7.52/7.76 714 -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)].
% 7.52/7.76 715 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A). [resolve(160,b,142,a)].
% 7.52/7.76 716 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(183,a,160,b)].
% 7.52/7.76 717 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(184,a,160,b)].
% 7.52/7.76 718 -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)].
% 7.52/7.76 719 -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)].
% 7.52/7.76 720 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(223,a,194,b)].
% 7.52/7.76 721 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(224,a,194,b)].
% 7.52/7.76 722 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(226,b,194,b)].
% 7.52/7.76 723 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(227,b,194,b)].
% 7.61/7.83 724 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(262,b,242,b)].
% 7.61/7.83 725 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(598,a,588,b)].
% 7.61/7.83 726 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(599,a,588,b)].
% 7.61/7.83 727 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(633,b,617,b)].
% 7.61/7.83 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(727,b,684,a)].
% 7.61/7.83 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(727,b,685,a)].
% 7.61/7.83 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(727,b,686,b)].
% 7.61/7.83 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(727,b,687,b)].
% 7.61/7.83 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(727,b,688,b)].
% 7.61/7.83 728 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(634,b,617,b)].
% 7.61/7.83 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(728,b,684,a)].
% 7.61/7.83 Derived: class_HOL_Otimes(tc_nat). [resolve(728,b,685,a)].
% 7.61/7.83 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(728,b,686,b)].
% 7.61/7.83 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(728,b,687,b)].
% 7.61/7.83 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(728,b,688,b)].
% 7.61/7.83 729 -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)].
% 7.61/7.83 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)].
% 7.61/7.83 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)].
% 7.61/7.83 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)].
% 7.61/7.83 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)].
% 7.61/7.83 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)].
% 7.61/7.83 730 -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)].
% 7.61/7.83 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)].
% 7.61/7.83 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)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(730,d,686,b)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(730,d,687,b)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(730,d,688,b)].
% 7.61/7.83 731 -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)].
% 7.61/7.83 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)].
% 7.61/7.83 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)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(731,d,686,b)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(731,d,687,b)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(731,d,688,b)].
% 7.61/7.83 732 -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)].
% 7.61/7.83 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)].
% 7.61/7.83 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)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Numeral_Onumber__ring(A). [resolve(732,d,686,b)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(732,d,687,b)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(732,d,688,b)].
% 7.61/7.83 733 -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)].
% 7.61/7.83 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)].
% 7.61/7.83 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)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Numeral_Onumber__ring(A). [resolve(733,d,686,b)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(733,d,687,b)].
% 7.61/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(733,d,688,b)].
% 7.61/7.83 734 -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)].
% 7.61/7.83 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)].
% 7.61/7.83 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)].
% 7.61/7.83 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_Numeral_Onumber__ring(A). [resolve(734,d,686,b)].
% 7.61/7.83 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_Power_Orecpower(A). [resolve(734,d,687,b)].
% 7.61/7.83 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_Ocomm__ring__1(A). [resolve(734,d,688,b)].
% 7.61/7.83 735 -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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 736 -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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 737 -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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 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)].
% 7.61/7.84 738 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(679,b,652,b)].
% 7.61/7.84 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(738,b,684,a)].
% 7.61/7.84 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(738,b,685,a)].
% 7.61/7.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(738,b,686,b)].
% 7.61/7.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(738,b,687,b)].
% 7.61/7.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(738,b,688,b)].
% 7.61/7.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(738,b,694,b)].
% 7.61/7.84 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(738,b,695,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(738,b,696,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(738,b,697,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(738,b,698,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(738,b,699,b)].
% 7.68/7.92 739 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(680,b,652,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(739,b,684,a)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(739,b,685,a)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(739,b,686,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(739,b,687,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(739,b,688,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(739,b,694,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(739,b,695,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(739,b,696,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(739,b,697,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(739,b,698,b)].
% 7.68/7.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(739,b,699,b)].
% 7.68/7.92 740 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(681,b,652,b)].
% 7.68/7.92 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(740,b,684,a)].
% 7.68/7.92 Derived: c_times(c_1,A,tc_nat) = A. [resolve(740,b,685,a)].
% 7.68/7.92 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(740,b,686,b)].
% 7.68/7.92 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(740,b,687,b)].
% 7.68/7.92 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(740,b,688,b)].
% 7.68/7.92 741 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(682,b,652,b)].
% 7.68/7.92 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(741,b,684,a)].
% 7.68/7.92 Derived: c_times(A,c_1,tc_nat) = A. [resolve(741,b,685,a)].
% 7.68/7.92 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(741,b,686,b)].
% 7.68/7.92 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(741,b,687,b)].
% 7.68/7.92 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(741,b,688,b)].
% 7.68/7.92 742 -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].
% 7.68/7.92 743 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom). [assumption].
% 7.68/7.92 744 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom). [assumption].
% 7.68/7.92 745 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom). [assumption].
% 7.68/7.92 746 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom). [assumption].
% 7.68/7.92 747 -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].
% 7.68/7.92 748 -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].
% 7.68/7.92 749 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_9) # label(axiom). [assumption].
% 7.83/8.08 750 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_9) # label(axiom). [assumption].
% 7.83/8.08 751 -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].
% 7.83/8.08 752 -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].
% 7.83/8.08 753 -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].
% 7.83/8.08 754 -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].
% 7.83/8.08 755 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_12) # label(axiom). [assumption].
% 7.83/8.08 756 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_5) # label(axiom). [assumption].
% 7.83/8.08 757 -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].
% 7.83/8.08 758 -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].
% 7.83/8.08 759 -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)].
% 7.83/8.08 760 -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)].
% 7.83/8.08 761 -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)].
% 7.83/8.08 762 -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)].
% 7.83/8.08 763 -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)].
% 7.83/8.08 764 -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)].
% 7.83/8.08 765 -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)].
% 7.83/8.08 766 -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)].
% 7.83/8.08 767 -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)].
% 7.83/8.08 768 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(107,b,102,a)].
% 7.83/8.08 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(768,a,754,b)].
% 7.83/8.08 769 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(107,b,103,a)].
% 7.83/8.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(769,a,754,b)].
% 7.83/8.08 770 -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)].
% 7.83/8.08 771 -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)].
% 8.06/8.26 772 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(183,a,182,b)].
% 8.06/8.26 773 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(184,a,182,b)].
% 8.06/8.26 774 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(223,a,220,b)].
% 8.06/8.26 775 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(224,a,220,b)].
% 8.06/8.26 776 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)].
% 8.06/8.26 777 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)].
% 8.06/8.26 778 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(346,b,345,b)].
% 8.06/8.26 779 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(380,a,379,b)].
% 8.06/8.26 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(779,b,748,b)].
% 8.06/8.26 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(779,b,753,b)].
% 8.06/8.26 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(779,b,754,b)].
% 8.06/8.26 780 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(381,a,379,b)].
% 8.06/8.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(780,b,748,b)].
% 8.06/8.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(780,b,753,b)].
% 8.06/8.26 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(780,b,754,b)].
% 8.06/8.26 781 c_times(c_1,A,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(598,a,597,b)].
% 8.06/8.26 782 c_times(A,c_1,B) = A | -class_Ring__and__Field_Osemiring__1__cancel(B). [resolve(599,a,597,b)].
% 8.06/8.26 783 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(676,a,664,b)].
% 8.06/8.26 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(783,b,743,a)].
% 8.06/8.26 Derived: class_HOL_Ozero(tc_nat). [resolve(783,b,744,a)].
% 8.06/8.26 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(783,b,745,b)].
% 8.06/8.26 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(783,b,746,b)].
% 8.06/8.26 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(783,b,747,b)].
% 8.06/8.26 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(783,b,748,b)].
% 8.06/8.26 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(783,b,749,b)].
% 8.06/8.26 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(783,b,750,b)].
% 8.06/8.26 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(783,b,751,b)].
% 8.06/8.26 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(783,b,752,b)].
% 8.06/8.26 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(783,b,753,b)].
% 8.06/8.26 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(783,b,754,b)].
% 8.06/8.26 784 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring__1_1) # label(axiom). [assumption].
% 8.06/8.26 785 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom). [assumption].
% 8.06/8.26 786 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom). [assumption].
% 8.06/8.26 787 -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].
% 8.06/8.26 788 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom). [assumption].
% 8.06/8.26 789 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom). [assumption].
% 8.06/8.26 790 -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].
% 8.13/8.42 791 -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].
% 8.13/8.42 792 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_11) # label(axiom). [assumption].
% 8.13/8.42 793 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom). [assumption].
% 8.13/8.42 794 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom). [assumption].
% 8.13/8.42 795 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom). [assumption].
% 8.13/8.42 796 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom). [assumption].
% 8.13/8.42 797 -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)].
% 8.13/8.42 798 -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)].
% 8.13/8.42 799 -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)].
% 8.13/8.42 800 -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)].
% 8.13/8.42 801 -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)].
% 8.13/8.42 802 -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)].
% 8.13/8.42 803 -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)].
% 8.13/8.42 804 -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)].
% 8.13/8.42 805 -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)].
% 8.13/8.42 806 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(71,a,99,b)].
% 8.13/8.42 807 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(100,a,99,b)].
% 8.13/8.42 808 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(102,a,99,b)].
% 8.13/8.42 809 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(103,a,99,b)].
% 8.13/8.42 810 -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)].
% 8.13/8.42 811 -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)].
% 8.13/8.42 812 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(183,a,178,b)].
% 8.13/8.42 813 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(184,a,178,b)].
% 8.13/8.42 814 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(217,a,212,b)].
% 8.13/8.42 815 -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)].
% 8.13/8.42 816 -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)].
% 8.22/8.46 817 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(223,a,212,b)].
% 8.22/8.46 818 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(224,a,212,b)].
% 8.22/8.46 819 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(226,b,212,b)].
% 8.22/8.46 820 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(227,b,212,b)].
% 8.22/8.46 821 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(307,a,304,b)].
% 8.22/8.46 822 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(308,a,304,b)].
% 8.22/8.46 823 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(346,b,343,b)].
% 8.22/8.46 824 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(380,a,373,b)].
% 8.22/8.46 825 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(381,a,373,b)].
% 8.22/8.46 826 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(386,b,373,b)].
% 8.22/8.46 827 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(389,c,373,b)].
% 8.22/8.46 828 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(390,c,373,b)].
% 8.22/8.46 829 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(391,b,373,b)].
% 8.22/8.46 830 -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)].
% 8.22/8.46 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)].
% 8.22/8.46 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)].
% 8.22/8.46 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)].
% 8.22/8.46 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)].
% 8.22/8.46 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)].
% 8.22/8.46 831 -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)].
% 8.22/8.46 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)].
% 8.22/8.46 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)].
% 8.22/8.46 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)].
% 8.22/8.46 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)].
% 8.30/8.50 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)].
% 8.30/8.50 832 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 833 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 834 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 835 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(598,a,595,b)].
% 8.30/8.50 836 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(599,a,595,b)].
% 8.30/8.50 837 -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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 838 -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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 839 -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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 840 -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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 841 -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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 842 -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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.50 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)].
% 8.30/8.52 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)].
% 8.30/8.52 843 -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)].
% 8.30/8.52 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)].
% 8.30/8.52 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)].
% 8.30/8.52 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)].
% 8.30/8.52 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)].
% 8.30/8.52 844 -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)].
% 8.30/8.52 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)].
% 8.30/8.52 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)].
% 8.30/8.52 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)].
% 8.30/8.52 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)].
% 8.30/8.52 845 -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)].
% 8.30/8.52 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)].
% 8.30/8.52 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)].
% 8.30/8.52 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)].
% 8.30/8.52 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)].
% 8.30/8.52 846 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(681,b,659,b)].
% 8.30/8.52 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(846,b,788,b)].
% 8.30/8.52 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(846,b,789,b)].
% 8.30/8.52 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(846,b,790,b)].
% 8.30/8.52 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(846,b,791,b)].
% 8.30/8.52 847 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(682,b,659,b)].
% 8.30/8.52 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(847,b,788,b)].
% 8.30/8.52 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(847,b,789,b)].
% 8.30/8.52 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(847,b,790,b)].
% 8.30/8.52 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(847,b,791,b)].
% 8.30/8.52 848 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(768,a,754,b)].
% 8.40/8.60 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(848,b,785,a)].
% 8.40/8.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(848,b,786,b)].
% 8.40/8.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(848,b,787,b)].
% 8.40/8.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(848,b,788,b)].
% 8.40/8.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(848,b,789,b)].
% 8.40/8.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(848,b,790,b)].
% 8.40/8.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(848,b,791,b)].
% 8.40/8.60 849 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(769,a,754,b)].
% 8.40/8.60 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(849,b,785,a)].
% 8.40/8.60 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(849,b,786,b)].
% 8.40/8.60 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(849,b,787,b)].
% 8.40/8.60 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(849,b,788,b)].
% 8.40/8.60 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(849,b,789,b)].
% 8.40/8.60 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(849,b,790,b)].
% 8.40/8.60 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(849,b,791,b)].
% 8.40/8.60 850 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(779,b,754,b)].
% 8.40/8.60 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(850,b,785,a)].
% 8.40/8.60 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(850,b,786,b)].
% 8.40/8.60 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(850,b,787,b)].
% 8.40/8.60 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(850,b,788,b)].
% 8.40/8.60 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(850,b,789,b)].
% 8.40/8.60 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(850,b,790,b)].
% 8.40/8.60 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(850,b,791,b)].
% 8.40/8.60 851 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(780,b,754,b)].
% 8.40/8.60 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(851,b,785,a)].
% 8.40/8.60 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(851,b,786,b)].
% 8.40/8.60 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(851,b,787,b)].
% 8.40/8.60 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(851,b,788,b)].
% 8.40/8.60 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(851,b,789,b)].
% 8.40/8.60 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(851,b,790,b)].
% 8.40/8.60 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(851,b,791,b)].
% 8.40/8.60 852 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(783,b,754,b)].
% 8.40/8.60 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(852,b,785,a)].
% 8.40/8.60 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(852,b,786,b)].
% 8.40/8.60 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(852,b,787,b)].
% 8.40/8.60 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(852,b,788,b)].
% 8.40/8.60 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(852,b,789,b)].
% 8.40/8.60 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(852,b,790,b)].
% 8.40/8.60 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(852,b,791,b)].
% 8.40/8.60 853 -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].
% 8.40/8.60 854 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom). [assumption].
% 8.40/8.60 855 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom). [assumption].
% 8.43/8.63 856 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom). [assumption].
% 8.43/8.63 857 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom). [assumption].
% 8.43/8.63 858 -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].
% 8.43/8.63 859 -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].
% 8.43/8.63 860 -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].
% 8.43/8.63 861 -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].
% 8.43/8.63 862 -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].
% 8.43/8.63 863 -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].
% 8.43/8.63 864 -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].
% 8.43/8.63 865 -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].
% 8.43/8.63 866 -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].
% 8.43/8.63 867 -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].
% 8.43/8.63 868 -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].
% 8.43/8.63 869 -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].
% 8.43/8.63 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(869,a,854,a)].
% 8.43/8.63 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(869,a,855,a)].
% 8.43/8.63 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(869,a,856,b)].
% 8.43/8.63 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Power_Orecpower(A). [resolve(869,a,857,b)].
% 8.43/8.63 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(869,a,858,b)].
% 8.43/8.63 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(869,a,864,b)].
% 8.43/8.63 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(869,a,865,b)].
% 8.43/8.63 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(869,a,866,b)].
% 8.43/8.63 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(869,a,867,b)].
% 8.43/8.63 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(869,a,868,b)].
% 8.43/8.63 870 -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].
% 8.43/8.63 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(870,a,854,a)].
% 8.43/8.63 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(870,a,855,a)].
% 8.43/8.63 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(870,a,856,b)].
% 8.43/8.63 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Power_Orecpower(A). [resolve(870,a,857,b)].
% 8.43/8.63 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(870,a,858,b)].
% 8.43/8.63 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(870,a,864,b)].
% 8.44/8.64 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(870,a,865,b)].
% 8.44/8.64 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(870,a,866,b)].
% 8.44/8.64 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(870,a,867,b)].
% 8.44/8.64 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(870,a,868,b)].
% 8.44/8.64 871 -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].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 872 -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].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.64 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)].
% 8.44/8.66 873 -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].
% 8.44/8.66 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(873,a,854,a)].
% 8.44/8.66 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(873,a,855,a)].
% 8.44/8.66 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Numeral_Onumber__ring(B). [resolve(873,a,856,b)].
% 8.44/8.66 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Power_Orecpower(B). [resolve(873,a,857,b)].
% 8.44/8.66 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)].
% 8.44/8.66 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(873,a,864,b)].
% 8.44/8.66 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oidom(B). [resolve(873,a,865,b)].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 874 -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].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 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)].
% 8.44/8.66 875 -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].
% 8.44/8.66 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(875,a,854,a)].
% 8.44/8.66 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(875,a,855,a)].
% 8.44/8.66 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Numeral_Onumber__ring(A). [resolve(875,a,856,b)].
% 8.44/8.66 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Power_Orecpower(A). [resolve(875,a,857,b)].
% 8.44/8.66 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(875,a,858,b)].
% 8.44/8.66 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(875,a,864,b)].
% 8.44/8.66 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(875,a,865,b)].
% 8.44/8.66 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(875,a,866,b)].
% 8.44/8.67 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(875,a,867,b)].
% 8.44/8.67 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__semidom(A). [resolve(875,a,868,b)].
% 8.44/8.67 876 -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].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 877 -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].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.44/8.67 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)].
% 8.58/8.80 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)].
% 8.58/8.80 878 -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].
% 8.58/8.80 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(878,a,854,a)].
% 8.58/8.80 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(878,a,855,a)].
% 8.58/8.80 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(878,a,856,b)].
% 8.58/8.80 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Power_Orecpower(A). [resolve(878,a,857,b)].
% 8.58/8.80 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(878,a,858,b)].
% 8.58/8.80 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(878,a,864,b)].
% 8.58/8.80 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(878,a,865,b)].
% 8.58/8.80 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(878,a,866,b)].
% 8.58/8.80 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(878,a,867,b)].
% 8.58/8.80 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(878,a,868,b)].
% 8.58/8.80 879 -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)].
% 8.58/8.80 880 -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)].
% 8.58/8.80 881 -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)].
% 8.58/8.80 882 -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)].
% 8.58/8.80 883 -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)].
% 8.58/8.80 884 -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)].
% 8.58/8.80 885 -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)].
% 8.58/8.80 886 -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)].
% 8.58/8.80 887 -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)].
% 8.58/8.80 888 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(71,a,82,b)].
% 8.58/8.80 889 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(100,a,82,b)].
% 8.58/8.80 890 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(102,a,82,b)].
% 8.58/8.80 891 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(103,a,82,b)].
% 8.58/8.80 892 -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)].
% 8.58/8.80 893 -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)].
% 8.58/8.80 894 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Ozero(A). [resolve(161,b,142,a)].
% 8.71/8.89 895 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(183,a,161,b)].
% 8.71/8.89 896 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(184,a,161,b)].
% 8.71/8.89 897 -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)].
% 8.71/8.89 898 -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)].
% 8.71/8.89 899 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(223,a,195,b)].
% 8.71/8.89 900 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(224,a,195,b)].
% 8.71/8.89 901 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(226,b,195,b)].
% 8.71/8.89 902 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(227,b,195,b)].
% 8.71/8.89 903 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(262,b,243,b)].
% 8.71/8.89 904 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)].
% 8.71/8.89 905 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)].
% 8.71/8.89 906 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(346,b,328,b)].
% 8.71/8.89 907 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(380,a,358,b)].
% 8.71/8.89 908 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(381,a,358,b)].
% 8.71/8.89 909 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(386,b,358,b)].
% 8.71/8.89 910 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)].
% 8.71/8.89 911 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)].
% 8.71/8.89 912 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(391,b,358,b)].
% 8.71/8.89 913 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(598,a,589,b)].
% 8.71/8.89 914 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(599,a,589,b)].
% 8.71/8.89 915 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(633,b,618,b)].
% 8.71/8.89 916 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(634,b,618,b)].
% 8.71/8.89 917 -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)].
% 8.71/8.89 918 -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)].
% 8.71/8.89 919 -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)].
% 8.71/8.89 920 -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)].
% 8.71/8.89 921 -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)].
% 8.71/8.89 922 -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)].
% 8.71/8.89 923 -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)].
% 9.04/9.30 924 -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)].
% 9.04/9.30 925 -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)].
% 9.04/9.30 926 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(681,b,653,b)].
% 9.04/9.30 927 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(682,b,653,b)].
% 9.04/9.30 928 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(738,b,694,b)].
% 9.04/9.30 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(928,b,854,a)].
% 9.04/9.30 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(928,b,855,a)].
% 9.04/9.30 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(928,b,856,b)].
% 9.04/9.30 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(928,b,857,b)].
% 9.04/9.30 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(928,b,858,b)].
% 9.04/9.30 929 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(739,b,694,b)].
% 9.04/9.30 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(929,b,854,a)].
% 9.04/9.30 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(929,b,855,a)].
% 9.04/9.30 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(929,b,856,b)].
% 9.04/9.30 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(929,b,857,b)].
% 9.04/9.30 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(929,b,858,b)].
% 9.04/9.30 930 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(779,b,748,b)].
% 9.04/9.30 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(930,b,855,a)].
% 9.04/9.30 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(930,b,857,b)].
% 9.04/9.30 931 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__semiring__1__cancel(B). [resolve(780,b,748,b)].
% 9.04/9.30 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(931,b,855,a)].
% 9.04/9.30 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(931,b,857,b)].
% 9.04/9.30 932 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(783,b,748,b)].
% 9.04/9.30 Derived: class_HOL_Ozero(tc_nat). [resolve(932,b,855,a)].
% 9.04/9.30 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(932,b,857,b)].
% 9.04/9.30 933 -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].
% 9.04/9.30 934 class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_30) # label(axiom). [assumption].
% 9.04/9.30 935 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom). [assumption].
% 9.04/9.30 936 -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_14) # label(axiom). [assumption].
% 9.04/9.30 937 -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].
% 9.04/9.30 938 -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].
% 9.04/9.30 939 -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].
% 9.04/9.30 940 -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].
% 9.04/9.30 941 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Ofield_0) # label(axiom). [assumption].
% 9.13/9.32 942 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oidom_0) # label(axiom). [assumption].
% 9.13/9.32 943 -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].
% 9.13/9.32 944 -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].
% 9.13/9.32 945 -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].
% 9.13/9.32 Derived: c_in(c_0,c_IntDef_OInts,tc_IntDef_Oint). [resolve(945,a,934,a)].
% 9.13/9.32 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Numeral_Onumber__ring(A). [resolve(945,a,935,b)].
% 9.13/9.32 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(945,a,941,b)].
% 9.13/9.32 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(945,a,942,b)].
% 9.13/9.32 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(945,a,943,b)].
% 9.13/9.32 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(945,a,944,b)].
% 9.13/9.32 946 -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].
% 9.13/9.32 Derived: c_in(c_1,c_IntDef_OInts,tc_IntDef_Oint). [resolve(946,a,934,a)].
% 9.13/9.32 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Numeral_Onumber__ring(A). [resolve(946,a,935,b)].
% 9.13/9.32 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(946,a,941,b)].
% 9.13/9.32 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(946,a,942,b)].
% 9.13/9.32 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(946,a,943,b)].
% 9.13/9.32 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(946,a,944,b)].
% 9.13/9.32 947 -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].
% 9.13/9.32 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(947,a,934,a)].
% 9.13/9.32 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)].
% 9.13/9.32 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)].
% 9.13/9.32 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)].
% 9.13/9.32 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)].
% 9.13/9.32 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)].
% 9.13/9.32 948 -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].
% 9.13/9.32 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)].
% 9.13/9.32 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)].
% 9.13/9.32 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)].
% 9.13/9.32 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)].
% 9.13/9.33 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_Oordered__field(B). [resolve(948,a,943,b)].
% 9.13/9.33 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_Oordered__idom(B). [resolve(948,a,944,b)].
% 9.13/9.33 949 -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].
% 9.13/9.33 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(949,a,934,a)].
% 9.13/9.33 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)].
% 9.13/9.33 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(949,a,941,b)].
% 9.13/9.33 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)].
% 9.13/9.33 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)].
% 9.13/9.33 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)].
% 9.13/9.33 950 -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].
% 9.13/9.33 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(950,a,934,a)].
% 9.13/9.33 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_Numeral_Onumber__ring(B). [resolve(950,a,935,b)].
% 9.13/9.33 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(950,a,941,b)].
% 9.13/9.33 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_Oidom(B). [resolve(950,a,942,b)].
% 9.13/9.33 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_Oordered__field(B). [resolve(950,a,943,b)].
% 9.13/9.33 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_Oordered__idom(B). [resolve(950,a,944,b)].
% 9.13/9.33 951 -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].
% 9.13/9.33 Derived: c_IntDef_Oof__int(c_1,tc_IntDef_Oint) = c_1. [resolve(951,a,934,a)].
% 9.13/9.33 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Numeral_Onumber__ring(A). [resolve(951,a,935,b)].
% 9.13/9.33 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(951,a,941,b)].
% 9.13/9.33 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(951,a,942,b)].
% 9.13/9.33 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(951,a,943,b)].
% 9.13/9.33 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(951,a,944,b)].
% 9.13/9.33 952 -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].
% 9.13/9.33 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(952,a,934,a)].
% 9.13/9.33 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_Numeral_Onumber__ring(C). [resolve(952,a,935,b)].
% 9.13/9.33 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(952,a,941,b)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 953 -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].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 954 -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].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 955 -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].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.34 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)].
% 9.13/9.36 956 -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].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 957 -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].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 958 -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].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 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)].
% 9.13/9.36 959 -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].
% 9.13/9.38 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)].
% 9.13/9.38 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)].
% 9.13/9.38 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)].
% 9.13/9.38 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)].
% 9.13/9.38 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)].
% 9.13/9.38 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)].
% 9.13/9.38 960 -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].
% 9.13/9.38 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)].
% 9.13/9.38 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)].
% 9.13/9.38 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)].
% 9.13/9.38 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)].
% 9.13/9.38 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)].
% 9.13/9.38 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)].
% 9.21/9.39 961 -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].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 962 -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].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 963 -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].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.21/9.39 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)].
% 9.30/9.49 964 -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)].
% 9.30/9.49 965 -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)].
% 9.30/9.49 966 -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)].
% 9.30/9.49 967 -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)].
% 9.30/9.49 968 -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)].
% 9.30/9.49 969 -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)].
% 9.30/9.49 970 -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)].
% 9.30/9.49 971 -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)].
% 9.30/9.49 972 -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)].
% 9.30/9.49 973 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(71,a,77,b)].
% 9.30/9.49 974 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(100,a,77,b)].
% 9.30/9.49 975 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(102,a,77,b)].
% 9.30/9.49 976 -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)].
% 9.30/9.49 977 -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)].
% 9.30/9.49 978 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(119,a,116,b)].
% 9.30/9.49 979 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(135,b,116,b)].
% 9.30/9.49 980 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(136,b,116,b)].
% 9.30/9.49 981 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(138,b,116,b)].
% 9.30/9.49 982 -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)].
% 9.30/9.49 983 -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)].
% 9.30/9.49 984 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(183,a,157,b)].
% 9.30/9.49 985 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(184,a,157,b)].
% 9.30/9.49 986 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(217,a,191,b)].
% 9.30/9.49 987 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(223,a,191,b)].
% 9.30/9.49 988 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(224,a,191,b)].
% 9.30/9.49 989 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(226,b,191,b)].
% 9.30/9.49 990 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(227,b,191,b)].
% 9.34/9.55 991 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(262,b,234,b)].
% 9.34/9.55 992 -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)].
% 9.34/9.55 993 -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)].
% 9.34/9.55 994 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(265,b,234,b)].
% 9.34/9.55 995 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(266,b,234,b)].
% 9.34/9.55 996 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(268,b,234,b)].
% 9.34/9.55 997 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(269,b,234,b)].
% 9.34/9.55 998 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)].
% 9.34/9.55 999 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)].
% 9.34/9.55 1000 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(346,b,326,b)].
% 9.34/9.55 1001 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(380,a,356,b)].
% 9.34/9.55 1002 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(381,a,356,b)].
% 9.34/9.55 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)].
% 9.34/9.55 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)].
% 9.34/9.55 1005 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(391,b,356,b)].
% 9.34/9.55 1006 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(410,a,397,b)].
% 9.34/9.55 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)].
% 9.34/9.55 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)].
% 9.34/9.55 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)].
% 9.34/9.55 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)].
% 9.34/9.55 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)].
% 9.34/9.55 1012 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(439,b,397,b)].
% 9.34/9.55 1013 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(440,b,397,b)].
% 9.34/9.55 1014 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(441,b,397,b)].
% 9.34/9.55 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)].
% 9.34/9.55 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)].
% 9.34/9.55 1017 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(444,b,397,b)].
% 9.34/9.55 1018 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(480,b,452,b)].
% 9.34/9.55 1019 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(598,a,587,b)].
% 9.34/9.55 1020 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(599,a,587,b)].
% 9.34/9.55 1021 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(633,b,616,b)].
% 9.34/9.55 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 1031 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(681,b,651,b)].
% 9.34/9.57 1032 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(682,b,651,b)].
% 9.34/9.57 1033 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(727,b,688,b)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.57 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 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)].
% 9.34/9.58 1043 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(738,b,688,b)].
% 9.34/9.58 1044 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(739,b,688,b)].
% 9.34/9.58 1045 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(740,b,688,b)].
% 9.34/9.58 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(1045,b,934,a)].
% 9.34/9.58 Derived: c_times(c_1,A,B) = A | -class_Numeral_Onumber__ring(B). [resolve(1045,b,935,b)].
% 9.34/9.58 1046 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(741,b,688,b)].
% 9.34/9.58 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(1046,b,934,a)].
% 9.34/9.58 Derived: c_times(A,c_1,B) = A | -class_Numeral_Onumber__ring(B). [resolve(1046,b,935,b)].
% 9.34/9.58 1047 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(783,b,747,b)].
% 9.34/9.58 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 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)].
% 9.34/9.60 1053 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(848,b,787,b)].
% 9.34/9.60 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1053,b,934,a)].
% 9.34/9.60 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(1053,b,935,b)].
% 9.34/9.60 1054 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(850,b,787,b)].
% 9.34/9.60 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1054,b,934,a)].
% 9.34/9.60 Derived: c_times(c_0,A,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(1054,b,935,b)].
% 9.34/9.60 1055 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring__1(B). [resolve(851,b,787,b)].
% 9.34/9.60 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1055,b,934,a)].
% 9.34/9.60 Derived: c_times(A,c_0,B) = c_0 | -class_Numeral_Onumber__ring(B). [resolve(1055,b,935,b)].
% 9.34/9.60 1056 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(852,b,787,b)].
% 9.34/9.60 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1056,b,934,a)].
% 9.34/9.60 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(1056,b,935,b)].
% 9.34/9.60 1057 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(869,a,858,b)].
% 9.34/9.60 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1057,b,934,a)].
% 9.34/9.60 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(1057,b,935,b)].
% 9.34/9.60 1058 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(870,a,858,b)].
% 9.34/9.61 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(1058,b,934,a)].
% 9.34/9.61 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Numeral_Onumber__ring(A). [resolve(1058,b,935,b)].
% 9.34/9.61 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)].
% 9.34/9.61 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)].
% 9.34/9.61 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)].
% 9.34/9.61 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)].
% 9.34/9.61 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)].
% 9.34/9.61 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_times(C,A,B),c_IntDef_ONats,B) | -class_Numeral_Onumber__ring(B). [resolve(1060,d,935,b)].
% 9.34/9.61 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)].
% 9.34/9.61 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(1061,b,934,a)].
% 9.34/9.61 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Numeral_Onumber__ring(B). [resolve(1061,b,935,b)].
% 9.34/9.61 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)].
% 9.34/9.61 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)].
% 9.34/9.61 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)].
% 9.34/9.61 1063 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(875,a,858,b)].
% 9.34/9.61 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(1063,b,934,a)].
% 9.34/9.61 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Numeral_Onumber__ring(A). [resolve(1063,b,935,b)].
% 9.34/9.61 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)].
% 9.34/9.61 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)].
% 9.34/9.61 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),C) = c_plus(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Numeral_Onumber__ring(C). [resolve(1064,b,935,b)].
% 9.34/9.61 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)].
% 9.34/9.61 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)].
% 9.34/9.61 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)].
% 9.34/9.61 1066 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(878,a,858,b)].
% 9.34/9.61 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(1066,b,934,a)].
% 9.34/9.61 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Numeral_Onumber__ring(A). [resolve(1066,b,935,b)].
% 9.34/9.61 1067 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(928,b,858,b)].
% 9.34/9.61 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1067,b,934,a)].
% 9.34/9.61 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(1067,b,935,b)].
% 9.34/9.61 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1067,b,941,b)].
% 9.34/9.61 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1067,b,942,b)].
% 9.43/9.70 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1067,b,943,b)].
% 9.43/9.70 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1067,b,944,b)].
% 9.43/9.70 1068 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(929,b,858,b)].
% 9.43/9.70 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1068,b,934,a)].
% 9.43/9.70 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(1068,b,935,b)].
% 9.43/9.70 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1068,b,941,b)].
% 9.43/9.70 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1068,b,942,b)].
% 9.43/9.70 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1068,b,943,b)].
% 9.43/9.70 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1068,b,944,b)].
% 9.43/9.70 1069 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom). [assumption].
% 9.43/9.70 1070 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom). [assumption].
% 9.43/9.70 1071 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom). [assumption].
% 9.43/9.70 1072 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom). [assumption].
% 9.43/9.70 1073 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom). [assumption].
% 9.43/9.70 1074 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom). [assumption].
% 9.43/9.70 1075 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom). [assumption].
% 9.43/9.70 1076 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom). [assumption].
% 9.43/9.70 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].
% 9.43/9.70 1078 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom). [assumption].
% 9.43/9.70 1079 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom). [assumption].
% 9.43/9.70 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1079,b,1069,a)].
% 9.43/9.70 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].
% 9.43/9.70 1081 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom). [assumption].
% 9.43/9.70 1082 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom). [assumption].
% 9.43/9.70 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].
% 9.43/9.70 1084 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom). [assumption].
% 9.43/9.70 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].
% 9.43/9.70 1086 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom). [assumption].
% 9.61/9.79 1087 -class_LOrder_Omeet__semilorder(A) | c_LOrder_Omeet(B,B,A) = B # label(cls_LOrder_Omeet__idempotent_0) # label(axiom). [assumption].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1087,a,1070,a)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1087,a,1071,a)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1087,a,1072,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1087,a,1073,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1087,a,1074,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1087,a,1075,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1087,a,1076,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1087,a,1077,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1087,a,1078,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1087,a,1079,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1087,a,1080,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1087,a,1081,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1087,a,1082,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1087,a,1083,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1087,a,1084,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1087,a,1085,b)].
% 9.61/9.79 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1087,a,1086,b)].
% 9.61/9.79 1088 -class_LOrder_Omeet__semilorder(A) | c_lessequals(B,B,A). [resolve(7,b,2,a)].
% 9.61/9.79 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1088,a,1070,a)].
% 9.61/9.79 Derived: c_lessequals(A,A,tc_nat). [resolve(1088,a,1071,a)].
% 9.61/9.79 Derived: c_lessequals(A,A,B) | -class_LOrder_Olorder(B). [resolve(1088,a,1072,b)].
% 9.61/9.79 1089 class_Orderings_Oord(A) | -class_LOrder_Omeet__semilorder(A). [resolve(18,a,7,b)].
% 9.61/9.79 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1089,b,1070,a)].
% 9.61/9.79 Derived: class_Orderings_Oord(tc_nat). [resolve(1089,b,1071,a)].
% 9.61/9.79 Derived: class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(1089,b,1072,b)].
% 9.61/9.79 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1089,b,1080,b)].
% 9.61/9.79 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1089,b,1081,b)].
% 9.61/9.79 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1089,b,1082,b)].
% 9.61/9.79 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1089,b,1083,b)].
% 9.61/9.79 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1089,b,1084,b)].
% 9.61/9.79 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1089,b,1085,b)].
% 9.61/9.79 1090 -c_less(A,A,B) | -class_LOrder_Omeet__semilorder(B). [resolve(33,a,7,b)].
% 9.61/9.79 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1090,b,1070,a)].
% 9.61/9.79 Derived: -c_less(A,A,tc_nat). [resolve(1090,b,1071,a)].
% 9.61/9.79 Derived: -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(1090,b,1072,b)].
% 9.61/9.79 1091 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(34,a,7,b)].
% 9.61/9.79 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1091,c,1070,a)].
% 9.61/9.79 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1091,c,1071,a)].
% 9.61/9.79 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1091,c,1072,b)].
% 9.61/9.79 1092 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Omeet__semilorder(B). [resolve(35,a,7,b)].
% 9.63/9.81 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1092,b,1070,a)].
% 9.63/9.81 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1092,b,1071,a)].
% 9.63/9.81 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(1092,b,1072,b)].
% 9.63/9.81 1093 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(36,a,7,b)].
% 9.63/9.81 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1093,c,1070,a)].
% 9.63/9.81 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1093,c,1071,a)].
% 9.63/9.81 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1093,c,1072,b)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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)].
% 9.63/9.81 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(1097,c,1070,a)].
% 9.63/9.81 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(1097,c,1071,a)].
% 9.63/9.81 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)].
% 9.63/9.81 1098 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Omeet__semilorder(C). [resolve(41,a,7,b)].
% 9.63/9.81 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1098,c,1070,a)].
% 9.63/9.81 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1098,c,1071,a)].
% 9.82/10.04 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1098,c,1072,b)].
% 9.82/10.04 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)].
% 9.82/10.04 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)].
% 9.82/10.04 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)].
% 9.82/10.04 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(1099,b,1072,b)].
% 9.82/10.04 1100 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom). [assumption].
% 9.82/10.04 1101 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom). [assumption].
% 9.82/10.04 1102 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom). [assumption].
% 9.82/10.04 1103 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom). [assumption].
% 9.82/10.04 1104 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom). [assumption].
% 9.82/10.04 1105 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom). [assumption].
% 9.82/10.04 1106 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom). [assumption].
% 9.82/10.04 1107 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom). [assumption].
% 9.82/10.04 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].
% 9.82/10.04 1109 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom). [assumption].
% 9.82/10.04 1110 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom). [assumption].
% 9.82/10.04 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].
% 9.82/10.04 1112 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom). [assumption].
% 9.82/10.04 1113 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 9.82/10.04 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].
% 9.82/10.04 1115 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom). [assumption].
% 9.82/10.04 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].
% 9.82/10.04 1117 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom). [assumption].
% 9.82/10.04 1118 -class_LOrder_Ojoin__semilorder(A) | c_LOrder_Ojoin(B,B,A) = B # label(cls_LOrder_Ojoin__idempotent_0) # label(axiom). [assumption].
% 9.82/10.04 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1118,a,1101,a)].
% 9.82/10.04 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1118,a,1102,a)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1118,a,1103,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1118,a,1104,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1118,a,1105,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1118,a,1106,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1118,a,1107,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1118,a,1108,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1118,a,1109,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1118,a,1110,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1118,a,1111,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1118,a,1112,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1118,a,1113,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1118,a,1114,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1118,a,1115,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1118,a,1116,b)].
% 10.13/10.36 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1118,a,1117,b)].
% 10.13/10.36 1119 -class_LOrder_Ojoin__semilorder(A) | c_lessequals(B,B,A). [resolve(5,b,2,a)].
% 10.13/10.36 1120 class_Orderings_Oord(A) | -class_LOrder_Ojoin__semilorder(A). [resolve(18,a,5,b)].
% 10.13/10.36 1121 -c_less(A,A,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(33,a,5,b)].
% 10.13/10.36 1122 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(34,a,5,b)].
% 10.13/10.36 1123 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(35,a,5,b)].
% 10.13/10.36 1124 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(36,a,5,b)].
% 10.13/10.36 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)].
% 10.13/10.36 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)].
% 10.13/10.36 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)].
% 10.13/10.36 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)].
% 10.13/10.36 1129 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Ojoin__semilorder(C). [resolve(41,a,5,b)].
% 10.13/10.36 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)].
% 10.13/10.36 1131 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom). [assumption].
% 10.13/10.36 1132 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom). [assumption].
% 10.13/10.36 1133 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom). [assumption].
% 10.13/10.36 1134 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom). [assumption].
% 10.13/10.36 1135 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom). [assumption].
% 10.13/10.36 1136 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom). [assumption].
% 10.34/10.60 1137 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom). [assumption].
% 10.34/10.60 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].
% 10.34/10.60 1139 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom). [assumption].
% 10.34/10.60 1140 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom). [assumption].
% 10.34/10.60 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].
% 10.34/10.60 1142 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom). [assumption].
% 10.34/10.60 1143 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom). [assumption].
% 10.34/10.60 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].
% 10.34/10.60 1145 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom). [assumption].
% 10.34/10.60 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].
% 10.34/10.60 1147 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom). [assumption].
% 10.34/10.60 1148 -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(6,b,2,a)].
% 10.34/10.60 1149 class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(18,a,6,b)].
% 10.34/10.60 1150 -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(33,a,6,b)].
% 10.34/10.60 1151 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(34,a,6,b)].
% 10.34/10.60 1152 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(35,a,6,b)].
% 10.34/10.60 1153 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(36,a,6,b)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 1158 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(41,a,6,b)].
% 10.34/10.60 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)].
% 10.34/10.60 1160 c_LOrder_Omeet(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1087,a,1072,b)].
% 10.34/10.60 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1160,b,1132,a)].
% 10.34/10.60 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1160,b,1133,a)].
% 10.34/10.60 1161 c_lessequals(A,A,B) | -class_LOrder_Olorder(B). [resolve(1088,a,1072,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1161,b,1132,a)].
% 10.34/10.60 Derived: c_lessequals(A,A,tc_nat). [resolve(1161,b,1133,a)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1161,b,1134,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1161,b,1135,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1161,b,1136,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1161,b,1137,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1161,b,1138,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1161,b,1139,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1161,b,1140,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1161,b,1141,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1161,b,1142,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1161,b,1143,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1161,b,1144,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1161,b,1145,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1161,b,1146,b)].
% 10.34/10.60 Derived: c_lessequals(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1161,b,1147,b)].
% 10.34/10.60 1162 class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(1089,b,1072,b)].
% 10.34/10.60 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1162,b,1132,a)].
% 10.34/10.60 Derived: class_Orderings_Oord(tc_nat). [resolve(1162,b,1133,a)].
% 10.34/10.60 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1162,b,1134,b)].
% 10.34/10.60 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1162,b,1135,b)].
% 10.34/10.60 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1162,b,1136,b)].
% 10.34/10.60 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1162,b,1137,b)].
% 10.34/10.60 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1162,b,1138,b)].
% 10.34/10.60 Derived: class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(1162,b,1139,b)].
% 10.34/10.60 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1162,b,1140,b)].
% 10.34/10.60 Derived: class_Orderings_Oord(A) | -class_Wellfounded__Recursion_Owellorder(A). [resolve(1162,b,1147,b)].
% 10.34/10.60 1163 -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(1090,b,1072,b)].
% 10.34/10.60 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1163,b,1132,a)].
% 10.34/10.60 Derived: -c_less(A,A,tc_nat). [resolve(1163,b,1133,a)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1163,b,1134,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1163,b,1135,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1163,b,1136,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1163,b,1137,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1163,b,1138,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1163,b,1139,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1163,b,1140,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1163,b,1141,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1163,b,1142,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1163,b,1143,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1163,b,1144,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1163,b,1145,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1163,b,1146,b)].
% 10.34/10.60 Derived: -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1163,b,1147,b)].
% 10.34/10.60 1164 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1091,c,1072,b)].
% 10.34/10.60 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1164,c,1132,a)].
% 10.34/10.60 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1164,c,1133,a)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1164,c,1139,b)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.60 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)].
% 10.34/10.61 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1164,c,1147,b)].
% 10.34/10.61 1165 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_LOrder_Olorder(B). [resolve(1092,b,1072,b)].
% 10.34/10.61 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1165,b,1132,a)].
% 10.34/10.61 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1165,b,1133,a)].
% 10.34/10.61 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1165,b,1134,b)].
% 10.34/10.61 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)].
% 10.34/10.61 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)].
% 10.34/10.61 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)].
% 10.34/10.61 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)].
% 10.34/10.61 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(1165,b,1139,b)].
% 10.34/10.61 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)].
% 10.34/10.61 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)].
% 10.34/10.61 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)].
% 10.34/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1165,b,1147,b)].
% 10.44/10.61 1166 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1093,c,1072,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1166,c,1132,a)].
% 10.44/10.61 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1166,c,1133,a)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1166,c,1139,b)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1166,c,1147,b)].
% 10.44/10.61 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)].
% 10.44/10.61 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(1167,c,1132,a)].
% 10.44/10.61 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(1167,c,1133,a)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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(1167,c,1138,b)].
% 10.44/10.61 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)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1167,c,1140,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1167,c,1141,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1167,c,1142,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1167,c,1143,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1167,c,1144,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1167,c,1145,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1167,c,1146,b)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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(1168,c,1132,a)].
% 10.44/10.61 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(1168,c,1133,a)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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(1168,c,1138,b)].
% 10.44/10.61 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)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1168,c,1140,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1168,c,1141,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1168,c,1142,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1168,c,1143,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1168,c,1144,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1168,c,1145,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1168,c,1146,b)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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(1169,c,1132,a)].
% 10.44/10.61 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(1169,c,1133,a)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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(1169,c,1138,b)].
% 10.44/10.61 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)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1169,c,1140,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1169,c,1141,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1169,c,1142,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1169,c,1143,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1169,c,1144,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1169,c,1145,b)].
% 10.44/10.61 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1169,c,1146,b)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1170,c,1140,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1170,c,1141,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1170,c,1142,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1170,c,1143,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1170,c,1144,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1170,c,1145,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1170,c,1146,b)].
% 10.44/10.61 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)].
% 10.44/10.61 1171 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_LOrder_Olorder(C). [resolve(1098,c,1072,b)].
% 10.44/10.61 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1171,c,1132,a)].
% 10.44/10.61 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1171,c,1133,a)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1171,c,1139,b)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1171,c,1147,b)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 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)].
% 10.44/10.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1172,b,1134,b)].
% 10.44/10.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1172,b,1135,b)].
% 10.44/10.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1172,b,1136,b)].
% 10.44/10.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1172,b,1137,b)].
% 10.44/10.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1172,b,1138,b)].
% 10.44/10.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(1172,b,1139,b)].
% 10.44/10.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1172,b,1140,b)].
% 10.44/10.61 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1172,b,1141,b)].
% 10.53/10.71 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)].
% 10.53/10.71 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)].
% 10.53/10.71 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)].
% 10.53/10.71 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)].
% 10.53/10.71 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)].
% 10.53/10.71 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)].
% 10.53/10.71 1173 c_LOrder_Ojoin(A,A,B) = A | -class_LOrder_Olorder(B). [resolve(1118,a,1103,b)].
% 10.53/10.71 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1173,b,1132,a)].
% 10.53/10.71 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1173,b,1133,a)].
% 10.53/10.71 1174 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom). [assumption].
% 10.53/10.71 1175 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom). [assumption].
% 10.53/10.71 1176 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom). [assumption].
% 10.53/10.71 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].
% 10.53/10.71 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].
% 10.53/10.71 1179 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom). [assumption].
% 10.53/10.71 1180 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 10.53/10.71 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].
% 10.53/10.71 1182 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom). [assumption].
% 10.53/10.71 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].
% 10.53/10.71 1184 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom). [assumption].
% 10.53/10.71 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].
% 10.53/10.71 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)].
% 10.53/10.71 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)].
% 10.53/10.71 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)].
% 10.53/10.71 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)].
% 10.53/10.72 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)].
% 10.53/10.72 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)].
% 10.53/10.72 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)].
% 10.53/10.72 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)].
% 10.53/10.72 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.73 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.74 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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)].
% 10.53/10.75 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].
% 10.53/10.75 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.76 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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].
% 10.53/10.77 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1194,a,1175,a)].
% 10.53/10.77 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1194,a,1176,a)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1194,a,1184,b)].
% 10.53/10.77 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].
% 10.53/10.77 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1195,a,1175,a)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.77 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)].
% 10.53/10.78 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1195,a,1182,b)].
% 10.53/10.78 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1195,a,1183,b)].
% 10.53/10.78 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1195,a,1184,b)].
% 10.53/10.78 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].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1196,a,1175,a)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1196,a,1176,a)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1196,a,1177,b)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1196,a,1178,b)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1196,a,1179,b)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1196,a,1180,b)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1196,a,1181,b)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1196,a,1182,b)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1196,a,1183,b)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1196,a,1184,b)].
% 10.53/10.78 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].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1197,a,1175,a)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1197,a,1176,a)].
% 10.53/10.78 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1197,a,1177,b)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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].
% 10.63/10.79 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)].
% 10.63/10.79 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(1198,a,1176,a)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.79 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)].
% 10.63/10.80 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].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.80 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.81 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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)].
% 10.63/10.83 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].
% 10.63/10.83 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1204,a,1175,a)].
% 10.63/10.84 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1204,a,1176,a)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1204,a,1184,b)].
% 10.63/10.84 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].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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)].
% 10.63/10.84 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].
% 10.63/10.84 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.85 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.63/10.88 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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].
% 10.75/10.90 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)].
% 10.75/10.90 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(1210,a,1176,a)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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].
% 10.75/10.90 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)].
% 10.75/10.90 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(1211,a,1176,a)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.75/10.90 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)].
% 10.76/10.91 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1212,a,1179,b)].
% 10.76/10.91 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1212,a,1180,b)].
% 10.76/10.91 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1212,a,1181,b)].
% 10.76/10.91 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1212,a,1182,b)].
% 10.76/10.91 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1212,a,1183,b)].
% 10.76/10.91 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)].
% 10.76/10.91 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].
% 10.76/10.91 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)].
% 10.76/10.91 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1213,a,1176,a)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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].
% 10.76/10.91 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)].
% 10.76/10.91 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1214,a,1176,a)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.91 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)].
% 10.76/10.92 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].
% 10.76/10.92 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1215,a,1175,a)].
% 10.76/10.92 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)].
% 10.76/10.92 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)].
% 10.76/10.92 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1215,a,1178,b)].
% 10.76/10.92 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1215,a,1179,b)].
% 10.76/10.92 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1215,a,1180,b)].
% 10.76/10.92 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1215,a,1181,b)].
% 10.76/10.92 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1215,a,1182,b)].
% 10.76/10.92 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1215,a,1183,b)].
% 10.76/10.92 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)].
% 10.76/10.92 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].
% 10.76/10.92 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)].
% 10.76/10.92 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1216,a,1176,a)].
% 10.76/10.92 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)].
% 10.76/10.92 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)].
% 10.76/10.92 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1216,a,1179,b)].
% 10.76/10.92 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)].
% 10.76/10.92 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)].
% 10.76/10.92 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)].
% 10.76/10.92 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)].
% 10.76/10.92 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)].
% 10.76/10.92 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].
% 10.76/10.92 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)].
% 10.76/10.92 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1217,a,1176,a)].
% 10.76/10.92 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)].
% 10.76/10.92 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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)].
% 10.76/10.93 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].
% 10.76/10.93 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1219,a,1175,a)].
% 10.76/10.93 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(1219,a,1176,a)].
% 10.76/10.93 Derived: c_Orderings_Omin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1219,a,1177,b)].
% 10.76/10.93 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1219,a,1178,b)].
% 10.76/10.93 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1219,a,1179,b)].
% 10.76/10.93 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1219,a,1180,b)].
% 10.76/10.93 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1219,a,1181,b)].
% 10.76/10.93 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1219,a,1182,b)].
% 10.76/10.93 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1219,a,1183,b)].
% 10.76/10.94 Derived: c_Orderings_Omin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1219,a,1184,b)].
% 10.76/10.94 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].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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].
% 10.76/10.94 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)].
% 10.76/10.94 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1221,a,1176,a)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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)].
% 10.76/10.94 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].
% 10.76/10.94 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)].
% 10.76/10.94 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1222,a,1176,a)].
% 10.76/10.94 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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)].
% 10.76/10.95 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].
% 10.76/10.95 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1224,a,1175,a)].
% 10.76/10.95 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(1224,a,1176,a)].
% 10.76/10.95 Derived: c_Orderings_Omax(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1224,a,1177,b)].
% 10.76/10.95 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1224,a,1178,b)].
% 10.76/10.95 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1224,a,1179,b)].
% 10.76/10.95 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1224,a,1180,b)].
% 10.76/10.95 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1224,a,1181,b)].
% 10.76/10.95 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1224,a,1182,b)].
% 10.76/10.98 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1224,a,1183,b)].
% 10.76/10.98 Derived: c_Orderings_Omax(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1224,a,1184,b)].
% 10.76/10.98 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].
% 10.76/10.98 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)].
% 10.76/10.98 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)].
% 10.76/10.98 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)].
% 10.76/10.98 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)].
% 10.76/10.98 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(1225,a,1179,b)].
% 10.76/10.98 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(1225,a,1180,b)].
% 10.76/10.98 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)].
% 10.76/10.98 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)].
% 10.76/10.98 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)].
% 10.76/10.98 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)].
% 10.76/10.98 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].
% 10.76/10.98 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)].
% 10.76/10.98 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(1226,a,1176,a)].
% 10.76/10.98 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)].
% 10.76/10.98 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)].
% 10.76/10.98 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1226,a,1179,b)].
% 10.76/10.98 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1226,a,1180,b)].
% 10.76/10.98 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)].
% 10.76/10.98 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)].
% 10.76/10.98 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)].
% 10.76/10.98 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)].
% 10.76/10.98 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].
% 10.76/10.98 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)].
% 10.76/10.99 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(1227,a,1176,a)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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].
% 10.76/10.99 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)].
% 10.76/10.99 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(1228,a,1176,a)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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)].
% 10.76/10.99 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].
% 10.76/10.99 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)].
% 10.76/10.99 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(1229,a,1176,a)].
% 10.76/10.99 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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].
% 10.86/11.00 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1230,a,1175,a)].
% 10.86/11.00 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1230,a,1176,a)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1230,a,1184,b)].
% 10.86/11.00 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].
% 10.86/11.00 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1231,a,1175,a)].
% 10.86/11.00 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1231,a,1176,a)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.00 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)].
% 10.86/11.01 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)].
% 10.86/11.01 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1231,a,1184,b)].
% 10.86/11.01 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].
% 10.86/11.01 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1232,a,1175,a)].
% 10.86/11.01 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1232,a,1176,a)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1232,a,1184,b)].
% 10.86/11.01 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].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.01 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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)].
% 10.86/11.02 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].
% 10.86/11.02 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.03 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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].
% 10.86/11.04 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1240,a,1175,a)].
% 10.86/11.04 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1240,a,1176,a)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.04 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)].
% 10.86/11.05 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)].
% 10.86/11.05 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)].
% 10.86/11.05 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1240,a,1184,b)].
% 10.86/11.05 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].
% 10.86/11.05 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)].
% 10.86/11.05 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)].
% 10.86/11.05 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)].
% 10.86/11.05 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(1241,a,1178,b)].
% 10.86/11.05 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__field(B). [resolve(1241,a,1179,b)].
% 10.86/11.05 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__idom(B). [resolve(1241,a,1180,b)].
% 10.86/11.05 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__ring__strict(B). [resolve(1241,a,1181,b)].
% 10.86/11.05 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__semidom(B). [resolve(1241,a,1182,b)].
% 10.86/11.05 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__semiring__strict(B). [resolve(1241,a,1183,b)].
% 10.86/11.05 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)].
% 10.86/11.05 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].
% 10.86/11.05 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)].
% 10.86/11.05 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)].
% 10.86/11.05 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)].
% 10.86/11.05 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)].
% 10.86/11.05 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)].
% 10.86/11.05 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)].
% 10.86/11.05 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)].
% 11.08/11.26 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)].
% 11.08/11.26 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)].
% 11.08/11.26 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)].
% 11.08/11.26 1243 -class_Orderings_Olinorder(A) | c_lessequals(B,B,A). [resolve(17,b,2,a)].
% 11.08/11.26 1244 class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(18,a,17,b)].
% 11.08/11.26 1245 -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(33,a,17,b)].
% 11.08/11.26 1246 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(34,a,17,b)].
% 11.08/11.26 1247 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(35,a,17,b)].
% 11.08/11.26 1248 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(36,a,17,b)].
% 11.08/11.26 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)].
% 11.08/11.26 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)].
% 11.08/11.26 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)].
% 11.08/11.26 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)].
% 11.08/11.26 1253 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(41,a,17,b)].
% 11.08/11.26 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)].
% 11.08/11.26 1255 c_LOrder_Omeet(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1087,a,1078,b)].
% 11.08/11.26 Derived: c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1255,b,1177,b)].
% 11.08/11.26 1256 c_LOrder_Ojoin(A,A,B) = A | -class_Orderings_Olinorder(B). [resolve(1118,a,1109,b)].
% 11.08/11.26 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1256,b,1177,b)].
% 11.08/11.26 1257 c_lessequals(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1161,b,1139,b)].
% 11.08/11.26 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1257,b,1175,a)].
% 11.08/11.26 Derived: c_lessequals(A,A,tc_nat). [resolve(1257,b,1176,a)].
% 11.08/11.26 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1257,b,1177,b)].
% 11.08/11.26 1258 class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(1162,b,1139,b)].
% 11.08/11.27 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1258,b,1175,a)].
% 11.08/11.27 Derived: class_Orderings_Oord(tc_nat). [resolve(1258,b,1176,a)].
% 11.08/11.27 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1258,b,1177,b)].
% 11.08/11.27 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1258,b,1178,b)].
% 11.08/11.27 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1258,b,1179,b)].
% 11.08/11.27 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1258,b,1180,b)].
% 11.08/11.27 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1258,b,1181,b)].
% 11.08/11.27 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1258,b,1182,b)].
% 11.08/11.27 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1258,b,1183,b)].
% 11.08/11.27 1259 -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(1163,b,1139,b)].
% 11.08/11.28 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1259,b,1175,a)].
% 11.08/11.28 Derived: -c_less(A,A,tc_nat). [resolve(1259,b,1176,a)].
% 11.08/11.28 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1259,b,1177,b)].
% 11.08/11.28 1260 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1164,c,1139,b)].
% 11.08/11.28 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1260,c,1175,a)].
% 11.08/11.28 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1260,c,1176,a)].
% 11.08/11.28 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)].
% 11.08/11.28 1261 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Orderings_Olinorder(B). [resolve(1165,b,1139,b)].
% 11.08/11.28 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1261,b,1175,a)].
% 11.08/11.28 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1261,b,1176,a)].
% 11.08/11.28 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)].
% 11.08/11.28 1262 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1166,c,1139,b)].
% 11.08/11.28 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1262,c,1175,a)].
% 11.08/11.28 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1262,c,1176,a)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.08/11.28 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)].
% 11.33/11.48 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)].
% 11.33/11.48 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)].
% 11.33/11.48 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)].
% 11.33/11.48 1267 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Orderings_Olinorder(C). [resolve(1171,c,1139,b)].
% 11.33/11.48 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1267,c,1175,a)].
% 11.33/11.48 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1267,c,1176,a)].
% 11.33/11.48 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)].
% 11.33/11.48 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)].
% 11.33/11.48 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)].
% 11.33/11.48 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)].
% 11.33/11.48 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)].
% 11.33/11.48 1269 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom). [assumption].
% 11.33/11.48 1270 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom). [assumption].
% 11.33/11.48 1271 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom). [assumption].
% 11.33/11.48 1272 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom). [assumption].
% 11.33/11.48 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].
% 11.33/11.48 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].
% 11.33/11.48 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].
% 11.33/11.48 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].
% 11.33/11.48 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].
% 11.33/11.48 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].
% 11.33/11.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1278,a,1276,b)].
% 11.33/11.48 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1278,a,1277,b)].
% 11.33/11.48 1279 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom). [assumption].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A). [resolve(1290,b,1269,a)].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 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].
% 11.38/11.55 Derived: -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A). [resolve(1294,b,1269,a)].
% 11.38/11.55 1295 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(14,b,2,a)].
% 11.38/11.55 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1295,a,1277,b)].
% 11.38/11.55 1296 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(18,a,14,b)].
% 11.38/11.55 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1296,b,1277,b)].
% 11.38/11.55 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1296,b,1289,b)].
% 11.38/11.55 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1296,b,1291,b)].
% 11.38/11.55 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1296,b,1292,b)].
% 11.79/11.93 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1296,b,1293,b)].
% 11.79/11.93 1297 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(33,a,14,b)].
% 11.79/11.93 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1297,b,1277,b)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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)].
% 11.79/11.93 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_Opordered__ab__group__add(B). [resolve(1306,b,1277,b)].
% 11.79/11.93 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].
% 11.79/11.93 1308 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom). [assumption].
% 11.79/11.93 1309 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom). [assumption].
% 11.79/11.93 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1317,a,1316,b)].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 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].
% 11.86/12.01 1327 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(16,b,2,a)].
% 11.86/12.01 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1327,a,1316,b)].
% 11.86/12.01 1328 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(18,a,16,b)].
% 11.86/12.01 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1328,b,1316,b)].
% 11.86/12.01 1329 -c_less(A,A,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(33,a,16,b)].
% 11.94/12.09 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1329,b,1316,b)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 11.94/12.09 1339 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(284,b,270,a)].
% 11.94/12.09 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)].
% 11.94/12.09 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1340,c,1310,b)].
% 11.94/12.09 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)].
% 11.94/12.09 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)].
% 12.29/12.42 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)].
% 12.29/12.42 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)].
% 12.29/12.42 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)].
% 12.29/12.42 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)].
% 12.29/12.42 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)].
% 12.29/12.42 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1341,c,1310,b)].
% 12.29/12.42 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)].
% 12.29/12.42 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)].
% 12.29/12.42 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)].
% 12.29/12.42 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)].
% 12.29/12.42 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)].
% 12.29/12.42 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)].
% 12.29/12.42 1342 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(323,b,309,a)].
% 12.29/12.42 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1342,a,1310,b)].
% 12.29/12.42 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1342,a,1311,b)].
% 12.29/12.42 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1342,a,1312,b)].
% 12.29/12.42 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1342,a,1313,b)].
% 12.29/12.42 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].
% 12.29/12.42 1344 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom). [assumption].
% 12.29/12.42 1345 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom). [assumption].
% 12.29/12.42 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].
% 12.29/12.42 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].
% 12.29/12.42 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].
% 12.29/12.42 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].
% 12.29/12.42 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].
% 12.29/12.42 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].
% 12.29/12.42 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].
% 12.29/12.46 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].
% 12.29/12.46 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].
% 12.29/12.46 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].
% 12.29/12.46 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].
% 12.29/12.46 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].
% 12.29/12.46 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].
% 12.29/12.46 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].
% 12.29/12.46 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].
% 12.29/12.46 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].
% 12.29/12.46 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].
% 12.29/12.46 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)].
% 12.29/12.46 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)].
% 12.29/12.46 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)].
% 12.29/12.46 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)].
% 12.29/12.46 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)].
% 12.29/12.46 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)].
% 12.29/12.46 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)].
% 12.29/12.46 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)].
% 12.29/12.46 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1362,a,1354,b)].
% 12.29/12.46 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)].
% 12.29/12.46 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)].
% 12.29/12.46 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)].
% 12.29/12.46 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.47 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.49 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.29/12.50 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.38/12.51 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 1370 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,B,A). [resolve(15,b,2,a)].
% 12.45/12.63 1371 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(18,a,15,b)].
% 12.45/12.63 1372 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(33,a,15,b)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.45/12.63 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)].
% 12.68/12.85 1384 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(346,b,322,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1384,b,1346,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1384,b,1347,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1384,b,1348,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1384,b,1349,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1384,b,1350,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1384,b,1351,b)].
% 12.68/12.85 1385 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1317,a,1316,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1385,b,1344,a)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1385,b,1345,a)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1385,b,1350,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1385,b,1351,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1385,b,1354,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1385,b,1355,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1385,b,1356,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1385,b,1357,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1385,b,1358,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1385,b,1359,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1385,b,1360,b)].
% 12.68/12.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1385,b,1361,b)].
% 12.68/12.85 1386 c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1327,a,1316,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1386,b,1344,a)].
% 12.68/12.85 Derived: c_lessequals(A,A,tc_nat). [resolve(1386,b,1345,a)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1386,b,1346,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1386,b,1347,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1386,b,1348,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1386,b,1349,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1386,b,1350,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1386,b,1351,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1386,b,1354,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1386,b,1355,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1386,b,1356,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1386,b,1357,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1386,b,1358,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1386,b,1359,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1386,b,1360,b)].
% 12.68/12.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1386,b,1361,b)].
% 12.68/12.85 1387 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(1328,b,1316,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1387,b,1344,a)].
% 12.68/12.85 Derived: class_Orderings_Oord(tc_nat). [resolve(1387,b,1345,a)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1387,b,1346,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1387,b,1347,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1387,b,1348,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1387,b,1349,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1387,b,1350,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1387,b,1351,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1387,b,1354,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1387,b,1355,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1387,b,1356,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1387,b,1357,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1387,b,1358,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1387,b,1359,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1387,b,1360,b)].
% 12.68/12.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1387,b,1361,b)].
% 12.68/12.85 1388 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(1329,b,1316,b)].
% 12.68/12.85 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1388,b,1344,a)].
% 12.68/12.85 Derived: -c_less(A,A,tc_nat). [resolve(1388,b,1345,a)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1388,b,1346,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1388,b,1347,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1388,b,1348,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1388,b,1349,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1388,b,1350,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1388,b,1351,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1388,b,1354,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1388,b,1355,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1388,b,1356,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1388,b,1357,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1388,b,1358,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1388,b,1359,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1388,b,1360,b)].
% 12.68/12.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1388,b,1361,b)].
% 12.68/12.85 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)].
% 12.68/12.85 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1389,c,1344,a)].
% 12.68/12.85 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1389,c,1345,a)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1390,b,1344,a)].
% 12.68/12.85 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1390,b,1345,a)].
% 12.68/12.85 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1390,b,1346,b)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.85 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1391,c,1344,a)].
% 12.68/12.86 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1391,c,1345,a)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1392,c,1344,a)].
% 12.68/12.86 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1392,c,1345,a)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1393,c,1344,a)].
% 12.68/12.86 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(1393,c,1345,a)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1394,c,1344,a)].
% 12.68/12.86 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(1394,c,1345,a)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1395,c,1344,a)].
% 12.68/12.86 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(1395,c,1345,a)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1396,c,1344,a)].
% 12.68/12.86 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1396,c,1345,a)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1397,b,1344,a)].
% 12.68/12.86 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(1397,b,1345,a)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.86 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1398,c,1344,a)].
% 12.68/12.87 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1398,c,1345,a)].
% 12.68/12.87 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1398,c,1346,b)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 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)].
% 12.68/12.87 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1399,c,1344,a)].
% 12.68/12.87 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1399,c,1345,a)].
% 12.68/12.87 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1399,c,1346,b)].
% 12.68/12.87 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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)].
% 12.90/13.08 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].
% 12.90/13.08 1401 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom). [assumption].
% 12.90/13.08 1402 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom). [assumption].
% 12.90/13.08 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].
% 12.90/13.08 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].
% 12.90/13.08 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].
% 12.90/13.08 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].
% 12.90/13.08 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].
% 12.90/13.08 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].
% 12.90/13.08 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].
% 12.90/13.08 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].
% 12.90/13.08 1411 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(12,b,2,a)].
% 12.90/13.08 1412 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(18,a,12,b)].
% 12.90/13.08 1413 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(33,a,12,b)].
% 12.90/13.08 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 1425 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(346,b,320,b)].
% 13.06/13.26 1426 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1087,a,1077,b)].
% 13.06/13.26 1427 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1118,a,1108,b)].
% 13.06/13.26 1428 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1161,b,1138,b)].
% 13.06/13.26 1429 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1162,b,1138,b)].
% 13.06/13.26 1430 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1163,b,1138,b)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.26 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.06/13.27 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)].
% 13.16/13.29 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)].
% 13.16/13.29 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)].
% 13.16/13.29 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)].
% 13.16/13.29 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)].
% 13.16/13.29 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)].
% 13.16/13.29 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)].
% 13.16/13.29 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)].
% 13.16/13.29 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)].
% 13.16/13.29 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)].
% 13.16/13.29 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1449,b,1401,a)].
% 13.16/13.29 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1449,b,1402,a)].
% 13.16/13.29 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)].
% 13.16/13.29 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)].
% 13.16/13.29 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset. [resolve(1450,f,1402,a)].
% 13.16/13.29 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)].
% 13.16/13.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1451,e,1401,a)].
% 13.16/13.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(1451,e,1402,a)].
% 13.16/13.29 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)].
% 13.16/13.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1452,e,1401,a)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.16/13.30 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)].
% 13.18/13.32 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)].
% 13.18/13.32 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1459,b,1401,a)].
% 13.18/13.32 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(1459,b,1402,a)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(1465,c,1402,a)].
% 13.18/13.32 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)].
% 13.18/13.32 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)].
% 13.18/13.32 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(1466,c,1402,a)].
% 13.18/13.32 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)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1468,c,1402,a)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1469,c,1402,a)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1471,c,1402,a)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1472,c,1402,a)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 1474 c_Orderings_Omin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1219,a,1177,b)].
% 13.21/13.33 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1474,b,1401,a)].
% 13.21/13.33 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(1474,b,1402,a)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 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)].
% 13.21/13.33 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1476,c,1402,a)].
% 13.21/13.33 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)].
% 13.21/13.35 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)].
% 13.21/13.35 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1477,c,1402,a)].
% 13.21/13.35 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)].
% 13.21/13.35 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)].
% 13.21/13.35 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)].
% 13.21/13.35 1479 c_Orderings_Omax(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1224,a,1177,b)].
% 13.21/13.35 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1479,b,1401,a)].
% 13.21/13.35 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(1479,b,1402,a)].
% 13.21/13.35 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)].
% 13.21/13.35 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)].
% 13.21/13.35 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)].
% 13.21/13.35 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)].
% 13.21/13.35 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)].
% 13.21/13.35 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(1481,b,1402,a)].
% 13.21/13.35 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)].
% 13.21/13.35 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)].
% 13.21/13.35 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(1482,b,1402,a)].
% 13.21/13.35 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)].
% 13.21/13.35 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)].
% 13.21/13.35 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(1483,b,1402,a)].
% 13.21/13.35 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)].
% 13.21/13.35 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)].
% 13.21/13.35 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(1484,b,1402,a)].
% 13.21/13.35 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)].
% 13.21/13.35 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1485,c,1401,a)].
% 13.21/13.35 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1485,c,1402,a)].
% 13.21/13.35 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)].
% 13.21/13.35 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1486,c,1401,a)].
% 13.21/13.36 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1486,c,1402,a)].
% 13.21/13.36 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)].
% 13.21/13.36 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1487,c,1401,a)].
% 13.21/13.36 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1487,c,1402,a)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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)].
% 13.21/13.36 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(1492,d,1402,a)].
% 13.21/13.36 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)].
% 13.21/13.37 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)].
% 13.21/13.37 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)].
% 13.21/13.37 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)].
% 13.21/13.37 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)].
% 13.21/13.37 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)].
% 13.21/13.37 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)].
% 13.21/13.37 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1495,c,1401,a)].
% 13.21/13.37 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1495,c,1402,a)].
% 13.21/13.37 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)].
% 13.21/13.37 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(1496,c,1401,a)].
% 13.21/13.37 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(1496,c,1402,a)].
% 13.21/13.37 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)].
% 13.21/13.37 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(1497,c,1401,a)].
% 13.21/13.37 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(1497,c,1402,a)].
% 13.21/13.37 1498 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1255,b,1177,b)].
% 13.21/13.37 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1498,b,1401,a)].
% 13.21/13.37 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1498,b,1402,a)].
% 13.21/13.37 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1498,b,1405,b)].
% 13.21/13.37 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1498,b,1406,b)].
% 13.21/13.37 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1498,b,1407,b)].
% 13.21/13.37 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1498,b,1408,b)].
% 13.21/13.37 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1498,b,1409,b)].
% 13.21/13.37 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1498,b,1410,b)].
% 13.21/13.37 1499 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1256,b,1177,b)].
% 13.21/13.37 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1499,b,1401,a)].
% 13.21/13.37 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1499,b,1402,a)].
% 13.21/13.37 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1499,b,1405,b)].
% 13.21/13.37 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1499,b,1406,b)].
% 13.21/13.37 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1499,b,1407,b)].
% 13.21/13.39 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1499,b,1408,b)].
% 13.21/13.39 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1499,b,1409,b)].
% 13.21/13.39 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1499,b,1410,b)].
% 13.21/13.39 1500 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1257,b,1177,b)].
% 13.21/13.39 1501 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1258,b,1177,b)].
% 13.21/13.39 1502 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1259,b,1177,b)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 1512 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1278,a,1276,b)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.21/13.39 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 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)].
% 13.30/13.42 1523 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1384,b,1350,b)].
% 13.30/13.42 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1523,b,1401,a)].
% 13.30/13.42 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1523,b,1402,a)].
% 13.30/13.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1523,b,1405,b)].
% 13.30/13.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1523,b,1406,b)].
% 13.30/13.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1523,b,1407,b)].
% 13.30/13.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1523,b,1408,b)].
% 13.30/13.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1523,b,1409,b)].
% 13.30/13.42 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1523,b,1410,b)].
% 13.30/13.42 1524 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1385,b,1350,b)].
% 13.30/13.42 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1524,b,1401,a)].
% 13.30/13.42 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1524,b,1402,a)].
% 13.30/13.42 1525 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1386,b,1350,b)].
% 13.30/13.42 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1525,b,1401,a)].
% 13.30/13.42 Derived: c_lessequals(A,A,tc_nat). [resolve(1525,b,1402,a)].
% 13.30/13.42 1526 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1387,b,1350,b)].
% 13.30/13.42 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1526,b,1401,a)].
% 13.30/13.42 Derived: class_Orderings_Oord(tc_nat). [resolve(1526,b,1402,a)].
% 13.30/13.42 1527 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1388,b,1350,b)].
% 13.30/13.44 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1527,b,1401,a)].
% 13.30/13.44 Derived: -c_less(A,A,tc_nat). [resolve(1527,b,1402,a)].
% 13.30/13.44 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)].
% 13.30/13.44 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1528,c,1401,a)].
% 13.30/13.44 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1528,c,1402,a)].
% 13.30/13.44 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)].
% 13.30/13.44 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1529,b,1401,a)].
% 13.30/13.44 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1529,b,1402,a)].
% 13.30/13.44 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)].
% 13.30/13.44 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1530,c,1401,a)].
% 13.30/13.44 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1530,c,1402,a)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 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)].
% 13.30/13.44 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1535,c,1401,a)].
% 13.30/13.44 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1535,c,1402,a)].
% 13.30/13.44 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)].
% 13.89/14.05 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1536,b,1401,a)].
% 13.89/14.05 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)].
% 13.89/14.05 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)].
% 13.89/14.05 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1537,c,1401,a)].
% 13.89/14.05 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1537,c,1402,a)].
% 13.89/14.05 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)].
% 13.89/14.05 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1538,c,1401,a)].
% 13.89/14.05 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1538,c,1402,a)].
% 13.89/14.05 1539 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom). [assumption].
% 13.89/14.05 1540 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom). [assumption].
% 13.89/14.05 1541 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom). [assumption].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 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].
% 13.89/14.05 1554 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom). [assumption].
% 13.89/14.05 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].
% 13.99/14.15 1556 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom). [assumption].
% 13.99/14.15 1557 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(31,b,2,a)].
% 13.99/14.15 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1557,a,1549,b)].
% 13.99/14.15 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1557,a,1550,b)].
% 13.99/14.15 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1557,a,1551,b)].
% 13.99/14.15 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1557,a,1552,b)].
% 13.99/14.15 1558 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(33,a,31,b)].
% 13.99/14.15 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1558,b,1549,b)].
% 13.99/14.15 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1558,b,1550,b)].
% 13.99/14.15 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1558,b,1551,b)].
% 13.99/14.15 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1558,b,1552,b)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.15 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)].
% 13.99/14.17 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_Opordered__comm__ring(B). [resolve(1562,c,1551,b)].
% 13.99/14.17 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_Opordered__comm__semiring(B). [resolve(1562,c,1552,b)].
% 13.99/14.17 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)].
% 13.99/14.17 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_Opordered__cancel__comm__semiring(C). [resolve(1563,c,1549,b)].
% 13.99/14.17 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_Opordered__cancel__semiring(C). [resolve(1563,c,1550,b)].
% 13.99/14.17 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_Opordered__comm__ring(C). [resolve(1563,c,1551,b)].
% 13.99/14.17 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_Opordered__comm__semiring(C). [resolve(1563,c,1552,b)].
% 13.99/14.17 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)].
% 13.99/14.17 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_Opordered__cancel__comm__semiring(B). [resolve(1564,c,1549,b)].
% 13.99/14.17 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_Opordered__cancel__semiring(B). [resolve(1564,c,1550,b)].
% 13.99/14.17 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_Opordered__comm__ring(B). [resolve(1564,c,1551,b)].
% 13.99/14.17 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_Opordered__comm__semiring(B). [resolve(1564,c,1552,b)].
% 13.99/14.17 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)].
% 13.99/14.17 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_Opordered__cancel__comm__semiring(C). [resolve(1565,c,1549,b)].
% 13.99/14.17 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_Opordered__cancel__semiring(C). [resolve(1565,c,1550,b)].
% 13.99/14.17 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_Opordered__comm__ring(C). [resolve(1565,c,1551,b)].
% 13.99/14.17 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_Opordered__comm__semiring(C). [resolve(1565,c,1552,b)].
% 13.99/14.17 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)].
% 13.99/14.17 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)].
% 13.99/14.17 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)].
% 13.99/14.17 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)].
% 13.99/14.17 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)].
% 13.99/14.20 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)].
% 13.99/14.20 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1567,b,1549,b)].
% 13.99/14.20 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1567,b,1550,b)].
% 13.99/14.20 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1567,b,1551,b)].
% 13.99/14.20 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1567,b,1552,b)].
% 13.99/14.20 1568 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(71,a,97,b)].
% 13.99/14.20 1569 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(100,a,97,b)].
% 13.99/14.20 1570 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(102,a,97,b)].
% 13.99/14.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1570,b,1543,b)].
% 13.99/14.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1570,b,1548,b)].
% 13.99/14.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1570,b,1549,b)].
% 13.99/14.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1570,b,1550,b)].
% 13.99/14.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1570,b,1552,b)].
% 13.99/14.20 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)].
% 13.99/14.20 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)].
% 13.99/14.20 1573 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(183,a,176,b)].
% 13.99/14.20 1574 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(184,a,176,b)].
% 13.99/14.20 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)].
% 13.99/14.20 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(1575,c,1543,b)].
% 13.99/14.20 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(1575,c,1547,b)].
% 13.99/14.20 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__semiring__strict(A). [resolve(1575,c,1548,b)].
% 13.99/14.20 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_Opordered__cancel__comm__semiring(A). [resolve(1575,c,1549,b)].
% 14.09/14.22 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.09/14.22 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.09/14.22 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)].
% 14.09/14.22 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_Oordered__comm__semiring__strict(A). [resolve(1576,c,1543,b)].
% 14.09/14.22 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_Oordered__semidom(A). [resolve(1576,c,1547,b)].
% 14.09/14.22 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_Oordered__semiring__strict(A). [resolve(1576,c,1548,b)].
% 14.09/14.22 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_Opordered__cancel__comm__semiring(A). [resolve(1576,c,1549,b)].
% 14.09/14.22 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_Opordered__cancel__semiring(A). [resolve(1576,c,1550,b)].
% 14.09/14.22 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_Opordered__comm__semiring(A). [resolve(1576,c,1552,b)].
% 14.09/14.22 1577 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(223,a,210,b)].
% 14.09/14.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1577,b,1552,b)].
% 14.09/14.22 1578 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(224,a,210,b)].
% 14.09/14.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1578,b,1552,b)].
% 14.09/14.22 1579 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(226,b,210,b)].
% 14.09/14.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1579,b,1543,b)].
% 14.09/14.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1579,b,1547,b)].
% 14.09/14.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1579,b,1548,b)].
% 14.09/14.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1579,b,1549,b)].
% 14.09/14.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1579,b,1550,b)].
% 14.09/14.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1579,b,1552,b)].
% 14.09/14.22 1580 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(227,b,210,b)].
% 14.09/14.22 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1580,b,1543,b)].
% 14.09/14.22 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1580,b,1547,b)].
% 14.09/14.22 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1580,b,1548,b)].
% 14.49/14.68 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1580,b,1549,b)].
% 14.49/14.68 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1580,b,1550,b)].
% 14.49/14.68 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1580,b,1552,b)].
% 14.49/14.68 1581 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A). [resolve(1294,b,1269,a)].
% 14.49/14.68 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1581,a,1550,b)].
% 14.49/14.68 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].
% 14.49/14.68 1583 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom). [assumption].
% 14.49/14.68 1584 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom). [assumption].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 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].
% 14.49/14.68 1597 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(27,b,2,a)].
% 14.49/14.68 1598 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(33,a,27,b)].
% 14.49/14.68 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)].
% 14.49/14.68 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)].
% 14.49/14.68 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)].
% 14.57/14.75 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)].
% 14.57/14.75 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)].
% 14.57/14.75 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)].
% 14.57/14.75 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)].
% 14.57/14.75 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)].
% 14.57/14.75 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)].
% 14.57/14.75 1608 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(71,a,93,b)].
% 14.57/14.75 1609 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(100,a,93,b)].
% 14.57/14.75 1610 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(102,a,93,b)].
% 14.57/14.75 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)].
% 14.57/14.75 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)].
% 14.57/14.75 1613 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(183,a,172,b)].
% 14.57/14.75 1614 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(184,a,172,b)].
% 14.57/14.75 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)].
% 14.57/14.75 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)].
% 14.57/14.75 1617 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(223,a,206,b)].
% 14.57/14.75 1618 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(224,a,206,b)].
% 14.57/14.75 1619 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(226,b,206,b)].
% 14.57/14.75 1620 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(227,b,206,b)].
% 14.57/14.75 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)].
% 14.57/14.75 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)].
% 14.57/14.75 1623 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(346,b,339,b)].
% 14.57/14.75 1624 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(380,a,369,b)].
% 14.57/14.75 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1624,b,1586,b)].
% 14.57/14.75 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1624,b,1591,b)].
% 14.57/14.75 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1624,b,1592,b)].
% 14.57/14.75 1625 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(381,a,369,b)].
% 14.87/15.03 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1625,b,1586,b)].
% 14.87/15.03 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1625,b,1591,b)].
% 14.87/15.03 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1625,b,1592,b)].
% 14.87/15.03 1626 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(386,b,369,b)].
% 14.87/15.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1626,b,1592,b)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 1629 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(391,b,369,b)].
% 14.87/15.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1629,b,1592,b)].
% 14.87/15.03 1630 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A). [resolve(1290,b,1269,a)].
% 14.87/15.03 1631 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1557,a,1550,b)].
% 14.87/15.03 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1631,b,1583,a)].
% 14.87/15.03 Derived: c_lessequals(A,A,tc_nat). [resolve(1631,b,1584,a)].
% 14.87/15.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1631,b,1585,b)].
% 14.87/15.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1631,b,1586,b)].
% 14.87/15.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1631,b,1587,b)].
% 14.87/15.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1631,b,1588,b)].
% 14.87/15.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1631,b,1589,b)].
% 14.87/15.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1631,b,1590,b)].
% 14.87/15.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1631,b,1591,b)].
% 14.87/15.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1631,b,1592,b)].
% 14.87/15.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1631,b,1596,b)].
% 14.87/15.03 1632 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1558,b,1550,b)].
% 14.87/15.03 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1632,b,1583,a)].
% 14.87/15.03 Derived: -c_less(A,A,tc_nat). [resolve(1632,b,1584,a)].
% 14.87/15.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1632,b,1585,b)].
% 14.87/15.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1632,b,1586,b)].
% 14.87/15.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1632,b,1587,b)].
% 14.87/15.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1632,b,1588,b)].
% 14.87/15.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1632,b,1589,b)].
% 14.87/15.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1632,b,1590,b)].
% 14.87/15.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1632,b,1591,b)].
% 14.87/15.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1632,b,1592,b)].
% 14.87/15.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1632,b,1596,b)].
% 14.87/15.03 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)].
% 14.87/15.03 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1633,c,1583,a)].
% 14.87/15.03 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1633,c,1584,a)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1634,b,1583,a)].
% 14.87/15.03 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1634,b,1584,a)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1635,c,1583,a)].
% 14.87/15.03 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1635,c,1584,a)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 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)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1636,c,1583,a)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1636,c,1584,a)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1636,c,1585,b)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1636,c,1586,b)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1636,c,1587,b)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1636,c,1588,b)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1636,c,1589,b)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1636,c,1590,b)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1636,c,1591,b)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1636,c,1592,b)].
% 14.87/15.03 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1636,c,1596,b)].
% 14.87/15.03 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)].
% 14.87/15.03 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1637,c,1583,a)].
% 14.87/15.03 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(1637,c,1584,a)].
% 14.87/15.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1637,c,1585,b)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1640,c,1583,a)].
% 14.87/15.04 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1640,c,1584,a)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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_Olordered__ring(B). [resolve(1641,b,1585,b)].
% 14.87/15.04 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__comm__semiring__strict(B). [resolve(1641,b,1586,b)].
% 14.87/15.04 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(1641,b,1587,b)].
% 14.87/15.04 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(1641,b,1588,b)].
% 14.87/15.04 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(1641,b,1589,b)].
% 14.87/15.04 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(1641,b,1590,b)].
% 14.87/15.04 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(1641,b,1591,b)].
% 14.87/15.04 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_Opordered__cancel__comm__semiring(B). [resolve(1641,b,1592,b)].
% 14.87/15.04 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_Opordered__ring(B). [resolve(1641,b,1596,b)].
% 14.87/15.04 1642 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1570,b,1550,b)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1642,b,1583,a)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1642,b,1584,a)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1642,b,1585,b)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1642,b,1586,b)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1642,b,1587,b)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1642,b,1588,b)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1642,b,1589,b)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1642,b,1590,b)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1642,b,1591,b)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1642,b,1592,b)].
% 14.87/15.04 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1642,b,1596,b)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 14.87/15.04 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 14.87/15.05 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1644,c,1588,b)].
% 14.87/15.05 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1644,c,1589,b)].
% 14.87/15.05 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1644,c,1590,b)].
% 14.87/15.05 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1644,c,1591,b)].
% 14.87/15.05 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_Opordered__cancel__comm__semiring(A). [resolve(1644,c,1592,b)].
% 14.87/15.05 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_Opordered__ring(A). [resolve(1644,c,1596,b)].
% 14.87/15.05 1645 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1579,b,1550,b)].
% 14.87/15.05 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(1645,b,1583,a)].
% 14.87/15.05 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(1645,b,1584,a)].
% 14.87/15.05 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1645,b,1585,b)].
% 14.87/15.05 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1645,b,1586,b)].
% 14.87/15.05 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1645,b,1587,b)].
% 14.87/15.05 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1645,b,1588,b)].
% 14.87/15.05 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1645,b,1589,b)].
% 14.87/15.05 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1645,b,1590,b)].
% 14.87/15.05 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1645,b,1591,b)].
% 14.87/15.05 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1645,b,1592,b)].
% 14.87/15.05 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1645,b,1596,b)].
% 14.87/15.05 1646 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1580,b,1550,b)].
% 14.87/15.05 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(1646,b,1583,a)].
% 14.87/15.05 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(1646,b,1584,a)].
% 14.87/15.05 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1646,b,1585,b)].
% 14.87/15.05 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1646,b,1586,b)].
% 14.87/15.05 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1646,b,1587,b)].
% 14.87/15.05 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1646,b,1588,b)].
% 14.87/15.05 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1646,b,1589,b)].
% 14.87/15.05 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1646,b,1590,b)].
% 14.87/15.05 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1646,b,1591,b)].
% 14.87/15.05 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1646,b,1592,b)].
% 14.87/15.05 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1646,b,1596,b)].
% 15.09/15.25 1647 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1581,a,1550,b)].
% 15.09/15.25 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1647,b,1583,a)].
% 15.09/15.25 Derived: class_Orderings_Oord(tc_nat). [resolve(1647,b,1584,a)].
% 15.09/15.25 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1647,b,1585,b)].
% 15.09/15.25 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1647,b,1586,b)].
% 15.09/15.25 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1647,b,1587,b)].
% 15.09/15.25 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1647,b,1588,b)].
% 15.09/15.25 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1647,b,1589,b)].
% 15.09/15.25 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1647,b,1590,b)].
% 15.09/15.25 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1647,b,1591,b)].
% 15.09/15.25 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1647,b,1592,b)].
% 15.09/15.25 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1647,b,1596,b)].
% 15.09/15.25 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].
% 15.09/15.25 1649 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom). [assumption].
% 15.09/15.25 1650 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom). [assumption].
% 15.09/15.25 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].
% 15.09/15.25 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].
% 15.09/15.25 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].
% 15.09/15.25 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].
% 15.09/15.25 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].
% 15.09/15.25 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].
% 15.09/15.25 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].
% 15.09/15.25 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].
% 15.09/15.25 1659 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(25,b,2,a)].
% 15.09/15.25 1660 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(33,a,25,b)].
% 15.09/15.25 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)].
% 15.09/15.25 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)].
% 15.09/15.25 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)].
% 15.09/15.25 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)].
% 15.18/15.31 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)].
% 15.18/15.31 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)].
% 15.18/15.31 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)].
% 15.18/15.31 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)].
% 15.18/15.31 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)].
% 15.18/15.31 1670 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(71,a,91,b)].
% 15.18/15.31 1671 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(100,a,91,b)].
% 15.18/15.31 1672 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(102,a,91,b)].
% 15.18/15.31 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)].
% 15.18/15.31 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)].
% 15.18/15.31 1675 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(183,a,170,b)].
% 15.18/15.31 1676 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(184,a,170,b)].
% 15.18/15.31 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)].
% 15.18/15.31 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)].
% 15.18/15.31 1679 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(223,a,204,b)].
% 15.18/15.31 1680 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(224,a,204,b)].
% 15.18/15.31 1681 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(226,b,204,b)].
% 15.18/15.31 1682 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(227,b,204,b)].
% 15.18/15.31 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)].
% 15.18/15.31 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)].
% 15.18/15.31 1685 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(346,b,337,b)].
% 15.18/15.31 1686 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(380,a,367,b)].
% 15.18/15.31 1687 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(381,a,367,b)].
% 15.18/15.31 1688 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(386,b,367,b)].
% 15.18/15.31 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)].
% 15.18/15.31 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)].
% 15.18/15.31 1691 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(391,b,367,b)].
% 15.32/15.43 1692 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1087,a,1085,b)].
% 15.32/15.43 1693 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1089,b,1085,b)].
% 15.32/15.43 1694 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1118,a,1116,b)].
% 15.32/15.43 1695 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1161,b,1146,b)].
% 15.32/15.43 1696 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1163,b,1146,b)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.43 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.44 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 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)].
% 15.32/15.45 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1713,e,1651,b)].
% 15.32/15.45 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1713,e,1652,b)].
% 15.32/15.45 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1713,e,1653,b)].
% 15.32/15.46 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)].
% 15.32/15.46 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)].
% 15.32/15.46 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)].
% 15.32/15.46 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1714,e,1651,b)].
% 15.32/15.46 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1714,e,1652,b)].
% 15.32/15.46 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1714,e,1653,b)].
% 15.32/15.46 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1714,e,1654,b)].
% 15.32/15.46 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1714,e,1655,b)].
% 15.32/15.46 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)].
% 15.32/15.46 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)].
% 15.32/15.46 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)].
% 15.32/15.46 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)].
% 15.32/15.46 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)].
% 15.32/15.46 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)].
% 15.32/15.46 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)].
% 15.32/15.46 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1716,f,1651,b)].
% 15.32/15.46 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1716,f,1652,b)].
% 15.32/15.46 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1716,f,1653,b)].
% 15.32/15.46 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1716,f,1654,b)].
% 15.32/15.46 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1716,f,1655,b)].
% 15.32/15.47 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)].
% 15.32/15.47 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1717,e,1651,b)].
% 15.32/15.47 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1717,e,1652,b)].
% 15.32/15.47 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1717,e,1653,b)].
% 15.32/15.47 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1717,e,1654,b)].
% 15.32/15.47 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1717,e,1655,b)].
% 15.32/15.47 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)].
% 15.32/15.47 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1718,e,1651,b)].
% 15.32/15.47 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1718,e,1652,b)].
% 15.32/15.47 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1718,e,1653,b)].
% 15.32/15.47 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1718,e,1654,b)].
% 15.32/15.47 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1718,e,1655,b)].
% 15.32/15.47 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)].
% 15.32/15.47 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)].
% 15.32/15.47 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)].
% 15.32/15.47 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)].
% 15.32/15.47 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)].
% 15.32/15.47 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)].
% 15.32/15.48 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)].
% 15.32/15.48 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1720,e,1651,b)].
% 15.32/15.48 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1720,e,1652,b)].
% 15.32/15.48 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1720,e,1653,b)].
% 15.32/15.48 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1720,e,1654,b)].
% 15.32/15.48 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1720,e,1655,b)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.48 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)].
% 15.32/15.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1723,d,1651,b)].
% 15.32/15.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1723,d,1652,b)].
% 15.32/15.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1723,d,1653,b)].
% 15.32/15.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1723,d,1654,b)].
% 15.32/15.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1723,d,1655,b)].
% 15.32/15.49 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)].
% 15.32/15.49 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1724,e,1651,b)].
% 15.32/15.49 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1724,e,1652,b)].
% 15.32/15.49 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1724,e,1653,b)].
% 15.32/15.49 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1724,e,1654,b)].
% 15.32/15.49 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1724,e,1655,b)].
% 15.32/15.49 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)].
% 15.32/15.49 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)].
% 15.32/15.49 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)].
% 15.32/15.49 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)].
% 15.32/15.49 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)].
% 15.32/15.49 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)].
% 15.32/15.49 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)].
% 15.32/15.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1726,d,1651,b)].
% 15.32/15.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(1726,d,1652,b)].
% 15.32/15.49 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(1726,d,1653,b)].
% 15.32/15.50 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)].
% 15.32/15.50 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)].
% 15.32/15.50 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)].
% 15.32/15.50 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)].
% 15.32/15.50 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)].
% 15.32/15.50 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)].
% 15.32/15.50 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)].
% 15.32/15.50 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)].
% 15.32/15.50 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)].
% 15.32/15.50 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1728,e,1651,b)].
% 15.32/15.50 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C). [resolve(1728,e,1652,b)].
% 15.32/15.50 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C). [resolve(1728,e,1653,b)].
% 15.32/15.50 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1728,e,1654,b)].
% 15.32/15.50 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1728,e,1655,b)].
% 15.32/15.50 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)].
% 15.32/15.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1729,d,1651,b)].
% 15.32/15.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1729,d,1652,b)].
% 15.32/15.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1729,d,1653,b)].
% 15.32/15.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1729,d,1654,b)].
% 15.32/15.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1729,d,1655,b)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.32/15.51 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.52 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 1740 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1219,a,1183,b)].
% 15.41/15.53 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1740,b,1651,b)].
% 15.41/15.53 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1740,b,1652,b)].
% 15.41/15.53 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1740,b,1653,b)].
% 15.41/15.53 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1740,b,1654,b)].
% 15.41/15.53 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1740,b,1655,b)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.53 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 1745 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1224,a,1183,b)].
% 15.41/15.54 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1745,b,1651,b)].
% 15.41/15.54 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1745,b,1652,b)].
% 15.41/15.54 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1745,b,1653,b)].
% 15.41/15.54 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1745,b,1654,b)].
% 15.41/15.54 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1745,b,1655,b)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.54 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.55 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.56 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.57 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.41/15.58 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 1764 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1258,b,1183,b)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.60 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.61 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)].
% 15.49/15.65 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1771,c,1655,b)].
% 15.49/15.65 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)].
% 15.49/15.65 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1772,c,1651,b)].
% 15.49/15.65 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1772,c,1652,b)].
% 15.49/15.65 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1772,c,1653,b)].
% 15.49/15.65 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1772,c,1654,b)].
% 15.49/15.65 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1772,c,1655,b)].
% 15.49/15.65 1773 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1385,b,1360,b)].
% 15.49/15.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1773,b,1651,b)].
% 15.49/15.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1773,b,1652,b)].
% 15.49/15.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1773,b,1653,b)].
% 15.49/15.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1773,b,1654,b)].
% 15.49/15.65 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1773,b,1655,b)].
% 15.49/15.65 1774 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1386,b,1360,b)].
% 15.49/15.65 1775 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1387,b,1360,b)].
% 15.49/15.65 1776 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1388,b,1360,b)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.49/15.65 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)].
% 15.58/15.69 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)].
% 15.58/15.69 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)].
% 15.58/15.69 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)].
% 15.58/15.69 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)].
% 15.58/15.69 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)].
% 15.58/15.69 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)].
% 15.58/15.69 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)].
% 15.58/15.69 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)].
% 15.58/15.69 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)].
% 15.58/15.69 1788 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1498,b,1410,b)].
% 15.58/15.69 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(1788,b,1649,a)].
% 15.58/15.69 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(1788,b,1650,a)].
% 15.58/15.69 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1788,b,1651,b)].
% 15.58/15.69 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1788,b,1652,b)].
% 15.58/15.69 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1788,b,1653,b)].
% 15.58/15.69 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1788,b,1654,b)].
% 15.58/15.69 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1788,b,1655,b)].
% 15.58/15.69 1789 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1499,b,1410,b)].
% 15.58/15.69 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(1789,b,1649,a)].
% 15.58/15.69 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(1789,b,1650,a)].
% 15.58/15.69 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1789,b,1651,b)].
% 15.58/15.69 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1789,b,1652,b)].
% 15.58/15.69 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1789,b,1653,b)].
% 15.58/15.69 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1789,b,1654,b)].
% 15.58/15.69 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1789,b,1655,b)].
% 15.58/15.69 1790 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1523,b,1410,b)].
% 15.58/15.69 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1790,b,1649,a)].
% 15.58/15.69 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1790,b,1650,a)].
% 15.58/15.69 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1790,b,1651,b)].
% 15.58/15.69 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1790,b,1652,b)].
% 15.58/15.69 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1790,b,1653,b)].
% 15.58/15.69 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1790,b,1654,b)].
% 15.58/15.69 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1790,b,1655,b)].
% 15.58/15.69 1791 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1570,b,1548,b)].
% 15.58/15.69 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)].
% 15.58/15.70 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)].
% 15.58/15.70 1794 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1579,b,1548,b)].
% 15.58/15.70 1795 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1580,b,1548,b)].
% 15.58/15.70 1796 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1624,b,1591,b)].
% 15.58/15.70 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1796,b,1649,a)].
% 15.58/15.70 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(1796,b,1650,a)].
% 15.58/15.70 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1796,b,1651,b)].
% 15.58/15.70 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(1796,b,1652,b)].
% 15.61/15.70 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1796,b,1653,b)].
% 15.61/15.70 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1796,b,1654,b)].
% 15.61/15.70 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1796,b,1655,b)].
% 15.61/15.70 1797 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1625,b,1591,b)].
% 15.61/15.70 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1797,b,1649,a)].
% 15.61/15.70 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(1797,b,1650,a)].
% 15.61/15.70 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1797,b,1651,b)].
% 15.61/15.70 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(1797,b,1652,b)].
% 15.61/15.70 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1797,b,1653,b)].
% 15.61/15.70 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1797,b,1654,b)].
% 15.61/15.70 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1797,b,1655,b)].
% 15.61/15.70 1798 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1631,b,1591,b)].
% 15.61/15.70 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1798,b,1649,a)].
% 15.61/15.70 Derived: c_lessequals(A,A,tc_nat). [resolve(1798,b,1650,a)].
% 15.61/15.70 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1798,b,1651,b)].
% 15.61/15.70 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1798,b,1652,b)].
% 15.61/15.70 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1798,b,1653,b)].
% 15.61/15.70 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1798,b,1654,b)].
% 15.61/15.70 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1798,b,1655,b)].
% 15.61/15.70 1799 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1632,b,1591,b)].
% 15.61/15.70 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1799,b,1649,a)].
% 15.61/15.70 Derived: -c_less(A,A,tc_nat). [resolve(1799,b,1650,a)].
% 15.61/15.70 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1799,b,1651,b)].
% 15.61/15.70 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1799,b,1652,b)].
% 15.61/15.70 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1799,b,1653,b)].
% 15.61/15.70 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1799,b,1654,b)].
% 15.61/15.70 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1799,b,1655,b)].
% 15.61/15.70 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)].
% 15.61/15.70 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1800,c,1649,a)].
% 15.61/15.70 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1800,c,1650,a)].
% 15.61/15.70 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1801,b,1649,a)].
% 15.61/15.71 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1801,b,1650,a)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1802,c,1649,a)].
% 15.61/15.71 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1802,c,1650,a)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 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)].
% 15.61/15.71 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1803,c,1649,a)].
% 15.61/15.71 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1803,c,1650,a)].
% 15.61/15.71 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1803,c,1651,b)].
% 15.61/15.71 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1803,c,1652,b)].
% 15.61/15.71 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1803,c,1653,b)].
% 15.61/15.72 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1803,c,1654,b)].
% 15.61/15.72 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1803,c,1655,b)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(1804,c,1650,a)].
% 15.61/15.72 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1804,c,1651,b)].
% 15.61/15.72 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1804,c,1652,b)].
% 15.61/15.72 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1804,c,1653,b)].
% 15.61/15.72 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1804,c,1654,b)].
% 15.61/15.72 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1804,c,1655,b)].
% 15.61/15.72 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)].
% 15.61/15.72 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1805,c,1649,a)].
% 15.61/15.72 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(1805,c,1650,a)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1806,c,1649,a)].
% 15.61/15.72 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(1806,c,1650,a)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1807,c,1649,a)].
% 15.61/15.72 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1807,c,1650,a)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1808,b,1649,a)].
% 15.61/15.72 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(1808,b,1650,a)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 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)].
% 15.61/15.72 1809 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1642,b,1591,b)].
% 15.61/15.72 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1809,b,1649,a)].
% 15.61/15.72 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1809,b,1650,a)].
% 15.61/15.72 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1809,b,1651,b)].
% 15.61/15.72 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1809,b,1652,b)].
% 15.63/15.73 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1809,b,1653,b)].
% 15.63/15.73 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1809,b,1654,b)].
% 15.63/15.73 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1809,b,1655,b)].
% 15.63/15.73 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)].
% 15.63/15.73 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)].
% 15.63/15.73 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)].
% 15.63/15.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 15.63/15.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 15.63/15.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 15.63/15.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 15.63/15.73 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 15.63/15.73 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)].
% 15.63/15.73 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)].
% 15.63/15.73 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)].
% 15.63/15.73 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 15.63/15.73 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 15.63/15.73 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 15.79/15.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1811,c,1654,b)].
% 15.79/15.93 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1811,c,1655,b)].
% 15.79/15.93 1812 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1645,b,1591,b)].
% 15.79/15.93 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(1812,b,1649,a)].
% 15.79/15.93 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(1812,b,1650,a)].
% 15.79/15.93 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1812,b,1651,b)].
% 15.79/15.93 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1812,b,1652,b)].
% 15.79/15.93 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1812,b,1653,b)].
% 15.79/15.93 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1812,b,1654,b)].
% 15.79/15.93 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1812,b,1655,b)].
% 15.79/15.93 1813 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1646,b,1591,b)].
% 15.79/15.93 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(1813,b,1649,a)].
% 15.79/15.93 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(1813,b,1650,a)].
% 15.79/15.93 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1813,b,1651,b)].
% 15.79/15.93 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1813,b,1652,b)].
% 15.79/15.93 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1813,b,1653,b)].
% 15.79/15.93 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1813,b,1654,b)].
% 15.79/15.93 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1813,b,1655,b)].
% 15.79/15.93 1814 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1647,b,1591,b)].
% 15.79/15.93 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1814,b,1649,a)].
% 15.79/15.93 Derived: class_Orderings_Oord(tc_nat). [resolve(1814,b,1650,a)].
% 15.79/15.93 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1814,b,1651,b)].
% 15.79/15.93 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1814,b,1652,b)].
% 15.79/15.93 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1814,b,1653,b)].
% 15.79/15.93 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1814,b,1654,b)].
% 15.79/15.93 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1814,b,1655,b)].
% 15.79/15.93 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].
% 15.79/15.93 1816 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom). [assumption].
% 15.79/15.93 1817 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom). [assumption].
% 15.79/15.93 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].
% 15.79/15.93 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].
% 15.79/15.93 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].
% 15.79/15.93 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].
% 15.93/16.05 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].
% 15.93/16.05 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].
% 15.93/16.05 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].
% 15.93/16.05 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1824,a,1818,b)].
% 15.93/16.05 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1824,a,1822,b)].
% 15.93/16.05 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].
% 15.93/16.05 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].
% 15.93/16.05 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].
% 15.93/16.05 1828 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(29,b,2,a)].
% 15.93/16.05 1829 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(33,a,29,b)].
% 15.93/16.05 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)].
% 15.93/16.05 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)].
% 15.93/16.05 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)].
% 15.93/16.05 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)].
% 15.93/16.05 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)].
% 15.93/16.05 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)].
% 15.93/16.05 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)].
% 15.93/16.05 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)].
% 15.93/16.05 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)].
% 15.93/16.05 1839 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(71,a,95,b)].
% 15.93/16.05 1840 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(100,a,95,b)].
% 15.93/16.05 1841 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(102,a,95,b)].
% 15.93/16.05 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)].
% 15.93/16.05 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)].
% 16.22/16.32 1844 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(183,a,174,b)].
% 16.22/16.32 1845 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(184,a,174,b)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 1848 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(223,a,208,b)].
% 16.22/16.32 1849 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(224,a,208,b)].
% 16.22/16.32 1850 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(226,b,208,b)].
% 16.22/16.32 1851 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(227,b,208,b)].
% 16.22/16.32 1852 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1296,b,1292,b)].
% 16.22/16.32 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1852,b,1823,b)].
% 16.22/16.32 1853 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1557,a,1552,b)].
% 16.22/16.32 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1853,b,1823,b)].
% 16.22/16.32 1854 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1558,b,1552,b)].
% 16.22/16.32 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1854,b,1823,b)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.22/16.32 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)].
% 16.39/16.56 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)].
% 16.39/16.56 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)].
% 16.39/16.56 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)].
% 16.39/16.56 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)].
% 16.39/16.56 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1863,b,1823,b)].
% 16.39/16.56 1864 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1570,b,1552,b)].
% 16.39/16.56 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1864,b,1823,b)].
% 16.39/16.56 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)].
% 16.39/16.56 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 16.39/16.56 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)].
% 16.39/16.56 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 16.39/16.56 1867 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1577,b,1552,b)].
% 16.39/16.56 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1867,b,1816,a)].
% 16.39/16.56 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1867,b,1817,a)].
% 16.39/16.56 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1867,b,1823,b)].
% 16.39/16.56 1868 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1578,b,1552,b)].
% 16.39/16.56 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1868,b,1823,b)].
% 16.39/16.56 1869 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1579,b,1552,b)].
% 16.39/16.56 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1869,b,1823,b)].
% 16.39/16.56 1870 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1580,b,1552,b)].
% 16.39/16.56 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1870,b,1823,b)].
% 16.39/16.56 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].
% 16.39/16.56 1872 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom). [assumption].
% 16.39/16.56 1873 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom). [assumption].
% 16.39/16.56 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].
% 16.39/16.56 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].
% 16.52/16.66 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].
% 16.52/16.66 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].
% 16.52/16.66 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].
% 16.52/16.66 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].
% 16.52/16.66 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].
% 16.52/16.66 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].
% 16.52/16.66 1882 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(26,b,2,a)].
% 16.52/16.66 1883 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(33,a,26,b)].
% 16.52/16.66 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)].
% 16.52/16.66 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)].
% 16.52/16.66 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)].
% 16.52/16.66 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)].
% 16.52/16.66 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)].
% 16.52/16.66 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)].
% 16.52/16.66 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)].
% 16.52/16.66 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)].
% 16.52/16.66 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)].
% 16.52/16.66 1893 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(71,a,92,b)].
% 16.52/16.66 1894 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(100,a,92,b)].
% 16.52/16.66 1895 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(102,a,92,b)].
% 16.52/16.66 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)].
% 16.52/16.66 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)].
% 16.82/16.94 1898 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(183,a,171,b)].
% 16.82/16.94 1899 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(184,a,171,b)].
% 16.82/16.94 1900 -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(221,c,205,b)].
% 16.82/16.94 1901 -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(222,c,205,b)].
% 16.82/16.94 1902 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(223,a,205,b)].
% 16.82/16.94 1903 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(224,a,205,b)].
% 16.82/16.94 1904 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(226,b,205,b)].
% 16.82/16.94 1905 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(227,b,205,b)].
% 16.82/16.94 1906 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(307,a,299,b)].
% 16.82/16.94 1907 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(308,a,299,b)].
% 16.82/16.94 1908 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(346,b,338,b)].
% 16.82/16.94 1909 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(380,a,368,b)].
% 16.82/16.94 1910 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(381,a,368,b)].
% 16.82/16.94 1911 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(386,b,368,b)].
% 16.82/16.94 1912 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(389,c,368,b)].
% 16.82/16.94 1913 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(390,c,368,b)].
% 16.82/16.94 1914 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(391,b,368,b)].
% 16.82/16.94 1915 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1296,b,1289,b)].
% 16.82/16.94 1916 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1557,a,1549,b)].
% 16.82/16.94 1917 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1558,b,1549,b)].
% 16.82/16.94 1918 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1559,c,1549,b)].
% 16.82/16.94 1919 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1560,b,1549,b)].
% 16.82/16.94 1920 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1561,c,1549,b)].
% 16.82/16.94 1921 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1562,c,1549,b)].
% 16.82/16.94 1922 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1563,c,1549,b)].
% 16.82/16.94 1923 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1564,c,1549,b)].
% 16.82/16.94 1924 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1565,c,1549,b)].
% 16.82/16.96 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)].
% 16.82/16.96 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)].
% 16.82/16.96 1927 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1570,b,1549,b)].
% 16.82/16.96 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)].
% 16.82/16.96 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)].
% 16.82/16.96 1930 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1579,b,1549,b)].
% 16.82/16.96 1931 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1580,b,1549,b)].
% 16.82/16.96 1932 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1624,b,1592,b)].
% 16.82/16.96 1933 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1625,b,1592,b)].
% 16.82/16.96 1934 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1626,b,1592,b)].
% 16.82/16.96 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)].
% 16.82/16.96 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1935,c,1872,a)].
% 16.82/16.96 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1935,c,1873,a)].
% 16.82/16.96 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)].
% 16.82/16.96 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1936,c,1872,a)].
% 16.82/16.96 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1936,c,1873,a)].
% 16.82/16.96 1937 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1629,b,1592,b)].
% 16.82/16.96 1938 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1631,b,1592,b)].
% 16.82/16.96 1939 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1632,b,1592,b)].
% 16.82/16.96 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)].
% 16.82/16.96 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)].
% 16.82/16.96 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)].
% 16.82/16.96 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)].
% 16.82/16.96 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)].
% 16.82/16.96 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)].
% 16.82/16.96 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)].
% 16.82/16.96 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)].
% 17.12/17.24 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)].
% 17.12/17.24 1949 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1642,b,1592,b)].
% 17.12/17.24 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)].
% 17.12/17.24 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)].
% 17.12/17.24 1952 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1645,b,1592,b)].
% 17.12/17.24 1953 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1646,b,1592,b)].
% 17.12/17.24 1954 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1647,b,1592,b)].
% 17.12/17.24 1955 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1824,a,1822,b)].
% 17.12/17.24 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(1955,b,1872,a)].
% 17.12/17.24 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(1955,b,1873,a)].
% 17.12/17.24 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1955,b,1874,b)].
% 17.12/17.24 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1955,b,1875,b)].
% 17.12/17.24 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1955,b,1876,b)].
% 17.12/17.24 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1955,b,1877,b)].
% 17.12/17.24 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].
% 17.12/17.24 1957 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom). [assumption].
% 17.12/17.24 1958 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom). [assumption].
% 17.12/17.24 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].
% 17.12/17.24 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].
% 17.12/17.24 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].
% 17.12/17.24 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].
% 17.12/17.24 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].
% 17.12/17.24 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].
% 17.12/17.24 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].
% 17.12/17.24 1966 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(20,b,2,a)].
% 17.12/17.24 1967 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(33,a,20,b)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 1977 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(71,a,86,b)].
% 17.12/17.28 1978 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(100,a,86,b)].
% 17.12/17.28 1979 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(102,a,86,b)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 1982 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(183,a,165,b)].
% 17.12/17.28 1983 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(184,a,165,b)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 1986 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(223,a,199,b)].
% 17.12/17.28 1987 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(224,a,199,b)].
% 17.12/17.28 1988 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(226,b,199,b)].
% 17.12/17.28 1989 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(227,b,199,b)].
% 17.12/17.28 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)].
% 17.12/17.28 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)].
% 17.12/17.28 1992 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(346,b,332,b)].
% 17.31/17.39 1993 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(380,a,362,b)].
% 17.31/17.39 1994 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(381,a,362,b)].
% 17.31/17.39 1995 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(386,b,362,b)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 1998 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(391,b,362,b)].
% 17.31/17.39 1999 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1087,a,1080,b)].
% 17.31/17.39 2000 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1089,b,1080,b)].
% 17.31/17.39 2001 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1118,a,1111,b)].
% 17.31/17.39 2002 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1161,b,1141,b)].
% 17.31/17.39 2003 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1163,b,1141,b)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.39 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.42 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 2047 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1219,a,1178,b)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 2052 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1224,a,1178,b)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.31/17.45 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 2071 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1258,b,1178,b)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 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)].
% 17.42/17.50 2080 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1385,b,1355,b)].
% 17.42/17.50 2081 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1386,b,1355,b)].
% 17.42/17.50 2082 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1387,b,1355,b)].
% 17.42/17.50 2083 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1388,b,1355,b)].
% 17.42/17.50 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 2095 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1498,b,1405,b)].
% 17.43/17.56 2096 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1499,b,1405,b)].
% 17.43/17.56 2097 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1523,b,1405,b)].
% 17.43/17.56 2098 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1570,b,1543,b)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 2101 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1579,b,1543,b)].
% 17.43/17.56 2102 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1580,b,1543,b)].
% 17.43/17.56 2103 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1624,b,1586,b)].
% 17.43/17.56 2104 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1625,b,1586,b)].
% 17.43/17.56 2105 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1631,b,1586,b)].
% 17.43/17.56 2106 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1632,b,1586,b)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.56 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 2116 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1642,b,1586,b)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 2119 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1645,b,1586,b)].
% 17.43/17.58 2120 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1646,b,1586,b)].
% 17.43/17.58 2121 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1647,b,1586,b)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.58 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.59 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)].
% 17.43/17.60 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2131,b,1957,a)].
% 17.43/17.60 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2131,b,1958,a)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.43/17.60 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2141,b,1957,a)].
% 17.53/17.61 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2141,b,1958,a)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.61 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(2147,c,1958,a)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(2148,c,1958,a)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2150,c,1958,a)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2151,c,1958,a)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 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)].
% 17.53/17.62 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2153,c,1958,a)].
% 17.53/17.62 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)].
% 17.53/17.63 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)].
% 17.53/17.63 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2154,c,1958,a)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 2156 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1740,b,1651,b)].
% 17.53/17.63 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(2156,b,1957,a)].
% 17.53/17.63 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(2156,b,1958,a)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2158,c,1958,a)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2159,c,1958,a)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 2161 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1745,b,1651,b)].
% 17.53/17.63 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(2161,b,1957,a)].
% 17.53/17.63 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(2161,b,1958,a)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 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)].
% 17.53/17.63 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(2163,b,1958,a)].
% 17.53/17.64 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)].
% 17.53/17.64 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)].
% 17.53/17.64 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(2164,b,1958,a)].
% 17.53/17.64 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)].
% 17.53/17.64 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)].
% 17.53/17.64 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(2165,b,1958,a)].
% 17.53/17.64 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)].
% 17.53/17.64 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)].
% 17.53/17.64 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(2166,b,1958,a)].
% 17.53/17.64 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)].
% 17.53/17.64 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(2167,c,1957,a)].
% 17.53/17.64 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(2167,c,1958,a)].
% 17.53/17.64 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)].
% 17.53/17.64 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(2168,c,1957,a)].
% 17.53/17.64 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(2168,c,1958,a)].
% 17.53/17.64 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)].
% 17.53/17.64 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(2169,c,1957,a)].
% 17.53/17.64 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(2169,c,1958,a)].
% 17.53/17.64 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)].
% 17.53/17.64 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)].
% 17.53/17.64 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)].
% 17.53/17.64 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)].
% 17.53/17.64 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)].
% 17.53/17.64 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)].
% 17.53/17.64 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)].
% 17.53/17.64 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(2177,c,1957,a)].
% 17.53/17.65 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(2177,c,1958,a)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.65 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 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)].
% 17.53/17.66 2188 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1773,b,1651,b)].
% 17.53/17.67 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)].
% 17.53/17.67 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)].
% 17.53/17.67 2191 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1788,b,1651,b)].
% 17.53/17.67 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(2191,b,1957,a)].
% 17.53/17.67 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(2191,b,1958,a)].
% 17.53/17.67 2192 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1789,b,1651,b)].
% 17.53/17.67 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(2192,b,1957,a)].
% 17.53/17.67 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(2192,b,1958,a)].
% 17.53/17.67 2193 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1790,b,1651,b)].
% 17.53/17.67 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2193,b,1957,a)].
% 17.53/17.67 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2193,b,1958,a)].
% 17.53/17.67 2194 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1796,b,1651,b)].
% 17.53/17.67 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2194,b,1957,a)].
% 17.53/17.67 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2194,b,1958,a)].
% 17.53/17.67 2195 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1797,b,1651,b)].
% 17.53/17.67 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2195,b,1957,a)].
% 17.53/17.67 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2195,b,1958,a)].
% 17.53/17.67 2196 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1798,b,1651,b)].
% 17.53/17.67 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2196,b,1957,a)].
% 17.53/17.67 Derived: c_lessequals(A,A,tc_nat). [resolve(2196,b,1958,a)].
% 17.53/17.67 2197 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1799,b,1651,b)].
% 17.53/17.67 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2197,b,1957,a)].
% 17.53/17.67 Derived: -c_less(A,A,tc_nat). [resolve(2197,b,1958,a)].
% 17.53/17.67 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)].
% 17.53/17.67 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2198,c,1957,a)].
% 17.53/17.67 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2198,c,1958,a)].
% 17.53/17.67 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)].
% 17.53/17.67 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2199,b,1957,a)].
% 17.53/17.67 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2199,b,1958,a)].
% 17.53/17.67 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)].
% 17.53/17.67 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2200,c,1957,a)].
% 17.53/17.67 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2200,c,1958,a)].
% 17.53/17.67 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)].
% 17.53/17.67 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)].
% 17.53/17.67 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)].
% 17.53/17.67 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)].
% 17.53/17.67 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)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 17.53/17.68 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2205,c,1957,a)].
% 17.53/17.68 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2205,c,1958,a)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 17.53/17.68 2207 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1809,b,1651,b)].
% 17.53/17.68 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2207,b,1957,a)].
% 17.53/17.68 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2207,b,1958,a)].
% 17.53/17.68 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)].
% 17.53/17.68 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2208,c,1957,a)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 17.53/17.68 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)].
% 18.21/18.36 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)].
% 18.21/18.36 2210 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1812,b,1651,b)].
% 18.21/18.36 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(2210,b,1957,a)].
% 18.21/18.36 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(2210,b,1958,a)].
% 18.21/18.36 2211 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1813,b,1651,b)].
% 18.21/18.36 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(2211,b,1957,a)].
% 18.21/18.36 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(2211,b,1958,a)].
% 18.21/18.36 2212 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1814,b,1651,b)].
% 18.21/18.36 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(2212,b,1957,a)].
% 18.21/18.36 Derived: class_Orderings_Oord(tc_nat). [resolve(2212,b,1958,a)].
% 18.21/18.36 2213 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1824,a,1818,b)].
% 18.21/18.36 2214 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1955,b,1874,b)].
% 18.21/18.36 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(2214,b,1957,a)].
% 18.21/18.36 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(2214,b,1958,a)].
% 18.21/18.36 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].
% 18.21/18.36 2216 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom). [assumption].
% 18.21/18.36 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].
% 18.21/18.36 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].
% 18.21/18.36 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].
% 18.21/18.36 2220 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom). [assumption].
% 18.21/18.36 2221 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom). [assumption].
% 18.21/18.36 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(2220,a,2221,a)].
% 18.21/18.36 2222 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom). [assumption].
% 18.21/18.36 2223 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom). [assumption].
% 18.21/18.36 2224 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom). [assumption].
% 18.21/18.36 2225 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom). [assumption].
% 18.21/18.36 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].
% 18.21/18.36 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].
% 18.21/18.36 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2227,b,2220,a)].
% 18.21/18.36 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2227,b,2222,a)].
% 18.21/18.36 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].
% 18.21/18.40 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2228,b,2220,a)].
% 18.21/18.40 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2228,b,2222,a)].
% 18.21/18.40 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].
% 18.21/18.40 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2229,b,2220,a)].
% 18.21/18.40 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].
% 18.21/18.40 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].
% 18.21/18.40 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].
% 18.21/18.40 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].
% 18.21/18.40 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(2233,a,2221,a)].
% 18.21/18.40 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)].
% 18.21/18.40 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)].
% 18.21/18.40 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)].
% 18.21/18.40 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)].
% 18.21/18.40 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(2233,a,2230,b)].
% 18.21/18.40 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)].
% 18.21/18.40 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)].
% 18.21/18.40 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].
% 18.21/18.40 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2234,a,2221,a)].
% 18.21/18.40 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)].
% 18.21/18.40 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)].
% 18.21/18.40 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)].
% 18.21/18.40 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)].
% 18.21/18.40 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(2234,a,2230,b)].
% 18.21/18.40 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)].
% 18.21/18.40 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)].
% 18.21/18.40 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].
% 18.33/18.42 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2235,a,2221,a)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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].
% 18.33/18.42 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2236,a,2221,a)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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].
% 18.33/18.42 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2237,a,2221,a)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.33/18.42 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].
% 18.33/18.42 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2238,a,2221,a)].
% 18.33/18.42 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)].
% 18.33/18.42 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 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)].
% 18.35/18.43 2241 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Onprt(c_0,A) = c_0 # label(cls_OrderedGroup_Onprt__0_0) # label(axiom). [assumption].
% 18.35/18.43 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2241,a,2221,a)].
% 18.35/18.43 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2241,a,2226,b)].
% 18.35/18.45 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2241,a,2227,b)].
% 18.35/18.45 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2241,a,2228,b)].
% 18.35/18.45 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2241,a,2229,b)].
% 18.35/18.45 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2241,a,2230,b)].
% 18.35/18.45 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2241,a,2231,b)].
% 18.35/18.45 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2241,a,2232,b)].
% 18.35/18.45 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].
% 18.35/18.45 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(2242,a,2221,a)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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].
% 18.35/18.45 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(2243,a,2221,a)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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)].
% 18.35/18.45 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].
% 18.35/18.45 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2244,a,2221,a)].
% 18.35/18.45 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2244,a,2226,b)].
% 18.35/18.45 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2244,a,2227,b)].
% 18.35/18.45 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2244,a,2228,b)].
% 18.35/18.45 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2244,a,2229,b)].
% 18.35/18.46 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2244,a,2230,b)].
% 18.35/18.46 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2244,a,2231,b)].
% 18.35/18.46 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2244,a,2232,b)].
% 18.35/18.46 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].
% 18.35/18.46 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_OrderedGroup_Onprt(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2245,a,2221,a)].
% 18.35/18.46 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)].
% 18.35/18.46 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)].
% 18.35/18.46 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)].
% 18.35/18.46 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)].
% 18.35/18.46 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)].
% 18.35/18.46 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)].
% 18.35/18.46 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)].
% 18.35/18.46 2246 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Opprt(c_0,A) = c_0 # label(cls_OrderedGroup_Opprt__0_0) # label(axiom). [assumption].
% 18.35/18.46 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2246,a,2221,a)].
% 18.35/18.46 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2246,a,2226,b)].
% 18.35/18.46 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2246,a,2227,b)].
% 18.35/18.46 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2246,a,2228,b)].
% 18.35/18.46 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2246,a,2229,b)].
% 18.35/18.46 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2246,a,2230,b)].
% 18.35/18.46 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2246,a,2231,b)].
% 18.35/18.46 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2246,a,2232,b)].
% 18.35/18.46 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].
% 18.35/18.46 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(2247,a,2221,a)].
% 18.35/18.46 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)].
% 18.35/18.46 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)].
% 18.35/18.46 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)].
% 18.35/18.46 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)].
% 18.35/18.46 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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].
% 18.35/18.48 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(2248,a,2221,a)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.35/18.48 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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].
% 18.44/18.53 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2252,a,2221,a)].
% 18.44/18.53 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2252,a,2226,b)].
% 18.44/18.53 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2252,a,2227,b)].
% 18.44/18.53 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2252,a,2228,b)].
% 18.44/18.53 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2252,a,2229,b)].
% 18.44/18.53 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2252,a,2230,b)].
% 18.44/18.53 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2252,a,2231,b)].
% 18.44/18.53 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2252,a,2232,b)].
% 18.44/18.53 2253 -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(B,B,A). [resolve(8,b,2,a)].
% 18.44/18.53 2254 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(18,a,8,b)].
% 18.44/18.53 2255 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(33,a,8,b)].
% 18.44/18.53 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)].
% 18.44/18.53 2257 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(35,a,8,b)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.44/18.53 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)].
% 18.65/18.73 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)].
% 18.65/18.73 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)].
% 18.65/18.73 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)].
% 18.65/18.73 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)].
% 18.65/18.73 2265 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(150,b,147,a)].
% 18.65/18.73 2266 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(150,b,148,a)].
% 18.65/18.73 2267 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(183,a,150,b)].
% 18.65/18.73 2268 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(184,a,150,b)].
% 18.65/18.73 2269 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(307,a,277,b)].
% 18.65/18.73 2270 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(308,a,277,b)].
% 18.65/18.73 2271 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(346,b,316,b)].
% 18.65/18.73 2272 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1087,a,1073,b)].
% 18.65/18.73 2273 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1118,a,1104,b)].
% 18.65/18.73 2274 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1161,b,1134,b)].
% 18.65/18.73 2275 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1162,b,1134,b)].
% 18.65/18.73 2276 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1163,b,1134,b)].
% 18.65/18.73 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)].
% 18.65/18.73 2278 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1165,b,1134,b)].
% 18.65/18.73 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)].
% 18.65/18.73 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)].
% 18.65/18.73 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)].
% 18.65/18.73 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)].
% 18.65/18.73 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)].
% 18.65/18.73 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)].
% 18.65/18.73 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)].
% 18.65/18.73 2286 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1340,c,1310,b)].
% 18.65/18.73 2287 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1341,c,1310,b)].
% 18.65/18.73 2288 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1342,a,1310,b)].
% 18.65/18.73 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)].
% 18.65/18.73 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)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 2297 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1384,b,1346,b)].
% 18.96/19.05 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2297,b,2229,b)].
% 18.96/19.05 2298 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1386,b,1346,b)].
% 18.96/19.05 2299 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1387,b,1346,b)].
% 18.96/19.05 2300 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1388,b,1346,b)].
% 18.96/19.05 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)].
% 18.96/19.05 2302 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1390,b,1346,b)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 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)].
% 18.96/19.05 2310 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1398,c,1346,b)].
% 18.96/19.05 2311 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group(C). [resolve(1399,c,1346,b)].
% 18.96/19.05 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].
% 18.96/19.05 2313 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom). [assumption].
% 18.96/19.05 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].
% 18.96/19.05 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].
% 18.96/19.05 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].
% 18.96/19.05 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].
% 19.05/19.15 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].
% 19.05/19.15 2319 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom). [assumption].
% 19.05/19.15 2320 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom). [assumption].
% 19.05/19.15 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].
% 19.05/19.15 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2321,a,2315,b)].
% 19.05/19.15 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2321,a,2316,b)].
% 19.05/19.15 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2321,a,2317,b)].
% 19.05/19.15 2322 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom). [assumption].
% 19.05/19.15 2323 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(30,b,2,a)].
% 19.05/19.15 2324 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(33,a,30,b)].
% 19.05/19.15 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)].
% 19.05/19.15 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)].
% 19.05/19.15 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)].
% 19.05/19.15 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)].
% 19.05/19.15 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)].
% 19.05/19.15 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)].
% 19.05/19.15 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)].
% 19.05/19.15 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)].
% 19.05/19.15 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)].
% 19.05/19.15 2334 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(71,a,96,b)].
% 19.05/19.15 2335 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(100,a,96,b)].
% 19.05/19.15 2336 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(102,a,96,b)].
% 19.05/19.15 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)].
% 19.05/19.15 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)].
% 19.05/19.15 2339 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(183,a,175,b)].
% 19.05/19.15 2340 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(184,a,175,b)].
% 19.05/19.15 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)].
% 19.05/19.17 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)].
% 19.05/19.17 2343 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(223,a,209,b)].
% 19.05/19.17 2344 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(224,a,209,b)].
% 19.05/19.17 2345 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(226,b,209,b)].
% 19.05/19.17 2346 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(227,b,209,b)].
% 19.05/19.17 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)].
% 19.05/19.17 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)].
% 19.05/19.17 2349 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(346,b,341,b)].
% 19.05/19.17 2350 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(380,a,371,b)].
% 19.05/19.17 2351 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(381,a,371,b)].
% 19.05/19.17 2352 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(386,b,371,b)].
% 19.05/19.17 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)].
% 19.05/19.17 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)].
% 19.05/19.17 2355 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(391,b,371,b)].
% 19.05/19.17 2356 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(410,a,405,b)].
% 19.05/19.17 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2356,b,2314,b)].
% 19.05/19.17 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2356,b,2315,b)].
% 19.05/19.17 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2356,b,2316,b)].
% 19.05/19.17 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2356,b,2317,b)].
% 19.05/19.17 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)].
% 19.05/19.17 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)].
% 19.05/19.17 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)].
% 19.05/19.17 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)].
% 19.05/19.17 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)].
% 19.05/19.17 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)].
% 19.05/19.17 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 2362 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(421,b,405,b)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 2365 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(433,b,405,b)].
% 19.26/19.35 2366 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(434,b,405,b)].
% 19.26/19.35 2367 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(439,b,405,b)].
% 19.26/19.35 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2367,b,2314,b)].
% 19.26/19.35 2368 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__ring(B). [resolve(440,b,405,b)].
% 19.26/19.35 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2368,b,2314,b)].
% 19.26/19.35 2369 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(441,b,405,b)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 2372 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(444,b,405,b)].
% 19.26/19.35 2373 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1296,b,1293,b)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.35 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2381,c,2314,b)].
% 19.26/19.41 2382 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1385,b,1361,b)].
% 19.26/19.41 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2382,b,2314,b)].
% 19.26/19.41 2383 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1386,b,1361,b)].
% 19.26/19.41 2384 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1387,b,1361,b)].
% 19.26/19.41 2385 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1388,b,1361,b)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 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)].
% 19.26/19.41 2397 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1631,b,1596,b)].
% 19.26/19.41 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2397,b,2314,b)].
% 19.26/19.41 2398 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1632,b,1596,b)].
% 19.26/19.41 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2398,b,2314,b)].
% 19.26/19.41 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 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)].
% 19.35/19.43 2408 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1642,b,1596,b)].
% 19.35/19.43 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2408,b,2314,b)].
% 19.35/19.43 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)].
% 19.35/19.43 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2409,c,2314,b)].
% 19.35/19.43 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)].
% 19.35/19.43 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2410,c,2314,b)].
% 19.63/19.71 2411 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1645,b,1596,b)].
% 19.63/19.71 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2411,b,2314,b)].
% 19.63/19.71 2412 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1646,b,1596,b)].
% 19.63/19.71 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2412,b,2314,b)].
% 19.63/19.71 2413 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1647,b,1596,b)].
% 19.63/19.71 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2413,b,2314,b)].
% 19.63/19.71 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].
% 19.63/19.71 2415 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom). [assumption].
% 19.63/19.71 2416 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom). [assumption].
% 19.63/19.71 2417 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom). [assumption].
% 19.63/19.71 2418 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom). [assumption].
% 19.63/19.71 2419 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom). [assumption].
% 19.63/19.71 2420 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom). [assumption].
% 19.63/19.71 2421 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom). [assumption].
% 19.63/19.71 2422 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom). [assumption].
% 19.63/19.71 2423 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom). [assumption].
% 19.63/19.71 2424 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom). [assumption].
% 19.63/19.71 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].
% 19.63/19.71 2426 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom). [assumption].
% 19.63/19.71 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].
% 19.63/19.71 2428 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom). [assumption].
% 19.63/19.71 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)].
% 19.63/19.71 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2414,a,2416,a)].
% 19.63/19.71 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)].
% 19.63/19.71 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)].
% 19.63/19.71 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)].
% 19.63/19.71 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)].
% 19.63/19.71 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)].
% 19.63/19.71 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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].
% 19.63/19.72 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)].
% 19.63/19.72 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2429,a,2416,a)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.72 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)].
% 19.63/19.74 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)].
% 19.63/19.74 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)].
% 19.63/19.74 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2430,a,2422,b)].
% 19.63/19.74 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2430,a,2423,b)].
% 19.63/19.74 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2430,a,2424,b)].
% 19.63/19.74 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2430,a,2425,b)].
% 19.63/19.74 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2430,a,2426,b)].
% 19.63/19.74 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2430,a,2427,b)].
% 19.63/19.74 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)].
% 19.63/19.74 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].
% 19.63/19.74 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)].
% 19.63/19.74 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2431,a,2416,a)].
% 19.63/19.74 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)].
% 19.63/19.74 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)].
% 19.63/19.74 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)].
% 19.63/19.74 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)].
% 19.63/19.74 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)].
% 19.63/19.74 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)].
% 19.63/19.74 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)].
% 19.63/19.74 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)].
% 19.63/19.74 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)].
% 19.63/19.74 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)].
% 19.63/19.74 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2431,a,2427,b)].
% 19.63/19.74 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)].
% 19.63/19.74 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].
% 19.63/19.75 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)].
% 19.63/19.75 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2432,a,2416,a)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.75 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)].
% 19.63/19.77 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2433,a,2426,b)].
% 19.63/19.77 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2433,a,2427,b)].
% 19.63/19.77 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)].
% 19.63/19.77 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].
% 19.63/19.77 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)].
% 19.63/19.77 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2434,a,2416,a)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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].
% 19.63/19.77 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)].
% 19.63/19.77 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2435,a,2416,a)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.63/19.77 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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].
% 19.71/19.78 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)].
% 19.71/19.78 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2436,a,2416,a)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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].
% 19.71/19.78 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)].
% 19.71/19.78 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2437,a,2416,a)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.78 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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].
% 19.71/19.80 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)].
% 19.71/19.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2438,a,2416,a)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2438,a,2423,b)].
% 19.71/19.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2438,a,2424,b)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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].
% 19.71/19.80 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)].
% 19.71/19.80 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2439,a,2416,a)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.80 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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].
% 19.71/19.81 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2440,a,2415,a)].
% 19.71/19.81 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(2440,a,2416,a)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 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)].
% 19.71/19.81 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2440,a,2422,b)].
% 19.71/19.81 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2440,a,2423,b)].
% 19.71/19.81 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2440,a,2424,b)].
% 19.71/19.81 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2440,a,2425,b)].
% 19.71/19.81 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2440,a,2426,b)].
% 19.71/19.81 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2440,a,2427,b)].
% 19.71/19.81 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)].
% 19.71/19.83 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].
% 19.71/19.83 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)].
% 19.71/19.83 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2441,a,2416,a)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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].
% 19.71/19.83 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)].
% 19.71/19.83 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2442,a,2416,a)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.83 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)].
% 19.71/19.84 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)].
% 19.71/19.84 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)].
% 19.71/19.84 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)].
% 19.71/19.84 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].
% 19.71/19.84 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2443,a,2415,a)].
% 19.71/19.84 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(2443,a,2416,a)].
% 19.71/19.84 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)].
% 19.71/19.84 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)].
% 19.71/19.84 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)].
% 19.71/19.84 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)].
% 19.71/19.84 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)].
% 19.71/19.84 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2443,a,2422,b)].
% 19.71/19.84 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2443,a,2423,b)].
% 19.71/19.84 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2443,a,2424,b)].
% 19.71/19.84 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2443,a,2425,b)].
% 19.71/19.84 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(2443,a,2426,b)].
% 19.71/19.84 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2443,a,2427,b)].
% 19.71/19.84 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)].
% 19.71/19.84 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].
% 19.71/19.84 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)].
% 19.71/19.84 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2444,a,2416,a)].
% 19.71/19.84 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)].
% 19.71/19.84 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)].
% 19.71/19.84 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)].
% 19.71/19.84 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)].
% 19.71/19.84 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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].
% 19.71/19.86 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)].
% 19.71/19.86 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2445,a,2416,a)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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].
% 19.71/19.86 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)].
% 19.71/19.86 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2446,a,2416,a)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.71/19.86 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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].
% 19.95/20.08 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)].
% 19.95/20.08 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2447,a,2416,a)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 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)].
% 19.95/20.08 2448 class_Orderings_Oord(tc_IntDef_Oint). [resolve(18,a,1,a)].
% 19.95/20.08 2449 class_Orderings_Oord(tc_nat). [resolve(18,a,3,a)].
% 19.95/20.08 2450 class_Orderings_Oord(tc_set(A)). [resolve(18,a,4,a)].
% 19.95/20.08 2451 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(18,a,9,b)].
% 19.95/20.08 2452 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(18,a,10,b)].
% 19.95/20.08 2453 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(18,a,11,b)].
% 19.95/20.08 2454 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(18,a,13,b)].
% 19.95/20.08 2455 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(32,b,18,a)].
% 19.95/20.08 2456 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(1079,b,1069,a)].
% 20.42/20.48 2457 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1089,b,1070,a)].
% 20.42/20.48 2458 class_Orderings_Oord(tc_nat). [resolve(1089,b,1071,a)].
% 20.42/20.48 2459 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1089,b,1081,b)].
% 20.42/20.48 2460 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1089,b,1082,b)].
% 20.42/20.48 2461 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1089,b,1083,b)].
% 20.42/20.48 2462 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1089,b,1084,b)].
% 20.42/20.48 2463 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1162,b,1132,a)].
% 20.42/20.48 2464 class_Orderings_Oord(tc_nat). [resolve(1162,b,1133,a)].
% 20.42/20.48 2465 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1162,b,1135,b)].
% 20.42/20.48 2466 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1162,b,1136,b)].
% 20.42/20.48 2467 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1162,b,1137,b)].
% 20.42/20.48 2468 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1162,b,1140,b)].
% 20.42/20.48 2469 class_Orderings_Oord(A) | -class_Wellfounded__Recursion_Owellorder(A). [resolve(1162,b,1147,b)].
% 20.42/20.48 2470 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1258,b,1175,a)].
% 20.42/20.48 2471 class_Orderings_Oord(tc_nat). [resolve(1258,b,1176,a)].
% 20.42/20.48 2472 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1258,b,1179,b)].
% 20.42/20.48 2473 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1258,b,1180,b)].
% 20.42/20.48 2474 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1258,b,1181,b)].
% 20.42/20.48 2475 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1258,b,1182,b)].
% 20.42/20.48 2476 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1296,b,1277,b)].
% 20.42/20.48 2477 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1296,b,1291,b)].
% 20.42/20.48 2478 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1387,b,1344,a)].
% 20.42/20.48 2479 class_Orderings_Oord(tc_nat). [resolve(1387,b,1345,a)].
% 20.42/20.48 2480 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1387,b,1347,b)].
% 20.42/20.48 2481 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1387,b,1348,b)].
% 20.42/20.48 2482 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1387,b,1349,b)].
% 20.42/20.48 2483 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1387,b,1351,b)].
% 20.42/20.48 2484 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1387,b,1354,b)].
% 20.42/20.48 2485 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1387,b,1356,b)].
% 20.42/20.48 2486 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1387,b,1357,b)].
% 20.42/20.48 2487 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1387,b,1358,b)].
% 20.42/20.48 2488 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1387,b,1359,b)].
% 20.42/20.48 2489 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1526,b,1401,a)].
% 20.42/20.48 2490 class_Orderings_Oord(tc_nat). [resolve(1526,b,1402,a)].
% 20.42/20.48 2491 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1647,b,1583,a)].
% 20.42/20.48 2492 class_Orderings_Oord(tc_nat). [resolve(1647,b,1584,a)].
% 20.42/20.48 2493 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1647,b,1585,b)].
% 20.42/20.48 2494 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1647,b,1587,b)].
% 20.42/20.48 2495 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1647,b,1588,b)].
% 20.42/20.48 2496 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1647,b,1589,b)].
% 20.42/20.48 2497 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1647,b,1590,b)].
% 20.42/20.48 2498 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1814,b,1649,a)].
% 20.42/20.48 2499 class_Orderings_Oord(tc_nat). [resolve(1814,b,1650,a)].
% 20.42/20.48 2500 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1814,b,1652,b)].
% 20.65/20.75 2501 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1814,b,1653,b)].
% 20.65/20.75 2502 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1814,b,1654,b)].
% 20.65/20.75 2503 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1814,b,1655,b)].
% 20.65/20.75 2504 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1852,b,1823,b)].
% 20.65/20.75 2505 class_Orderings_Oord(tc_IntDef_Oint). [resolve(2212,b,1957,a)].
% 20.65/20.75 2506 class_Orderings_Oord(tc_nat). [resolve(2212,b,1958,a)].
% 20.65/20.75 2507 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2413,b,2314,b)].
% 20.65/20.75 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].
% 20.65/20.75 2509 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom). [assumption].
% 20.65/20.75 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].
% 20.65/20.75 2511 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom). [assumption].
% 20.65/20.75 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].
% 20.65/20.75 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].
% 20.65/20.75 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].
% 20.65/20.75 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].
% 20.65/20.75 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].
% 20.65/20.75 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].
% 20.65/20.75 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(2517,a,2509,a)].
% 20.65/20.75 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2517,a,2513,b)].
% 20.65/20.75 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2517,a,2514,b)].
% 20.65/20.75 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2517,a,2515,b)].
% 20.65/20.75 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2517,a,2516,b)].
% 20.65/20.75 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].
% 20.65/20.75 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(2518,a,2509,a)].
% 20.65/20.75 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2518,a,2513,b)].
% 20.65/20.75 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2518,a,2514,b)].
% 20.65/20.75 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2518,a,2515,b)].
% 20.65/20.75 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2518,a,2516,b)].
% 20.65/20.75 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].
% 20.65/20.75 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)].
% 20.65/20.77 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)].
% 20.65/20.77 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)].
% 20.65/20.77 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)].
% 20.65/20.77 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)].
% 20.65/20.77 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].
% 20.65/20.77 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2520,a,2509,a)].
% 20.65/20.77 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2520,a,2513,b)].
% 20.65/20.77 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2520,a,2514,b)].
% 20.65/20.77 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2520,a,2515,b)].
% 20.65/20.77 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2520,a,2516,b)].
% 20.65/20.77 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].
% 20.65/20.77 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(2521,a,2509,a)].
% 20.65/20.77 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2521,a,2513,b)].
% 20.65/20.77 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(2521,a,2514,b)].
% 20.65/20.77 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2521,a,2515,b)].
% 20.65/20.77 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2521,a,2516,b)].
% 20.65/20.77 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].
% 20.65/20.77 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2522,a,2509,a)].
% 20.65/20.77 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2522,a,2513,b)].
% 20.65/20.77 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2522,a,2514,b)].
% 20.65/20.77 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2522,a,2515,b)].
% 20.65/20.77 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2522,a,2516,b)].
% 20.65/20.77 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].
% 20.65/20.77 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)].
% 20.65/20.77 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)].
% 20.65/20.77 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)].
% 20.65/20.77 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)].
% 20.65/20.77 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)].
% 20.65/20.77 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].
% 20.65/20.77 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(2524,a,2509,a)].
% 20.65/20.77 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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].
% 20.65/20.78 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2525,a,2509,a)].
% 20.65/20.78 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2525,a,2513,b)].
% 20.65/20.78 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2525,a,2514,b)].
% 20.65/20.78 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2525,a,2515,b)].
% 20.65/20.78 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)].
% 20.65/20.78 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].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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].
% 20.65/20.78 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2527,a,2509,a)].
% 20.65/20.78 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2527,a,2513,b)].
% 20.65/20.78 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2527,a,2514,b)].
% 20.65/20.78 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2527,a,2515,b)].
% 20.65/20.78 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2527,a,2516,b)].
% 20.65/20.78 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].
% 20.65/20.78 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(2528,a,2509,a)].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.65/20.78 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)].
% 20.76/20.85 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)].
% 20.76/20.85 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].
% 20.76/20.85 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2530,a,2509,a)].
% 20.76/20.85 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2530,a,2513,b)].
% 20.76/20.85 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2530,a,2514,b)].
% 20.76/20.85 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2530,a,2515,b)].
% 20.76/20.85 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)].
% 20.76/20.85 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].
% 20.76/20.85 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(2531,a,2509,a)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 2532 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(B,B,A). [resolve(9,b,2,a)].
% 20.76/20.85 2533 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(33,a,9,b)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.76/20.85 2543 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(151,b,147,a)].
% 20.76/20.85 2544 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(151,b,148,a)].
% 20.76/20.85 2545 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(183,a,151,b)].
% 20.76/20.85 2546 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(184,a,151,b)].
% 20.76/20.85 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)].
% 20.76/20.85 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)].
% 20.95/21.02 2549 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(346,b,317,b)].
% 20.95/21.02 2550 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1087,a,1074,b)].
% 20.95/21.02 2551 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1118,a,1105,b)].
% 20.95/21.02 2552 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1161,b,1135,b)].
% 20.95/21.02 2553 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1163,b,1135,b)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 2565 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1342,a,1311,b)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 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)].
% 20.95/21.02 2574 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1384,b,1347,b)].
% 20.95/21.02 2575 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1386,b,1347,b)].
% 20.95/21.02 2576 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1388,b,1347,b)].
% 20.95/21.02 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2590,c,2509,a)].
% 21.06/21.19 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)].
% 21.06/21.19 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2591,b,2509,a)].
% 21.06/21.19 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)].
% 21.06/21.19 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(2592,c,2509,a)].
% 21.06/21.19 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)].
% 21.06/21.19 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(2593,b,2509,a)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 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)].
% 21.06/21.19 2596 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2241,a,2226,b)].
% 21.06/21.19 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2596,b,2509,a)].
% 21.16/21.23 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)].
% 21.16/21.23 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(2597,c,2509,a)].
% 21.16/21.23 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)].
% 21.16/21.23 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(2598,c,2509,a)].
% 21.16/21.23 2599 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2244,a,2226,b)].
% 21.16/21.23 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2599,b,2509,a)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 2601 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(2246,a,2226,b)].
% 21.16/21.23 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(2601,b,2509,a)].
% 21.16/21.23 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)].
% 21.16/21.23 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(2602,c,2509,a)].
% 21.16/21.23 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)].
% 21.16/21.23 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(2603,c,2509,a)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 2607 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(2252,a,2226,b)].
% 21.16/21.23 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2607,b,2509,a)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.23 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.16/21.26 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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].
% 21.36/21.46 2629 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom). [assumption].
% 21.36/21.46 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].
% 21.36/21.46 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].
% 21.36/21.46 2632 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom). [assumption].
% 21.36/21.46 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].
% 21.36/21.46 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].
% 21.36/21.46 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].
% 21.36/21.46 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].
% 21.36/21.46 2637 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(11,b,2,a)].
% 21.36/21.46 2638 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(33,a,11,b)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.36/21.46 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)].
% 21.55/21.64 2648 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(153,b,147,a)].
% 21.55/21.64 2649 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(153,b,148,a)].
% 21.55/21.64 2650 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(183,a,153,b)].
% 21.55/21.64 2651 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(184,a,153,b)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 2654 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(346,b,319,b)].
% 21.55/21.64 2655 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1087,a,1076,b)].
% 21.55/21.64 2656 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1118,a,1107,b)].
% 21.55/21.64 2657 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1161,b,1137,b)].
% 21.55/21.64 2658 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1163,b,1137,b)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 2670 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1342,a,1313,b)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.55/21.64 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 2679 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1384,b,1349,b)].
% 21.76/21.81 2680 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1386,b,1349,b)].
% 21.76/21.81 2681 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1388,b,1349,b)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 2693 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2228,b,2220,a)].
% 21.76/21.81 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(2693,a,2629,a)].
% 21.76/21.81 2694 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2228,b,2222,a)].
% 21.76/21.81 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(2694,a,2629,a)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 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)].
% 21.76/21.81 2703 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2241,a,2228,b)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 2706 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2244,a,2228,b)].
% 21.76/21.87 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)].
% 21.76/21.87 2708 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(2246,a,2228,b)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 2714 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(2252,a,2228,b)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.76/21.87 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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].
% 21.99/22.08 2736 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom). [assumption].
% 21.99/22.08 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].
% 21.99/22.08 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].
% 21.99/22.08 2739 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom). [assumption].
% 21.99/22.08 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].
% 21.99/22.08 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].
% 21.99/22.08 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].
% 21.99/22.08 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].
% 21.99/22.08 2744 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(10,b,2,a)].
% 21.99/22.08 2745 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(33,a,10,b)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 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)].
% 21.99/22.08 2755 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(152,b,147,a)].
% 22.15/22.24 2756 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(152,b,148,a)].
% 22.15/22.24 2757 c_plus(A,c_0,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(183,a,152,b)].
% 22.15/22.24 2758 c_plus(c_0,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(184,a,152,b)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 2761 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(346,b,318,b)].
% 22.15/22.24 2762 c_LOrder_Omeet(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1087,a,1075,b)].
% 22.15/22.24 2763 c_LOrder_Ojoin(A,A,B) = A | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1118,a,1106,b)].
% 22.15/22.24 2764 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1161,b,1136,b)].
% 22.15/22.24 2765 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1163,b,1136,b)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 2777 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1342,a,1312,b)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.15/22.24 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)].
% 22.37/22.41 2786 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1384,b,1348,b)].
% 22.37/22.41 2787 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1386,b,1348,b)].
% 22.37/22.41 2788 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1388,b,1348,b)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 2800 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2227,b,2220,a)].
% 22.37/22.41 2801 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(2227,b,2222,a)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 2810 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2241,a,2227,b)].
% 22.37/22.41 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)].
% 22.37/22.41 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)].
% 22.37/22.41 2813 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2244,a,2227,b)].
% 22.37/22.47 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)].
% 22.37/22.47 2815 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(2246,a,2227,b)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 2821 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(2252,a,2227,b)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.37/22.47 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)].
% 22.61/22.66 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)].
% 22.61/22.66 2842 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom). [assumption].
% 22.61/22.66 2843 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom). [assumption].
% 22.61/22.66 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].
% 22.61/22.66 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].
% 22.61/22.66 2846 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom). [assumption].
% 22.61/22.66 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].
% 22.61/22.66 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].
% 22.61/22.66 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].
% 22.61/22.66 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].
% 22.61/22.66 2851 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(19,b,2,a)].
% 22.61/22.66 2852 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(33,a,19,b)].
% 22.61/22.66 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)].
% 22.61/22.66 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)].
% 22.61/22.66 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)].
% 22.61/22.66 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)].
% 22.61/22.66 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)].
% 22.61/22.66 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)].
% 22.61/22.66 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)].
% 22.61/22.66 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)].
% 22.61/22.66 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)].
% 22.61/22.66 2862 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(71,a,85,b)].
% 22.61/22.66 2863 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(100,a,85,b)].
% 22.61/22.66 2864 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(102,a,85,b)].
% 22.61/22.66 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)].
% 22.61/22.66 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)].
% 22.61/22.69 2867 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(183,a,164,b)].
% 22.61/22.69 2868 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(184,a,164,b)].
% 22.61/22.69 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)].
% 22.61/22.69 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)].
% 22.61/22.69 2871 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(223,a,198,b)].
% 22.61/22.69 2872 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(224,a,198,b)].
% 22.61/22.69 2873 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(226,b,198,b)].
% 22.61/22.69 2874 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(227,b,198,b)].
% 22.61/22.69 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)].
% 22.61/22.69 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)].
% 22.61/22.69 2877 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(346,b,331,b)].
% 22.61/22.69 2878 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(380,a,361,b)].
% 22.61/22.69 2879 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(381,a,361,b)].
% 22.61/22.69 2880 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(386,b,361,b)].
% 22.61/22.69 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)].
% 22.61/22.69 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)].
% 22.61/22.69 2883 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(391,b,361,b)].
% 22.61/22.69 2884 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(410,a,400,b)].
% 22.61/22.69 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)].
% 22.61/22.69 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)].
% 22.61/22.69 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)].
% 22.61/22.69 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)].
% 22.61/22.69 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)].
% 22.61/22.69 2890 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(421,b,400,b)].
% 22.61/22.69 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)].
% 22.61/22.69 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)].
% 22.61/22.69 2893 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(433,b,400,b)].
% 22.61/22.69 2894 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(434,b,400,b)].
% 22.61/22.69 2895 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(439,b,400,b)].
% 22.78/22.83 2896 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(440,b,400,b)].
% 22.78/22.83 2897 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(441,b,400,b)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 2900 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(444,b,400,b)].
% 22.78/22.83 2901 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1087,a,1079,b)].
% 22.78/22.83 2902 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1118,a,1110,b)].
% 22.78/22.83 2903 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1161,b,1140,b)].
% 22.78/22.83 2904 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1163,b,1140,b)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 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)].
% 22.78/22.83 2922 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1385,b,1354,b)].
% 22.78/22.83 2923 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1386,b,1354,b)].
% 22.78/22.83 2924 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1388,b,1354,b)].
% 22.78/22.83 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 2936 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1631,b,1585,b)].
% 22.92/22.98 2937 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1632,b,1585,b)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 2947 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1642,b,1585,b)].
% 22.92/22.98 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)].
% 22.92/22.98 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)].
% 22.92/22.98 2950 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1645,b,1585,b)].
% 22.92/22.98 2951 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1646,b,1585,b)].
% 22.92/22.98 2952 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(2229,b,2220,a)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 2961 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2241,a,2229,b)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 2964 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2244,a,2229,b)].
% 22.92/23.00 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)].
% 22.92/23.00 2966 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2246,a,2229,b)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 2972 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2252,a,2229,b)].
% 22.92/23.00 2973 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2297,b,2229,b)].
% 22.92/23.00 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2973,b,2843,a)].
% 22.92/23.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2973,b,2848,b)].
% 22.92/23.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2973,b,2849,b)].
% 22.92/23.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2973,b,2850,b)].
% 22.92/23.00 2974 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2356,b,2314,b)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 2980 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2367,b,2314,b)].
% 22.92/23.00 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2980,b,2843,a)].
% 22.92/23.00 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2980,b,2848,b)].
% 22.92/23.00 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2980,b,2849,b)].
% 22.92/23.00 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2980,b,2850,b)].
% 22.92/23.00 2981 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2368,b,2314,b)].
% 22.92/23.00 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2981,b,2843,a)].
% 22.92/23.00 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2981,b,2848,b)].
% 22.92/23.00 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2981,b,2849,b)].
% 22.92/23.00 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2981,b,2850,b)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.00 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 2990 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2382,b,2314,b)].
% 22.92/23.01 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(2990,b,2843,a)].
% 22.92/23.01 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2990,b,2848,b)].
% 22.92/23.01 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2990,b,2849,b)].
% 22.92/23.01 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2990,b,2850,b)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2991,c,2843,a)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2992,c,2843,a)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 2993 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2397,b,2314,b)].
% 22.92/23.01 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2993,b,2843,a)].
% 22.92/23.01 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2993,b,2848,b)].
% 22.92/23.01 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2993,b,2849,b)].
% 22.92/23.01 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2993,b,2850,b)].
% 22.92/23.01 2994 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2398,b,2314,b)].
% 22.92/23.01 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2994,b,2843,a)].
% 22.92/23.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2994,b,2848,b)].
% 22.92/23.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2994,b,2849,b)].
% 22.92/23.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2994,b,2850,b)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2995,c,2843,a)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2996,b,2843,a)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2997,c,2843,a)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2998,c,2843,a)].
% 22.92/23.01 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2998,c,2848,b)].
% 22.92/23.01 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2998,c,2849,b)].
% 22.92/23.01 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2998,c,2850,b)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2999,c,2843,a)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(3000,c,2843,a)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(3001,c,2843,a)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3002,c,2843,a)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(3003,b,2843,a)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 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)].
% 22.92/23.01 3004 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2408,b,2314,b)].
% 22.92/23.01 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3004,b,2843,a)].
% 22.92/23.02 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3004,b,2848,b)].
% 22.92/23.02 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3004,b,2849,b)].
% 22.92/23.02 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3004,b,2850,b)].
% 22.92/23.02 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)].
% 22.92/23.02 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)].
% 22.92/23.02 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 22.92/23.02 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 22.92/23.02 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_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)].
% 22.92/23.02 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)].
% 22.92/23.02 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)].
% 22.92/23.02 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 22.92/23.02 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 22.92/23.02 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 22.92/23.02 3007 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2411,b,2314,b)].
% 22.92/23.02 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(3007,b,2843,a)].
% 22.92/23.02 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3007,b,2848,b)].
% 22.92/23.02 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3007,b,2849,b)].
% 22.92/23.02 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3007,b,2850,b)].
% 22.92/23.02 3008 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2412,b,2314,b)].
% 22.92/23.02 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(3008,b,2843,a)].
% 22.92/23.02 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3008,b,2848,b)].
% 22.92/23.02 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3008,b,2849,b)].
% 22.92/23.02 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3008,b,2850,b)].
% 22.92/23.02 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 3029 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2517,a,2513,b)].
% 23.01/23.06 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(3029,c,2843,a)].
% 23.01/23.06 3030 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2518,a,2513,b)].
% 23.01/23.06 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(3030,b,2843,a)].
% 23.01/23.06 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)].
% 23.01/23.06 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)].
% 23.01/23.06 3032 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2520,a,2513,b)].
% 23.01/23.06 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3032,c,2843,a)].
% 23.01/23.06 3033 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Olordered__ring(A). [resolve(2521,a,2513,b)].
% 23.01/23.06 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(3033,b,2843,a)].
% 23.01/23.06 3034 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2522,a,2513,b)].
% 23.67/23.75 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3034,b,2843,a)].
% 23.67/23.75 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)].
% 23.67/23.75 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)].
% 23.67/23.75 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)].
% 23.67/23.75 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3036,c,2843,a)].
% 23.67/23.75 3037 c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2525,a,2513,b)].
% 23.67/23.75 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3037,b,2843,a)].
% 23.67/23.75 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)].
% 23.67/23.75 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)].
% 23.67/23.75 3039 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2527,a,2513,b)].
% 23.67/23.75 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3039,b,2843,a)].
% 23.67/23.75 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)].
% 23.67/23.75 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(3040,c,2843,a)].
% 23.67/23.75 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)].
% 23.67/23.75 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)].
% 23.67/23.75 3042 -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2530,a,2513,b)].
% 23.67/23.75 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3042,b,2843,a)].
% 23.67/23.75 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)].
% 23.67/23.75 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(3043,c,2843,a)].
% 23.67/23.75 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].
% 23.67/23.75 3045 class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_55) # label(axiom). [assumption].
% 23.67/23.75 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].
% 23.67/23.75 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].
% 23.67/23.75 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].
% 23.67/23.75 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].
% 23.67/23.75 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].
% 23.67/23.75 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].
% 23.67/23.75 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].
% 23.67/23.75 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)].
% 23.67/23.76 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)].
% 23.67/23.76 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)].
% 23.67/23.76 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].
% 23.67/23.76 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)].
% 23.67/23.76 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)].
% 23.67/23.76 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)].
% 23.67/23.76 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].
% 23.67/23.76 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)].
% 23.67/23.76 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)].
% 23.67/23.76 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)].
% 23.67/23.76 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].
% 23.67/23.76 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)].
% 23.67/23.76 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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)].
% 23.67/23.77 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].
% 23.77/23.78 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)].
% 23.77/23.78 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)].
% 23.77/23.78 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)].
% 23.77/23.78 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].
% 23.77/23.78 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)].
% 23.77/23.78 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)].
% 23.77/23.78 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)].
% 23.77/23.78 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].
% 23.77/23.78 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)].
% 23.77/23.78 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)].
% 23.77/23.78 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)].
% 23.77/23.78 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].
% 23.77/23.78 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)].
% 23.77/23.78 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)].
% 23.77/23.79 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)].
% 23.77/23.79 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].
% 23.77/23.79 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)].
% 23.77/23.79 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)].
% 23.77/23.79 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)].
% 23.77/23.79 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].
% 23.77/23.79 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)].
% 23.77/23.79 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)].
% 23.77/23.79 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)].
% 23.77/23.79 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].
% 23.77/23.79 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)].
% 23.77/23.79 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)].
% 23.77/23.79 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)].
% 23.77/23.80 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].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.77/23.80 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)].
% 23.81/23.87 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].
% 23.81/23.87 Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0. [resolve(3076,a,3045,a)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 3077 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,B,A). [resolve(23,b,2,a)].
% 23.81/23.87 3078 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(33,a,23,b)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 3088 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(71,a,89,b)].
% 23.81/23.87 3089 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(100,a,89,b)].
% 23.81/23.87 3090 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(102,a,89,b)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 3093 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(183,a,168,b)].
% 23.81/23.87 3094 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(184,a,168,b)].
% 23.81/23.87 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)].
% 23.81/23.87 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)].
% 23.81/23.87 3097 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(223,a,202,b)].
% 23.91/23.95 3098 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(224,a,202,b)].
% 23.91/23.95 3099 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(226,b,202,b)].
% 23.91/23.95 3100 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(227,b,202,b)].
% 23.91/23.95 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)].
% 23.91/23.95 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)].
% 23.91/23.95 3103 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(346,b,335,b)].
% 23.91/23.95 3104 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(380,a,365,b)].
% 23.91/23.95 3105 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(381,a,365,b)].
% 23.91/23.95 3106 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(386,b,365,b)].
% 23.91/23.95 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)].
% 23.91/23.95 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)].
% 23.91/23.95 3109 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(391,b,365,b)].
% 23.91/23.95 3110 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(410,a,403,b)].
% 23.91/23.95 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)].
% 23.91/23.95 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)].
% 23.91/23.95 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)].
% 23.91/23.95 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)].
% 23.91/23.95 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)].
% 23.91/23.95 3116 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(421,b,403,b)].
% 23.91/23.95 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)].
% 23.91/23.95 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)].
% 23.91/23.95 3119 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(433,b,403,b)].
% 23.91/23.95 3120 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(434,b,403,b)].
% 23.91/23.95 3121 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(439,b,403,b)].
% 23.91/23.95 3122 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(440,b,403,b)].
% 23.91/23.95 3123 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(441,b,403,b)].
% 23.91/23.95 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)].
% 23.91/23.95 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)].
% 23.91/23.95 3126 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(444,b,403,b)].
% 23.91/23.95 3127 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1087,a,1083,b)].
% 23.91/23.98 3128 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1118,a,1114,b)].
% 23.91/23.98 3129 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1161,b,1144,b)].
% 23.91/23.98 3130 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1163,b,1144,b)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.91/23.98 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.01 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)].
% 23.99/24.04 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)].
% 23.99/24.04 3174 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1219,a,1181,b)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 3179 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1224,a,1181,b)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 23.99/24.04 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 3206 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1385,b,1358,b)].
% 24.08/24.09 3207 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1386,b,1358,b)].
% 24.08/24.09 3208 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1388,b,1358,b)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 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)].
% 24.08/24.09 3220 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1498,b,1408,b)].
% 24.08/24.09 3221 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1499,b,1408,b)].
% 24.08/24.09 3222 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1523,b,1408,b)].
% 24.08/24.09 3223 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1631,b,1589,b)].
% 24.10/24.11 3224 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1632,b,1589,b)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 3234 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1642,b,1589,b)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 3237 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1645,b,1589,b)].
% 24.10/24.11 3238 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1646,b,1589,b)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.11 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.10/24.12 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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)].
% 24.12/24.13 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(3253,e,3046,b)].
% 24.12/24.13 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(3253,e,3047,b)].
% 24.12/24.13 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)].
% 24.12/24.14 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__field(B). [resolve(3254,e,3046,b)].
% 24.12/24.14 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(3254,e,3047,b)].
% 24.12/24.14 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)].
% 24.12/24.14 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(3255,d,3046,b)].
% 24.12/24.14 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(3255,d,3047,b)].
% 24.12/24.14 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)].
% 24.12/24.14 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_Ring__and__Field_Oordered__field(B). [resolve(3256,d,3046,b)].
% 24.12/24.14 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_Ring__and__Field_Oordered__idom(B). [resolve(3256,d,3047,b)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.14 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.15 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)].
% 24.12/24.16 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)].
% 24.12/24.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3270,c,3046,b)].
% 24.12/24.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3270,c,3047,b)].
% 24.12/24.16 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)].
% 24.12/24.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(3271,c,3046,b)].
% 24.12/24.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(3271,c,3047,b)].
% 24.12/24.16 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)].
% 24.12/24.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3272,d,3046,b)].
% 24.12/24.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3272,d,3047,b)].
% 24.12/24.16 3273 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1740,b,1654,b)].
% 24.12/24.16 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3273,b,3046,b)].
% 24.12/24.16 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3273,b,3047,b)].
% 24.12/24.16 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)].
% 24.12/24.16 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3274,b,3046,b)].
% 24.12/24.16 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3274,b,3047,b)].
% 24.12/24.16 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)].
% 24.12/24.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3275,c,3046,b)].
% 24.12/24.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3275,c,3047,b)].
% 24.12/24.16 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)].
% 24.12/24.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3276,c,3046,b)].
% 24.12/24.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3276,c,3047,b)].
% 24.12/24.16 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)].
% 24.12/24.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3277,d,3046,b)].
% 24.12/24.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3277,d,3047,b)].
% 24.12/24.16 3278 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1745,b,1654,b)].
% 24.12/24.16 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3278,b,3046,b)].
% 24.12/24.16 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3278,b,3047,b)].
% 24.12/24.16 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 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)].
% 24.12/24.17 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3287,c,3046,b)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.18 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 3305 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1773,b,1654,b)].
% 24.12/24.19 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)].
% 24.12/24.19 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)].
% 24.12/24.19 3308 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1788,b,1654,b)].
% 24.12/24.19 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3308,b,3046,b)].
% 24.12/24.19 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3308,b,3047,b)].
% 24.12/24.19 3309 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1789,b,1654,b)].
% 24.12/24.19 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3309,b,3046,b)].
% 24.12/24.19 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3309,b,3047,b)].
% 24.12/24.19 3310 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1790,b,1654,b)].
% 24.12/24.19 3311 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1796,b,1654,b)].
% 24.21/24.25 3312 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1797,b,1654,b)].
% 24.21/24.25 3313 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1798,b,1654,b)].
% 24.21/24.25 3314 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1799,b,1654,b)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 3324 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1809,b,1654,b)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 3327 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1812,b,1654,b)].
% 24.21/24.25 3328 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1813,b,1654,b)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.25 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 3337 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2241,a,2232,b)].
% 24.21/24.26 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3337,b,3046,b)].
% 24.21/24.26 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3337,b,3047,b)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 3340 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2244,a,2232,b)].
% 24.21/24.26 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3340,b,3046,b)].
% 24.21/24.26 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3340,b,3047,b)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 3342 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2246,a,2232,b)].
% 24.21/24.26 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3342,b,3046,b)].
% 24.21/24.26 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3342,b,3047,b)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.26 3348 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2252,a,2232,b)].
% 24.21/24.26 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3348,b,3046,b)].
% 24.21/24.26 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3348,b,3047,b)].
% 24.21/24.26 3349 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2321,a,2317,b)].
% 24.21/24.26 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3349,b,3046,b)].
% 24.21/24.26 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3349,b,3047,b)].
% 24.21/24.26 3350 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2356,b,2317,b)].
% 24.21/24.26 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3350,b,3046,b)].
% 24.21/24.26 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3350,b,3047,b)].
% 24.21/24.26 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)].
% 24.21/24.26 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.28 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.21/24.30 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 3376 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2517,a,2516,b)].
% 24.31/24.32 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3376,c,3046,b)].
% 24.31/24.32 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3376,c,3047,b)].
% 24.31/24.32 3377 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2518,a,2516,b)].
% 24.31/24.32 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3377,b,3046,b)].
% 24.31/24.32 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3377,b,3047,b)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 3379 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2520,a,2516,b)].
% 24.31/24.32 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3379,c,3046,b)].
% 24.31/24.32 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3379,c,3047,b)].
% 24.31/24.32 3380 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2521,a,2516,b)].
% 24.31/24.32 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3380,b,3046,b)].
% 24.31/24.32 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3380,b,3047,b)].
% 24.31/24.32 3381 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2522,a,2516,b)].
% 24.31/24.32 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3381,b,3046,b)].
% 24.31/24.32 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3381,b,3047,b)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.32 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)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3384,b,3046,b)].
% 24.31/24.33 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3384,b,3047,b)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 3386 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2527,a,2516,b)].
% 24.31/24.33 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3386,b,3046,b)].
% 24.31/24.33 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3386,b,3047,b)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3389,b,3046,b)].
% 24.31/24.33 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3389,b,3047,b)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 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)].
% 24.31/24.33 3391 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2973,b,2850,b)].
% 24.31/24.33 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(3391,b,3045,a)].
% 24.31/24.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3391,b,3046,b)].
% 24.31/24.33 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3391,b,3047,b)].
% 24.31/24.33 3392 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2980,b,2850,b)].
% 24.31/24.33 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(3392,b,3045,a)].
% 24.31/24.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3392,b,3046,b)].
% 24.31/24.33 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3392,b,3047,b)].
% 24.31/24.33 3393 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2981,b,2850,b)].
% 24.31/24.33 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(3393,b,3045,a)].
% 24.31/24.33 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3393,b,3046,b)].
% 24.31/24.34 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3393,b,3047,b)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.34 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 3402 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2990,b,2850,b)].
% 24.31/24.35 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(3402,b,3045,a)].
% 24.31/24.35 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3402,b,3046,b)].
% 24.31/24.35 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3402,b,3047,b)].
% 24.31/24.35 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)].
% 24.31/24.35 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(3403,c,3045,a)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(3404,c,3045,a)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 3405 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2993,b,2850,b)].
% 24.31/24.35 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(3405,b,3045,a)].
% 24.31/24.35 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3405,b,3046,b)].
% 24.31/24.35 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3405,b,3047,b)].
% 24.31/24.35 3406 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2994,b,2850,b)].
% 24.31/24.35 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(3406,b,3045,a)].
% 24.31/24.35 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3406,b,3046,b)].
% 24.31/24.35 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3406,b,3047,b)].
% 24.31/24.35 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)].
% 24.31/24.35 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3407,c,3045,a)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(3408,b,3045,a)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3409,c,3045,a)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(3411,c,3045,a)].
% 24.31/24.35 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(3411,c,3046,b)].
% 24.31/24.35 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3411,c,3047,b)].
% 24.31/24.35 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)].
% 24.31/24.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(3412,c,3045,a)].
% 24.31/24.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3412,c,3046,b)].
% 24.31/24.35 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3412,c,3047,b)].
% 24.31/24.35 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)].
% 24.31/24.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(3413,c,3045,a)].
% 24.31/24.35 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(3413,c,3046,b)].
% 24.31/24.35 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3413,c,3047,b)].
% 24.31/24.35 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)].
% 24.31/24.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(3414,c,3045,a)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.31/24.35 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)].
% 24.50/24.54 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)].
% 24.50/24.54 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3415,b,3046,b)].
% 24.50/24.54 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3415,b,3047,b)].
% 24.50/24.54 3416 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3004,b,2850,b)].
% 24.50/24.54 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(3416,b,3045,a)].
% 24.50/24.54 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3416,b,3046,b)].
% 24.50/24.54 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3416,b,3047,b)].
% 24.50/24.54 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)].
% 24.50/24.54 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3417,c,3045,a)].
% 24.50/24.54 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3417,c,3046,b)].
% 24.50/24.54 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3417,c,3047,b)].
% 24.50/24.54 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)].
% 24.50/24.54 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3418,c,3045,a)].
% 24.50/24.54 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3418,c,3046,b)].
% 24.50/24.54 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3418,c,3047,b)].
% 24.50/24.54 3419 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3007,b,2850,b)].
% 24.50/24.54 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(3419,b,3045,a)].
% 24.50/24.54 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3419,b,3046,b)].
% 24.50/24.54 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3419,b,3047,b)].
% 24.50/24.54 3420 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(3008,b,2850,b)].
% 24.50/24.54 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(3420,b,3045,a)].
% 24.50/24.54 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3420,b,3046,b)].
% 24.50/24.54 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3420,b,3047,b)].
% 24.50/24.54 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].
% 24.50/24.56 3422 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom). [assumption].
% 24.50/24.56 3423 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom). [assumption].
% 24.50/24.56 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].
% 24.50/24.56 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].
% 24.50/24.56 3426 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom). [assumption].
% 24.50/24.56 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].
% 24.50/24.56 3428 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom). [assumption].
% 24.50/24.56 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].
% 24.50/24.56 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(3429,a,3422,a)].
% 24.50/24.56 Derived: c_0 != c_NatArith_Oof__nat(A,tc_nat) | c_0 = A. [resolve(3429,a,3423,a)].
% 24.50/24.56 Derived: c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3429,a,3424,b)].
% 24.50/24.56 Derived: c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3429,a,3425,b)].
% 24.50/24.56 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].
% 24.50/24.56 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(3430,a,3422,a)].
% 24.50/24.56 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_nat). [resolve(3430,a,3423,a)].
% 24.50/24.56 Derived: c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3430,a,3424,b)].
% 24.50/24.56 Derived: c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3430,a,3425,b)].
% 24.50/24.56 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].
% 24.50/24.56 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3431,a,3422,a)].
% 24.50/24.56 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(3431,a,3423,a)].
% 24.50/24.56 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3431,a,3424,b)].
% 24.50/24.56 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3431,a,3425,b)].
% 24.50/24.56 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].
% 24.50/24.56 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)].
% 24.50/24.56 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)].
% 24.50/24.56 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)].
% 24.50/24.56 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)].
% 24.50/24.56 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].
% 24.50/24.56 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)].
% 24.50/24.56 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)].
% 24.50/24.58 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)].
% 24.50/24.58 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)].
% 24.50/24.58 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].
% 24.50/24.58 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3434,a,3422,a)].
% 24.50/24.58 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_0 | A = c_0. [resolve(3434,a,3423,a)].
% 24.50/24.58 Derived: c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3434,a,3424,b)].
% 24.50/24.58 Derived: c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3434,a,3425,b)].
% 24.50/24.58 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].
% 24.50/24.58 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(3435,a,3422,a)].
% 24.50/24.58 Derived: c_NatArith_Oof__nat(c_0,tc_nat) = c_0. [resolve(3435,a,3423,a)].
% 24.50/24.58 Derived: c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3435,a,3424,b)].
% 24.50/24.58 Derived: c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3435,a,3425,b)].
% 24.50/24.58 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].
% 24.50/24.58 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(3436,a,3422,a)].
% 24.50/24.58 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_NatArith_Oof__nat(B,tc_nat) | A = B. [resolve(3436,a,3423,a)].
% 24.50/24.58 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)].
% 24.50/24.58 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)].
% 24.50/24.58 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].
% 24.50/24.58 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3437,a,3422,a)].
% 24.50/24.58 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat) | A = c_0. [resolve(3437,a,3423,a)].
% 24.50/24.58 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)].
% 24.50/24.58 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)].
% 24.50/24.58 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].
% 24.50/24.58 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3438,a,3422,a)].
% 24.50/24.58 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_nat),c_0,tc_nat). [resolve(3438,a,3423,a)].
% 24.50/24.58 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)].
% 24.50/24.58 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)].
% 24.50/24.58 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].
% 24.50/24.58 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)].
% 24.50/24.58 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)].
% 24.50/24.58 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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].
% 24.60/24.61 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3441,a,3422,a)].
% 24.60/24.61 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3441,a,3424,b)].
% 24.60/24.61 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3441,a,3425,b)].
% 24.60/24.61 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].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.61 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)].
% 24.60/24.62 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)].
% 24.60/24.62 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].
% 24.60/24.62 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)].
% 24.60/24.62 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)].
% 24.60/24.62 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)].
% 24.60/24.62 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)].
% 24.60/24.62 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].
% 24.60/24.62 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)].
% 24.60/24.62 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)].
% 24.60/24.62 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)].
% 24.60/24.62 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)].
% 24.60/24.62 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].
% 24.60/24.62 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)].
% 24.60/24.62 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)].
% 24.60/24.62 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)].
% 24.60/24.62 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)].
% 24.60/24.62 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].
% 24.60/24.62 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)].
% 24.60/24.62 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)].
% 24.60/24.66 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)].
% 24.60/24.66 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)].
% 24.60/24.66 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].
% 24.60/24.66 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(3449,a,3422,a)].
% 24.60/24.66 Derived: -c_lessequals(c_1,c_0,tc_nat). [resolve(3449,a,3423,a)].
% 24.60/24.66 Derived: -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3449,a,3424,b)].
% 24.60/24.66 Derived: -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3449,a,3425,b)].
% 24.60/24.66 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].
% 24.60/24.66 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(3450,a,3422,a)].
% 24.60/24.66 Derived: -c_less(c_1,c_0,tc_nat). [resolve(3450,a,3423,a)].
% 24.60/24.66 Derived: -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3450,a,3424,b)].
% 24.60/24.66 Derived: -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3450,a,3425,b)].
% 24.60/24.66 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].
% 24.60/24.66 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(3451,a,3422,a)].
% 24.60/24.66 Derived: c_less(c_0,c_1,tc_nat). [resolve(3451,a,3423,a)].
% 24.60/24.66 Derived: c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3451,a,3424,b)].
% 24.60/24.66 Derived: c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3451,a,3425,b)].
% 24.60/24.66 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].
% 24.60/24.66 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(3452,a,3422,a)].
% 24.60/24.66 Derived: c_lessequals(c_0,c_1,tc_nat). [resolve(3452,a,3423,a)].
% 24.60/24.66 Derived: c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3452,a,3424,b)].
% 24.60/24.66 Derived: c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3452,a,3425,b)].
% 24.60/24.66 3453 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,B,A). [resolve(24,b,2,a)].
% 24.60/24.66 3454 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(33,a,24,b)].
% 24.60/24.66 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)].
% 24.60/24.66 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)].
% 24.60/24.66 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)].
% 24.60/24.66 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)].
% 24.60/24.66 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)].
% 24.60/24.66 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)].
% 24.60/24.66 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)].
% 24.60/24.66 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)].
% 24.60/24.66 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)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 3473 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(71,a,90,b)].
% 24.70/24.69 3474 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(100,a,90,b)].
% 24.70/24.69 3475 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(102,a,90,b)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 3478 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(183,a,169,b)].
% 24.70/24.69 3479 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(184,a,169,b)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 3482 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(223,a,203,b)].
% 24.70/24.69 3483 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(224,a,203,b)].
% 24.70/24.69 3484 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(226,b,203,b)].
% 24.70/24.69 3485 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(227,b,203,b)].
% 24.70/24.69 3486 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(249,b,228,a)].
% 24.70/24.69 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)].
% 24.70/24.69 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)].
% 24.70/24.69 3489 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(346,b,336,b)].
% 24.72/24.74 3490 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(380,a,366,b)].
% 24.72/24.74 3491 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(381,a,366,b)].
% 24.72/24.74 3492 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(386,b,366,b)].
% 24.72/24.74 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)].
% 24.72/24.74 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)].
% 24.72/24.74 3495 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(391,b,366,b)].
% 24.72/24.74 3496 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(598,a,594,b)].
% 24.72/24.74 3497 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(599,a,594,b)].
% 24.72/24.74 3498 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(633,b,623,b)].
% 24.72/24.74 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)].
% 24.72/24.74 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)].
% 24.72/24.74 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)].
% 24.72/24.74 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)].
% 24.72/24.74 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)].
% 24.72/24.74 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)].
% 24.72/24.74 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)].
% 24.72/24.74 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)].
% 24.72/24.74 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)].
% 24.72/24.74 3508 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(681,b,658,b)].
% 24.72/24.74 3509 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(682,b,658,b)].
% 24.72/24.74 3510 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(738,b,699,b)].
% 24.72/24.74 3511 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(739,b,699,b)].
% 24.72/24.74 3512 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(779,b,753,b)].
% 24.72/24.74 3513 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(780,b,753,b)].
% 24.72/24.74 3514 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(869,a,868,b)].
% 24.72/24.74 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(3514,b,3423,a)].
% 24.72/24.74 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3514,b,3424,b)].
% 24.72/24.74 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3514,b,3425,b)].
% 24.72/24.74 3515 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(870,a,868,b)].
% 24.72/24.74 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(3515,b,3423,a)].
% 24.72/24.74 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3515,b,3424,b)].
% 24.72/24.74 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3515,b,3425,b)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(3518,b,3423,a)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 3520 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__semidom(A). [resolve(875,a,868,b)].
% 24.72/24.75 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(3520,b,3423,a)].
% 24.72/24.75 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(3520,b,3424,b)].
% 24.72/24.75 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3520,b,3425,b)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.75 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)].
% 24.72/24.79 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)].
% 24.72/24.79 3523 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(878,a,868,b)].
% 24.72/24.79 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(3523,b,3423,a)].
% 24.72/24.79 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3523,b,3424,b)].
% 24.72/24.79 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3523,b,3425,b)].
% 24.72/24.79 3524 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1087,a,1084,b)].
% 24.72/24.79 3525 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1118,a,1115,b)].
% 24.72/24.79 3526 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1161,b,1145,b)].
% 24.72/24.79 3527 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1163,b,1145,b)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.72/24.79 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.82 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 3571 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1219,a,1182,b)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 3576 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1224,a,1182,b)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.85 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 3603 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1385,b,1359,b)].
% 24.83/24.89 3604 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1386,b,1359,b)].
% 24.83/24.89 3605 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1388,b,1359,b)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 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)].
% 24.83/24.89 3617 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1498,b,1409,b)].
% 24.83/24.89 3618 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1499,b,1409,b)].
% 24.93/24.92 3619 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1523,b,1409,b)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 3622 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1579,b,1547,b)].
% 24.93/24.92 3623 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1580,b,1547,b)].
% 24.93/24.92 3624 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1631,b,1590,b)].
% 24.93/24.92 3625 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1632,b,1590,b)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 3635 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1642,b,1590,b)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 3638 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1645,b,1590,b)].
% 24.93/24.92 3639 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1646,b,1590,b)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.92 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.94 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 3674 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1740,b,1655,b)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 3679 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1745,b,1655,b)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.96 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 3706 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1773,b,1655,b)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 24.93/24.98 3709 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1788,b,1655,b)].
% 24.93/24.98 3710 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1789,b,1655,b)].
% 24.93/24.98 3711 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1790,b,1655,b)].
% 24.93/24.98 3712 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1796,b,1655,b)].
% 24.93/24.98 3713 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1797,b,1655,b)].
% 24.93/24.98 3714 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1798,b,1655,b)].
% 24.93/24.98 3715 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1799,b,1655,b)].
% 24.93/24.98 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)].
% 24.93/24.98 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)].
% 25.03/25.04 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)].
% 25.03/25.04 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)].
% 25.03/25.04 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)].
% 25.03/25.04 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)].
% 25.03/25.04 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)].
% 25.03/25.04 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)].
% 25.03/25.04 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)].
% 25.03/25.04 3725 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1809,b,1655,b)].
% 25.03/25.04 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)].
% 25.03/25.04 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)].
% 25.03/25.04 3728 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1812,b,1655,b)].
% 25.03/25.04 3729 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1813,b,1655,b)].
% 25.03/25.04 3730 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1955,b,1877,b)].
% 25.03/25.04 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3730,b,3424,b)].
% 25.03/25.04 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3730,b,3425,b)].
% 25.03/25.04 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)].
% 25.03/25.04 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3731,c,3423,a)].
% 25.03/25.04 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)].
% 25.03/25.04 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3732,c,3423,a)].
% 25.03/25.04 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)].
% 25.03/25.04 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)].
% 25.03/25.04 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)].
% 25.03/25.04 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3734,c,3423,a)].
% 25.03/25.04 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)].
% 25.03/25.04 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3735,c,3423,a)].
% 25.03/25.04 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)].
% 25.03/25.04 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)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(3737,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(3738,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(3739,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(3740,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3741,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(3742,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 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)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3744,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(3745,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(3746,d,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(3747,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(3748,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(3749,c,3423,a)].
% 25.31/25.29 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)].
% 25.31/25.29 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(3750,c,3423,a)].
% 25.31/25.29 3751 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom). [assumption].
% 25.31/25.29 3752 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom). [assumption].
% 25.31/25.29 3753 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom). [assumption].
% 25.33/25.36 3754 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom). [assumption].
% 25.33/25.36 3755 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom). [assumption].
% 25.33/25.36 3756 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom). [assumption].
% 25.33/25.36 3757 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom). [assumption].
% 25.33/25.36 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].
% 25.33/25.36 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].
% 25.33/25.36 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)].
% 25.33/25.36 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)].
% 25.33/25.36 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)].
% 25.33/25.36 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)].
% 25.33/25.36 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)].
% 25.33/25.36 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)].
% 25.33/25.36 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)].
% 25.33/25.36 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)].
% 25.33/25.36 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)].
% 25.33/25.36 3769 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(71,a,84,b)].
% 25.33/25.36 3770 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(100,a,84,b)].
% 25.33/25.36 3771 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(102,a,84,b)].
% 25.33/25.36 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)].
% 25.33/25.36 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)].
% 25.33/25.36 3774 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(183,a,163,b)].
% 25.33/25.36 3775 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(184,a,163,b)].
% 25.33/25.36 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)].
% 25.33/25.36 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)].
% 25.33/25.36 3778 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(223,a,197,b)].
% 25.33/25.38 3779 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(224,a,197,b)].
% 25.33/25.38 3780 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(226,b,197,b)].
% 25.33/25.38 3781 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(227,b,197,b)].
% 25.33/25.38 3782 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(307,a,291,b)].
% 25.33/25.38 3783 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(308,a,291,b)].
% 25.33/25.38 3784 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(346,b,330,b)].
% 25.33/25.38 3785 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(380,a,360,b)].
% 25.33/25.38 3786 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(381,a,360,b)].
% 25.33/25.38 3787 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(386,b,360,b)].
% 25.33/25.38 3788 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(389,c,360,b)].
% 25.33/25.38 3789 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(390,c,360,b)].
% 25.33/25.38 3790 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(391,b,360,b)].
% 25.33/25.38 3791 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(410,a,399,b)].
% 25.33/25.38 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3791,b,3753,b)].
% 25.33/25.38 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)].
% 25.33/25.38 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)].
% 25.33/25.38 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)].
% 25.33/25.38 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)].
% 25.33/25.38 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)].
% 25.33/25.38 3797 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(421,b,399,b)].
% 25.33/25.38 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)].
% 25.33/25.38 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3798,c,3753,b)].
% 25.33/25.38 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)].
% 25.33/25.38 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_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)].
% 25.33/25.38 3800 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(433,b,399,b)].
% 25.33/25.38 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3800,b,3753,b)].
% 25.33/25.38 3801 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(434,b,399,b)].
% 25.33/25.38 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3801,b,3753,b)].
% 25.33/25.38 3802 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(439,b,399,b)].
% 25.33/25.38 3803 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(440,b,399,b)].
% 25.33/25.38 3804 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(441,b,399,b)].
% 25.33/25.38 3805 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(442,c,399,b)].
% 25.43/25.41 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3805,c,3753,b)].
% 25.43/25.41 3806 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(443,c,399,b)].
% 25.43/25.41 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3806,c,3753,b)].
% 25.43/25.41 3807 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(444,b,399,b)].
% 25.43/25.41 3808 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(511,b,501,b)].
% 25.43/25.41 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3808,b,3753,b)].
% 25.43/25.41 3809 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(598,a,591,b)].
% 25.43/25.41 3810 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(599,a,591,b)].
% 25.43/25.41 3811 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(633,b,620,b)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.41 3821 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(681,b,655,b)].
% 25.43/25.41 3822 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(682,b,655,b)].
% 25.43/25.41 3823 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(738,b,696,b)].
% 25.43/25.41 3824 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(739,b,696,b)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.41 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3826,c,3753,b)].
% 25.43/25.41 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)].
% 25.43/25.41 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 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)].
% 25.43/25.42 3839 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(846,b,789,b)].
% 25.43/25.42 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3839,b,3753,b)].
% 25.43/25.42 3840 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(847,b,789,b)].
% 25.43/25.44 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3840,b,3753,b)].
% 25.43/25.44 3841 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(848,b,789,b)].
% 25.43/25.44 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3841,b,3753,b)].
% 25.43/25.44 3842 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(850,b,789,b)].
% 25.43/25.44 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3842,b,3753,b)].
% 25.43/25.44 3843 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(851,b,789,b)].
% 25.43/25.44 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3843,b,3753,b)].
% 25.43/25.44 3844 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(869,a,865,b)].
% 25.43/25.44 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3844,b,3753,b)].
% 25.43/25.44 3845 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oidom(A). [resolve(870,a,865,b)].
% 25.43/25.44 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3845,b,3753,b)].
% 25.43/25.44 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)].
% 25.43/25.44 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)].
% 25.43/25.44 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)].
% 25.43/25.44 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)].
% 25.43/25.44 3848 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oidom(B). [resolve(873,a,865,b)].
% 25.43/25.44 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3848,b,3753,b)].
% 25.43/25.44 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)].
% 25.43/25.44 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)].
% 25.43/25.44 3850 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(875,a,865,b)].
% 25.43/25.44 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3850,b,3753,b)].
% 25.43/25.44 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)].
% 25.43/25.44 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)].
% 25.43/25.44 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)].
% 25.43/25.44 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)].
% 25.43/25.44 3853 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(878,a,865,b)].
% 25.43/25.44 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3853,b,3753,b)].
% 25.43/25.44 3854 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(945,a,942,b)].
% 25.43/25.44 Derived: c_in(c_0,c_IntDef_OInts,tc_IntDef_Oint). [resolve(3854,b,3752,a)].
% 25.43/25.44 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3854,b,3753,b)].
% 25.43/25.44 3855 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oidom(A). [resolve(946,a,942,b)].
% 25.43/25.44 Derived: c_in(c_1,c_IntDef_OInts,tc_IntDef_Oint). [resolve(3855,b,3752,a)].
% 25.43/25.44 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3855,b,3753,b)].
% 25.43/25.44 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)].
% 25.43/25.44 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 3860 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(951,a,942,b)].
% 25.43/25.45 Derived: c_IntDef_Oof__int(c_1,tc_IntDef_Oint) = c_1. [resolve(3860,b,3752,a)].
% 25.43/25.45 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3860,b,3753,b)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.45 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.43/25.46 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)].
% 25.91/25.88 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)].
% 25.91/25.88 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)].
% 25.91/25.88 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)].
% 25.91/25.88 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)].
% 25.91/25.88 3873 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1067,b,942,b)].
% 25.91/25.88 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3873,b,3753,b)].
% 25.91/25.88 3874 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1068,b,942,b)].
% 25.91/25.88 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3874,b,3753,b)].
% 25.91/25.88 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].
% 25.91/25.88 3876 class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_58) # label(axiom). [assumption].
% 25.91/25.88 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].
% 25.91/25.88 3878 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_21) # label(axiom). [assumption].
% 25.91/25.88 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].
% 25.91/25.88 3880 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_28) # label(axiom). [assumption].
% 25.91/25.88 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].
% 25.91/25.88 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].
% 25.91/25.88 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].
% 25.91/25.88 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)].
% 25.91/25.88 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)].
% 25.91/25.88 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].
% 25.91/25.88 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)].
% 25.91/25.88 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)].
% 25.91/25.88 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].
% 25.91/25.89 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)].
% 25.91/25.89 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)].
% 25.91/25.89 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].
% 25.91/25.89 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)].
% 25.91/25.89 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)].
% 25.91/25.89 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].
% 25.91/25.89 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)].
% 25.91/25.89 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)].
% 25.91/25.89 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].
% 25.91/25.89 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)].
% 25.91/25.89 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)].
% 25.91/25.89 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].
% 25.91/25.89 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)].
% 25.91/25.89 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)].
% 25.91/25.89 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].
% 25.91/25.89 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)].
% 25.91/25.89 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)].
% 25.91/25.89 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].
% 25.91/25.89 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)].
% 25.91/25.89 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)].
% 25.91/25.89 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].
% 25.91/25.89 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)].
% 25.91/25.89 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)].
% 25.91/25.89 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].
% 25.91/25.89 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)].
% 25.91/25.89 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)].
% 25.91/25.89 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].
% 25.91/25.90 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)].
% 25.91/25.90 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)].
% 25.91/25.90 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].
% 25.91/25.90 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)].
% 25.91/25.90 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)].
% 25.91/25.90 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].
% 25.91/25.90 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)].
% 25.91/25.90 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)].
% 25.91/25.90 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].
% 25.91/25.90 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)].
% 25.91/25.90 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)].
% 25.91/25.90 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].
% 25.91/25.90 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)].
% 25.91/25.90 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)].
% 25.91/25.91 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].
% 25.91/25.91 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)].
% 25.91/25.91 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)].
% 25.91/25.91 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].
% 25.91/25.91 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)].
% 25.91/25.91 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)].
% 25.91/25.91 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].
% 25.91/25.91 Derived: c_0 != c_IntDef_Oof__int(A,tc_IntDef_Oint) | c_0 = A. [resolve(3901,a,3876,a)].
% 25.91/25.91 Derived: c_0 != c_IntDef_Oof__int(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__field(B). [resolve(3901,a,3877,b)].
% 25.91/25.91 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].
% 25.91/25.91 Derived: c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint). [resolve(3902,a,3876,a)].
% 25.91/25.91 Derived: c_0 = c_IntDef_Oof__int(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3902,a,3877,b)].
% 25.91/25.91 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].
% 25.91/25.91 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)].
% 25.91/25.91 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)].
% 25.91/25.91 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].
% 25.91/25.91 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)].
% 25.91/25.91 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)].
% 25.91/25.91 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].
% 25.91/25.92 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)].
% 25.91/25.92 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)].
% 25.91/25.92 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].
% 25.91/25.92 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)].
% 25.91/25.92 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)].
% 25.91/25.92 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].
% 25.91/25.92 Derived: c_IntDef_Oof__int(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3907,a,3876,a)].
% 25.91/25.92 Derived: c_IntDef_Oof__int(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(3907,a,3877,b)].
% 25.91/25.92 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].
% 25.91/25.92 Derived: c_IntDef_Oof__int(c_0,tc_IntDef_Oint) = c_0. [resolve(3908,a,3876,a)].
% 25.91/25.92 Derived: c_IntDef_Oof__int(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(3908,a,3877,b)].
% 25.91/25.92 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].
% 25.91/25.92 Derived: c_IntDef_Oof__int(A,tc_IntDef_Oint) != c_IntDef_Oof__int(B,tc_IntDef_Oint) | A = B. [resolve(3909,a,3876,a)].
% 25.91/25.92 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)].
% 25.91/25.92 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].
% 25.91/25.92 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)].
% 25.91/25.92 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)].
% 25.91/25.92 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].
% 25.91/25.92 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)].
% 25.91/25.92 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)].
% 25.91/25.92 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].
% 25.91/25.92 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)].
% 25.91/25.92 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)].
% 25.91/25.92 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].
% 25.91/25.92 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)].
% 25.91/25.92 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.95 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].
% 25.91/25.95 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)].
% 25.91/25.95 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)].
% 25.91/25.96 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].
% 25.91/25.96 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)].
% 25.91/25.96 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)].
% 25.91/25.96 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].
% 25.91/25.96 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)].
% 25.91/25.96 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)].
% 25.91/25.96 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].
% 25.91/25.96 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)].
% 25.91/25.96 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)].
% 25.91/25.96 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].
% 25.91/25.96 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)].
% 25.91/25.96 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)].
% 25.91/25.96 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].
% 25.91/25.96 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)].
% 25.91/25.96 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)].
% 25.91/25.96 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].
% 25.91/25.96 Derived: -c_IntDef_Oneg(c_0,tc_IntDef_Oint). [resolve(3931,a,3876,a)].
% 25.91/25.97 Derived: -c_IntDef_Oneg(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3931,a,3877,b)].
% 25.91/25.97 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].
% 25.91/25.97 Derived: -c_IntDef_Oneg(c_1,tc_IntDef_Oint). [resolve(3932,a,3876,a)].
% 25.91/25.97 Derived: -c_IntDef_Oneg(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3932,a,3877,b)].
% 25.91/25.97 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].
% 25.91/25.97 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)].
% 25.91/25.97 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)].
% 25.91/25.97 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].
% 25.91/25.97 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)].
% 25.91/25.97 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)].
% 25.91/25.97 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].
% 25.91/25.97 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)].
% 25.91/25.97 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)].
% 25.91/25.97 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].
% 25.91/25.97 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)].
% 25.91/25.97 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)].
% 25.91/25.97 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].
% 25.91/25.97 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)].
% 25.91/25.97 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)].
% 25.91/25.97 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].
% 26.01/25.98 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)].
% 26.01/25.98 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)].
% 26.01/25.98 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].
% 26.01/25.98 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)].
% 26.01/25.98 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)].
% 26.01/25.98 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].
% 26.01/25.98 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)].
% 26.01/25.98 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)].
% 26.01/25.98 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].
% 26.01/25.98 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)].
% 26.01/25.98 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)].
% 26.01/25.98 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].
% 26.01/25.98 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)].
% 26.01/25.98 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)].
% 26.01/25.98 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].
% 26.01/25.98 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)].
% 26.01/25.98 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)].
% 26.01/25.98 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].
% 26.01/25.98 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)].
% 26.01/25.98 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)].
% 26.01/25.98 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].
% 26.01/25.98 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)].
% 26.01/25.98 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)].
% 26.01/25.98 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].
% 26.01/25.98 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)].
% 26.01/25.98 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)].
% 26.01/25.98 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].
% 26.01/25.98 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)].
% 26.01/25.98 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)].
% 26.01/25.98 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].
% 26.03/25.99 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)].
% 26.03/25.99 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)].
% 26.03/25.99 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].
% 26.03/25.99 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)].
% 26.03/25.99 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)].
% 26.03/25.99 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].
% 26.03/25.99 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)].
% 26.03/25.99 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)].
% 26.03/25.99 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].
% 26.03/25.99 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)].
% 26.03/25.99 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)].
% 26.03/25.99 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].
% 26.03/25.99 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)].
% 26.03/25.99 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)].
% 26.03/25.99 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].
% 26.03/26.00 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)].
% 26.03/26.00 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)].
% 26.03/26.00 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].
% 26.03/26.00 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)].
% 26.03/26.00 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)].
% 26.03/26.00 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].
% 26.03/26.00 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)].
% 26.03/26.00 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)].
% 26.03/26.00 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].
% 26.03/26.00 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)].
% 26.03/26.00 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)].
% 26.03/26.00 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].
% 26.03/26.00 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)].
% 26.03/26.00 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)].
% 26.03/26.00 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].
% 26.03/26.00 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)].
% 26.03/26.00 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)].
% 26.03/26.00 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].
% 26.03/26.00 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)].
% 26.03/26.00 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)].
% 26.03/26.00 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].
% 26.05/26.02 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)].
% 26.05/26.02 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)].
% 26.05/26.02 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].
% 26.05/26.02 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)].
% 26.05/26.02 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)].
% 26.05/26.02 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].
% 26.05/26.02 Derived: c_HOL_Oabs(c_1,tc_IntDef_Oint) = c_1. [resolve(3962,a,3876,a)].
% 26.05/26.02 Derived: c_HOL_Oabs(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(3962,a,3877,b)].
% 26.05/26.02 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].
% 26.05/26.02 Derived: A != c_times(A,B,tc_IntDef_Oint) | A = c_0 | B = c_1. [resolve(3963,a,3876,a)].
% 26.05/26.02 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)].
% 26.05/26.02 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].
% 26.05/26.02 Derived: c_0 = c_times(c_0,A,tc_IntDef_Oint). [resolve(3964,a,3876,a)].
% 26.05/26.02 Derived: c_0 = c_times(c_0,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3964,a,3877,b)].
% 26.05/26.02 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].
% 26.05/26.02 Derived: A = c_times(A,c_1,tc_IntDef_Oint). [resolve(3965,a,3876,a)].
% 26.05/26.02 Derived: A = c_times(A,c_1,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3965,a,3877,b)].
% 26.05/26.02 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].
% 26.05/26.02 Derived: c_times(A,B,tc_IntDef_Oint) != A | A = c_0 | B = c_1. [resolve(3966,a,3876,a)].
% 26.05/26.02 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)].
% 26.05/26.02 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].
% 26.05/26.02 Derived: A != c_times(B,A,tc_IntDef_Oint) | A = c_0 | B = c_1. [resolve(3967,a,3876,a)].
% 26.05/26.02 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)].
% 26.05/26.02 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].
% 26.05/26.02 Derived: c_0 = c_times(A,c_0,tc_IntDef_Oint). [resolve(3968,a,3876,a)].
% 26.05/26.02 Derived: c_0 = c_times(A,c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3968,a,3877,b)].
% 26.05/26.02 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].
% 26.05/26.02 Derived: A = c_times(c_1,A,tc_IntDef_Oint). [resolve(3969,a,3876,a)].
% 26.05/26.02 Derived: A = c_times(c_1,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(3969,a,3877,b)].
% 26.05/26.02 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].
% 26.05/26.02 Derived: c_times(A,B,tc_IntDef_Oint) != B | B = c_0 | A = c_1. [resolve(3970,a,3876,a)].
% 26.05/26.02 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)].
% 26.06/26.05 3971 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(22,b,2,a)].
% 26.06/26.05 3972 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(33,a,22,b)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.05 3991 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(71,a,88,b)].
% 26.06/26.05 3992 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(100,a,88,b)].
% 26.06/26.05 3993 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(102,a,88,b)].
% 26.06/26.05 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)].
% 26.06/26.05 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)].
% 26.06/26.07 3996 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(183,a,167,b)].
% 26.06/26.07 3997 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(184,a,167,b)].
% 26.06/26.07 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)].
% 26.06/26.07 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)].
% 26.06/26.07 4000 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(223,a,201,b)].
% 26.06/26.07 4001 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(224,a,201,b)].
% 26.06/26.07 4002 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(226,b,201,b)].
% 26.06/26.07 4003 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(227,b,201,b)].
% 26.06/26.07 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)].
% 26.06/26.07 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)].
% 26.06/26.07 4006 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(346,b,334,b)].
% 26.06/26.07 4007 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(380,a,364,b)].
% 26.06/26.07 4008 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(381,a,364,b)].
% 26.06/26.07 4009 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(386,b,364,b)].
% 26.06/26.07 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)].
% 26.06/26.07 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)].
% 26.06/26.07 4012 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(391,b,364,b)].
% 26.06/26.07 4013 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(410,a,402,b)].
% 26.06/26.07 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)].
% 26.06/26.07 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)].
% 26.06/26.07 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)].
% 26.06/26.07 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)].
% 26.06/26.07 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)].
% 26.06/26.07 4019 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(421,b,402,b)].
% 26.06/26.07 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)].
% 26.06/26.07 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)].
% 26.06/26.07 4022 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(433,b,402,b)].
% 26.06/26.07 4023 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(434,b,402,b)].
% 26.06/26.07 4024 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(439,b,402,b)].
% 26.06/26.07 4025 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(440,b,402,b)].
% 26.06/26.10 4026 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(441,b,402,b)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 4029 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(444,b,402,b)].
% 26.06/26.10 4030 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(511,b,503,b)].
% 26.06/26.10 4031 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(598,a,593,b)].
% 26.06/26.10 4032 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(599,a,593,b)].
% 26.06/26.10 4033 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(633,b,622,b)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 4043 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(681,b,657,b)].
% 26.06/26.10 4044 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(682,b,657,b)].
% 26.06/26.10 4045 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(738,b,698,b)].
% 26.06/26.10 4046 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(739,b,698,b)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.06/26.10 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 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)].
% 26.15/26.11 4061 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(846,b,791,b)].
% 26.15/26.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4061,b,3877,b)].
% 26.15/26.11 4062 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(847,b,791,b)].
% 26.15/26.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4062,b,3877,b)].
% 26.15/26.11 4063 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(848,b,791,b)].
% 26.15/26.11 4064 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(850,b,791,b)].
% 26.15/26.11 4065 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(851,b,791,b)].
% 26.15/26.11 4066 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(869,a,867,b)].
% 26.15/26.11 4067 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(870,a,867,b)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 4072 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(875,a,867,b)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 4075 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(878,a,867,b)].
% 26.15/26.13 4076 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(945,a,944,b)].
% 26.15/26.13 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4076,b,3877,b)].
% 26.15/26.13 4077 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(946,a,944,b)].
% 26.15/26.13 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4077,b,3877,b)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 4082 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(951,a,944,b)].
% 26.15/26.13 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(4082,b,3877,b)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.13 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 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)].
% 26.15/26.15 4095 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1067,b,944,b)].
% 26.15/26.15 4096 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1068,b,944,b)].
% 26.15/26.17 4097 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1087,a,1082,b)].
% 26.15/26.17 4098 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1118,a,1113,b)].
% 26.15/26.17 4099 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1161,b,1143,b)].
% 26.15/26.17 4100 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1163,b,1143,b)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.15/26.17 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.19 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)].
% 26.22/26.21 4144 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1219,a,1180,b)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 4149 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1224,a,1180,b)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.21 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 4176 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1385,b,1357,b)].
% 26.22/26.25 4177 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1386,b,1357,b)].
% 26.22/26.25 4178 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1388,b,1357,b)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 4190 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1498,b,1407,b)].
% 26.22/26.25 4191 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1499,b,1407,b)].
% 26.22/26.25 4192 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1523,b,1407,b)].
% 26.22/26.25 4193 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1631,b,1588,b)].
% 26.22/26.25 4194 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1632,b,1588,b)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.25 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 4204 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1642,b,1588,b)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 4207 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1645,b,1588,b)].
% 26.22/26.26 4208 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1646,b,1588,b)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.26 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 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)].
% 26.22/26.27 4243 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1740,b,1653,b)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 4248 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1745,b,1653,b)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.22/26.29 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)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 4275 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1773,b,1653,b)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 4278 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1788,b,1653,b)].
% 26.34/26.30 4279 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1789,b,1653,b)].
% 26.34/26.30 4280 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1790,b,1653,b)].
% 26.34/26.30 4281 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1796,b,1653,b)].
% 26.34/26.30 4282 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1797,b,1653,b)].
% 26.34/26.30 4283 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1798,b,1653,b)].
% 26.34/26.30 4284 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1799,b,1653,b)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.30 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)].
% 26.34/26.31 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)].
% 26.34/26.31 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)].
% 26.34/26.31 4294 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1809,b,1653,b)].
% 26.34/26.31 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)].
% 26.34/26.31 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)].
% 26.34/26.31 4297 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1812,b,1653,b)].
% 26.39/26.35 4298 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1813,b,1653,b)].
% 26.39/26.35 4299 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1955,b,1876,b)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 4308 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2241,a,2231,b)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 4311 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2244,a,2231,b)].
% 26.39/26.35 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)].
% 26.39/26.35 4313 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2246,a,2231,b)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 4319 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2252,a,2231,b)].
% 26.39/26.35 4320 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2321,a,2316,b)].
% 26.39/26.35 4321 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2356,b,2316,b)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.35 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 4342 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2517,a,2515,b)].
% 26.39/26.39 4343 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2518,a,2515,b)].
% 26.39/26.39 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)].
% 26.39/26.39 4345 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2520,a,2515,b)].
% 26.39/26.39 4346 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(2521,a,2515,b)].
% 26.39/26.39 4347 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2522,a,2515,b)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 4350 c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2525,a,2515,b)].
% 26.39/26.39 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)].
% 26.39/26.39 4352 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2527,a,2515,b)].
% 26.39/26.39 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)].
% 26.39/26.39 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)].
% 26.39/26.39 4355 -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2530,a,2515,b)].
% 26.39/26.39 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)].
% 26.39/26.39 4357 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2973,b,2849,b)].
% 26.39/26.39 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)].
% 26.39/26.40 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_minus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4358,c,3876,a)].
% 26.39/26.40 Derived: -class_Numeral_Onumber(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4358,c,3877,b)].
% 26.39/26.40 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)].
% 26.39/26.40 Derived: -class_Numeral_Onumber(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4359,c,3876,a)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 4363 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2980,b,2849,b)].
% 26.39/26.40 4364 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2981,b,2849,b)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 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)].
% 26.39/26.40 4373 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2990,b,2849,b)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 4376 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2993,b,2849,b)].
% 26.39/26.41 4377 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2994,b,2849,b)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 4387 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3004,b,2849,b)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 4390 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3007,b,2849,b)].
% 26.39/26.41 4391 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3008,b,2849,b)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.41 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.39/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.42 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.43 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 Derived: c_times(A,B,tc_IntDef_Oint) != c_0 | B = c_0 | A = c_0. [resolve(4416,d,3876,a)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 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)].
% 26.48/26.44 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(4422,e,3877,b)].
% 26.48/26.44 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)].
% 26.48/26.44 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(4423,f,3876,a)].
% 26.48/26.44 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(4423,f,3877,b)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(4424,e,3877,b)].
% 26.48/26.45 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)].
% 26.48/26.45 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(4425,e,3876,a)].
% 26.48/26.45 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(4425,e,3877,b)].
% 26.48/26.45 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)].
% 26.48/26.45 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(4426,b,3876,a)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.45 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(4436,b,3876,a)].
% 26.48/26.45 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)].
% 26.48/26.45 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.46 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 4451 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3273,b,3047,b)].
% 26.48/26.47 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(4451,b,3876,a)].
% 26.48/26.47 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4451,b,3877,b)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4455,d,3877,b)].
% 26.48/26.47 4456 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3278,b,3047,b)].
% 26.48/26.47 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(4456,b,3876,a)].
% 26.48/26.47 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4456,b,3877,b)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(4457,b,3877,b)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4458,b,3877,b)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(4462,c,3876,a)].
% 26.48/26.47 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)].
% 26.48/26.47 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)].
% 26.48/26.47 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(4463,c,3876,a)].
% 26.48/26.47 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)].
% 26.48/26.48 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)].
% 26.48/26.48 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(4464,c,3876,a)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(4472,c,3876,a)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 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)].
% 26.48/26.48 4475 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3308,b,3047,b)].
% 26.48/26.48 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(4475,b,3876,a)].
% 26.48/26.48 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4475,b,3877,b)].
% 26.48/26.48 4476 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3309,b,3047,b)].
% 26.48/26.48 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(4476,b,3876,a)].
% 26.48/26.48 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4476,b,3877,b)].
% 26.48/26.48 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)].
% 26.48/26.48 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(4477,c,3876,a)].
% 26.48/26.48 Derived: -c_lessequals(c_plus(A,A,B),c_0,B) | c_lessequals(A,c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4477,c,3877,b)].
% 26.48/26.48 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)].
% 26.48/26.48 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4478,c,3876,a)].
% 26.48/26.48 Derived: -c_lessequals(A,c_0,B) | c_lessequals(c_plus(A,A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4478,c,3877,b)].
% 26.48/26.48 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)].
% 26.55/26.49 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4479,c,3876,a)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(4480,b,3876,a)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4481,c,3876,a)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(4482,b,3876,a)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 4485 c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3337,b,3047,b)].
% 26.55/26.49 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(4485,b,3876,a)].
% 26.55/26.49 Derived: c_OrderedGroup_Onprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4485,b,3877,b)].
% 26.55/26.49 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)].
% 26.55/26.49 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(4486,c,3876,a)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(4487,c,3876,a)].
% 26.55/26.49 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)].
% 26.55/26.49 4488 c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3340,b,3047,b)].
% 26.55/26.49 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4488,b,3876,a)].
% 26.55/26.49 Derived: c_lessequals(c_OrderedGroup_Onprt(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4488,b,3877,b)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 4490 c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3342,b,3047,b)].
% 26.55/26.49 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(4490,b,3876,a)].
% 26.55/26.49 Derived: c_OrderedGroup_Opprt(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4490,b,3877,b)].
% 26.55/26.49 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)].
% 26.55/26.49 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(4491,c,3876,a)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(4492,c,3876,a)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 4496 c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3348,b,3047,b)].
% 26.55/26.49 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4496,b,3876,a)].
% 26.55/26.49 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4496,b,3877,b)].
% 26.55/26.49 4497 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3349,b,3047,b)].
% 26.55/26.49 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(4497,b,3876,a)].
% 26.55/26.49 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4497,b,3877,b)].
% 26.55/26.49 4498 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3350,b,3047,b)].
% 26.55/26.49 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(4498,b,3876,a)].
% 26.55/26.49 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4498,b,3877,b)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.49 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.50 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 4519 c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3376,c,3047,b)].
% 26.55/26.51 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(4519,c,3876,a)].
% 26.55/26.51 Derived: c_0 != c_HOL_Oabs(A,B) | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4519,c,3877,b)].
% 26.55/26.51 4520 c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3377,b,3047,b)].
% 26.55/26.51 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(4520,b,3876,a)].
% 26.55/26.51 Derived: c_0 = c_HOL_Oabs(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4520,b,3877,b)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 4522 c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3379,c,3047,b)].
% 26.55/26.51 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4522,c,3876,a)].
% 26.55/26.51 Derived: c_HOL_Oabs(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4522,c,3877,b)].
% 26.55/26.51 4523 c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3380,b,3047,b)].
% 26.55/26.51 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(4523,b,3876,a)].
% 26.55/26.51 Derived: c_HOL_Oabs(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4523,b,3877,b)].
% 26.55/26.51 4524 c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3381,b,3047,b)].
% 26.55/26.51 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4524,b,3876,a)].
% 26.55/26.51 Derived: c_lessequals(c_0,c_HOL_Oabs(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4524,b,3877,b)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(4526,c,3876,a)].
% 26.55/26.51 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)].
% 26.55/26.51 4527 c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3384,b,3047,b)].
% 26.55/26.51 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4527,b,3876,a)].
% 26.55/26.51 Derived: c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4527,b,3877,b)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 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)].
% 26.55/26.51 4529 -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3386,b,3047,b)].
% 26.55/26.51 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4529,b,3876,a)].
% 26.55/26.51 Derived: -c_less(c_HOL_Oabs(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4529,b,3877,b)].
% 26.55/26.52 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)].
% 26.55/26.52 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(4530,c,3876,a)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 4532 -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3389,b,3047,b)].
% 26.55/26.52 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4532,b,3876,a)].
% 26.55/26.52 Derived: -c_less(c_0,c_HOL_Oabs(c_0,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4532,b,3877,b)].
% 26.55/26.52 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)].
% 26.55/26.52 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(4533,c,3876,a)].
% 26.55/26.52 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)].
% 26.55/26.52 4534 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3391,b,3047,b)].
% 26.55/26.52 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(4534,b,3876,a)].
% 26.55/26.52 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4534,b,3877,b)].
% 26.55/26.52 4535 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3392,b,3047,b)].
% 26.55/26.52 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(4535,b,3876,a)].
% 26.55/26.52 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4535,b,3877,b)].
% 26.55/26.52 4536 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3393,b,3047,b)].
% 26.55/26.52 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(4536,b,3876,a)].
% 26.55/26.52 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4536,b,3877,b)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.52 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 4545 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3402,b,3047,b)].
% 26.55/26.53 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(4545,b,3876,a)].
% 26.55/26.53 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4545,b,3877,b)].
% 26.55/26.53 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)].
% 26.55/26.53 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(4546,c,3876,a)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(4547,c,3876,a)].
% 26.55/26.53 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)].
% 26.55/26.53 4548 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3405,b,3047,b)].
% 26.55/26.53 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(4548,b,3876,a)].
% 26.55/26.53 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4548,b,3877,b)].
% 26.55/26.53 4549 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3406,b,3047,b)].
% 26.55/26.53 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(4549,b,3876,a)].
% 26.55/26.53 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4549,b,3877,b)].
% 26.55/26.53 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)].
% 26.55/26.53 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(4550,c,3876,a)].
% 26.55/26.53 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)].
% 26.55/26.53 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)].
% 26.55/26.53 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(4551,b,3876,a)].
% 26.55/26.53 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)].
% 26.55/26.54 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)].
% 26.55/26.54 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(4552,c,3876,a)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(4556,c,3877,b)].
% 26.55/26.54 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)].
% 26.55/26.54 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(4557,c,3876,a)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 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)].
% 26.55/26.54 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4558,b,3877,b)].
% 26.55/26.54 4559 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3416,b,3047,b)].
% 26.55/26.54 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(4559,b,3876,a)].
% 26.55/26.54 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4559,b,3877,b)].
% 26.55/26.54 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)].
% 26.55/26.55 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)].
% 26.55/26.55 Derived: -class_Numeral_Onumber(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4560,c,3877,b)].
% 26.55/26.55 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)].
% 26.55/26.55 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)].
% 26.55/26.55 Derived: -class_Numeral_Onumber(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4561,c,3877,b)].
% 26.55/26.55 4562 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3419,b,3047,b)].
% 26.55/26.55 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(4562,b,3876,a)].
% 26.55/26.55 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4562,b,3877,b)].
% 26.55/26.55 4563 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3420,b,3047,b)].
% 26.55/26.55 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(4563,b,3876,a)].
% 26.55/26.55 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4563,b,3877,b)].
% 26.55/26.55 4564 c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(3429,a,3425,b)].
% 26.55/26.55 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(4564,c,3876,a)].
% 26.55/26.55 Derived: c_0 != c_NatArith_Oof__nat(A,B) | c_0 = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4564,c,3877,b)].
% 26.55/26.55 4565 c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3430,a,3425,b)].
% 26.55/26.55 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(4565,b,3876,a)].
% 26.55/26.55 Derived: c_0 = c_NatArith_Oof__nat(c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4565,b,3877,b)].
% 26.55/26.55 4566 c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3431,a,3425,b)].
% 26.55/26.55 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(4566,b,3876,a)].
% 26.55/26.55 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4566,b,3877,b)].
% 26.55/26.55 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)].
% 26.55/26.55 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)].
% 26.55/26.55 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)].
% 26.55/26.55 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)].
% 26.55/26.55 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)].
% 26.55/26.55 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)].
% 26.55/26.55 4569 c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(3434,a,3425,b)].
% 26.55/26.55 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(4569,c,3876,a)].
% 26.55/26.56 Derived: c_NatArith_Oof__nat(A,B) != c_0 | A = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(4569,c,3877,b)].
% 26.55/26.56 4570 c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3435,a,3425,b)].
% 26.55/26.56 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(4570,b,3876,a)].
% 26.55/26.56 Derived: c_NatArith_Oof__nat(c_0,A) = c_0 | -class_Ring__and__Field_Oordered__field(A). [resolve(4570,b,3877,b)].
% 26.55/26.56 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)].
% 26.55/26.56 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(4571,c,3876,a)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(4572,c,3876,a)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4573,b,3876,a)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 4576 -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(3441,a,3425,b)].
% 26.55/26.56 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(4576,b,3876,a)].
% 26.55/26.56 Derived: -c_less(c_NatArith_Oof__nat(A,B),c_0,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(4576,b,3877,b)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.55/26.56 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 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)].
% 26.63/26.57 4584 -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3449,a,3425,b)].
% 26.63/26.57 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(4584,b,3876,a)].
% 26.63/26.57 Derived: -c_lessequals(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4584,b,3877,b)].
% 26.63/26.57 4585 -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3450,a,3425,b)].
% 26.63/26.57 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(4585,b,3876,a)].
% 26.63/26.57 Derived: -c_less(c_1,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4585,b,3877,b)].
% 26.63/26.57 4586 c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3451,a,3425,b)].
% 26.63/26.57 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(4586,b,3876,a)].
% 26.63/26.57 Derived: c_less(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4586,b,3877,b)].
% 26.63/26.57 4587 c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3452,a,3425,b)].
% 26.63/26.57 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(4587,b,3876,a)].
% 26.63/26.57 Derived: c_lessequals(c_0,c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4587,b,3877,b)].
% 26.63/26.57 4588 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3514,b,3425,b)].
% 26.64/26.57 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(4588,b,3876,a)].
% 26.64/26.57 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4588,b,3877,b)].
% 26.64/26.57 4589 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3515,b,3425,b)].
% 26.64/26.57 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(4589,b,3876,a)].
% 26.64/26.57 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4589,b,3877,b)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(4592,b,3876,a)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 4594 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(3520,b,3425,b)].
% 26.64/26.57 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(4594,b,3876,a)].
% 26.64/26.57 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(4594,b,3877,b)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 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)].
% 26.64/26.57 4597 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3523,b,3425,b)].
% 26.64/26.57 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(4597,b,3876,a)].
% 26.64/26.57 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4597,b,3877,b)].
% 30.35/30.36 4598 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3730,b,3425,b)].
% 30.35/30.36 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(4598,b,3876,a)].
% 30.35/30.36 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(4598,b,3877,b)].
% 30.35/30.36 4599 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(32,b,2,a)].
% 30.35/30.36 4600 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom). [assumption].
% 30.35/30.36 4601 -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(33,a,32,b)].
% 30.35/30.36 4602 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(34,a,32,b)].
% 30.35/30.36 4603 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(35,a,32,b)].
% 30.35/30.36 4604 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(36,a,32,b)].
% 30.35/30.36 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)].
% 30.35/30.36 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)].
% 30.35/30.36 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)].
% 30.35/30.36 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)].
% 30.35/30.36 4609 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(41,a,32,b)].
% 30.35/30.36 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)].
% 30.35/30.36 4611 c_LOrder_Omeet(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1087,a,1086,b)].
% 30.35/30.36 4612 c_LOrder_Ojoin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1118,a,1117,b)].
% 30.35/30.36 4613 c_lessequals(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1161,b,1147,b)].
% 30.35/30.36 4614 -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1163,b,1147,b)].
% 30.35/30.36 4615 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1164,c,1147,b)].
% 30.35/30.36 4616 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1165,b,1147,b)].
% 30.35/30.36 4617 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1166,c,1147,b)].
% 30.35/30.36 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)].
% 30.35/30.36 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)].
% 30.35/30.36 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)].
% 30.35/30.36 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)].
% 30.35/30.36 4622 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1171,c,1147,b)].
% 30.35/30.36 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)].
% 30.35/30.36 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 4633 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1194,a,1184,b)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 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)].
% 30.35/30.37 4643 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1204,a,1184,b)].
% 30.35/30.37 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 4658 c_Orderings_Omin(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1219,a,1184,b)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 4663 c_Orderings_Omax(A,A,B) = A | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1224,a,1184,b)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 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)].
% 30.44/30.38 4669 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1230,a,1184,b)].
% 30.44/30.38 4670 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1231,a,1184,b)].
% 30.44/30.38 4671 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1232,a,1184,b)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 4679 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(1240,a,1184,b)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 30.49/30.47 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)].
% 31.25/31.20 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)].
% 31.25/31.20 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)].
% 31.25/31.20 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)].
% 31.25/31.20 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)].
% 31.25/31.20 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)].
% 31.25/31.20 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)].
% 31.25/31.20 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)].
% 31.25/31.20 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].
% 31.25/31.20 4703 -class_Ring__and__Field_Ofield(A) | class_HOL_Oinverse(A) # label(clsrel_Ring__and__Field_Ofield_30) # label(axiom). [assumption].
% 31.25/31.20 4704 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ofield_4) # label(axiom). [assumption].
% 31.25/31.20 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].
% 31.25/31.20 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)].
% 31.25/31.20 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].
% 31.25/31.20 Derived: c_divide(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(4706,a,4702,b)].
% 31.25/31.20 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].
% 31.25/31.20 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)].
% 31.25/31.20 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].
% 31.25/31.20 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)].
% 31.25/31.20 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].
% 31.25/31.20 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)].
% 31.25/31.20 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].
% 31.25/31.20 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)].
% 31.25/31.20 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].
% 31.25/31.20 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)].
% 31.25/31.20 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].
% 31.25/31.20 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)].
% 31.25/31.20 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].
% 31.25/31.23 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)].
% 31.25/31.23 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].
% 31.25/31.23 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)].
% 31.25/31.23 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].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 4727 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(183,a,162,b)].
% 31.25/31.23 4728 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(184,a,162,b)].
% 31.25/31.23 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)].
% 31.25/31.23 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)].
% 31.25/31.23 4731 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(226,b,196,b)].
% 31.25/31.23 4732 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(227,b,196,b)].
% 31.25/31.23 4733 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(307,a,290,b)].
% 31.25/31.23 4734 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(308,a,290,b)].
% 31.25/31.23 4735 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(380,a,359,b)].
% 31.25/31.23 4736 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(381,a,359,b)].
% 31.25/31.24 4737 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(389,c,359,b)].
% 31.25/31.24 4738 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(390,c,359,b)].
% 31.25/31.24 4739 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(410,a,398,b)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 4747 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(433,b,398,b)].
% 31.25/31.24 4748 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(434,b,398,b)].
% 31.25/31.24 4749 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(439,b,398,b)].
% 31.25/31.24 4750 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(440,b,398,b)].
% 31.25/31.24 4751 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(442,c,398,b)].
% 31.25/31.24 4752 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(443,c,398,b)].
% 31.25/31.24 4753 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(598,a,590,b)].
% 31.25/31.24 4754 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(599,a,590,b)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 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)].
% 31.25/31.24 4764 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(681,b,654,b)].
% 31.25/31.25 4765 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(682,b,654,b)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 4780 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(846,b,788,b)].
% 31.25/31.25 4781 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(847,b,788,b)].
% 31.25/31.25 4782 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(850,b,788,b)].
% 31.25/31.25 4783 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(851,b,788,b)].
% 31.25/31.25 4784 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(869,a,864,b)].
% 31.25/31.25 4785 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(870,a,864,b)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.25/31.25 4788 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(873,a,864,b)].
% 31.25/31.25 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)].
% 31.25/31.25 4790 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(875,a,864,b)].
% 31.25/31.25 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)].
% 31.25/31.25 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)].
% 31.49/31.43 4793 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(878,a,864,b)].
% 31.49/31.43 4794 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(945,a,941,b)].
% 31.49/31.43 4795 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(946,a,941,b)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 4800 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(951,a,941,b)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 4813 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3791,b,3753,b)].
% 31.49/31.43 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)].
% 31.49/31.43 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)].
% 31.49/31.43 4816 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3800,b,3753,b)].
% 31.49/31.43 4817 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3801,b,3753,b)].
% 31.49/31.44 4818 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3805,c,3753,b)].
% 31.49/31.44 4819 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3806,c,3753,b)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 4834 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3839,b,3753,b)].
% 31.49/31.44 4835 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3840,b,3753,b)].
% 31.49/31.44 4836 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3842,b,3753,b)].
% 31.49/31.44 4837 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3843,b,3753,b)].
% 31.49/31.44 4838 c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3844,b,3753,b)].
% 31.49/31.44 4839 c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3845,b,3753,b)].
% 31.49/31.44 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)].
% 31.49/31.44 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)].
% 31.49/31.44 4842 c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3848,b,3753,b)].
% 31.49/31.44 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)].
% 31.49/31.44 4844 c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3850,b,3753,b)].
% 31.49/31.44 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)].
% 32.80/32.79 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)].
% 32.80/32.79 4847 -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3853,b,3753,b)].
% 32.80/32.79 4848 c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3854,b,3753,b)].
% 32.80/32.79 4849 c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3855,b,3753,b)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 4854 c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3860,b,3753,b)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79 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)].
% 32.80/32.79
% 32.80/32.79 ============================== end predicate elimination =============
% 32.80/32.79
% 32.80/32.79 Auto_denials: (non-Horn, no changes).
% 32.80/32.79
% 32.80/32.79 Term ordering decisions:
% 32.80/32.79 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_K=1. c_IntDef_OInteg=1. c_Wellfounded__Relations_Oless__than=1. v_evs3=1. c_Extraction_Osumbool_OLeft=1. c_Extraction_Osumbool_ORight=1. c_List_Onibble_ONibble0=1. c_List_Onibble_ONibble1=1. c_List_Onibble_ONibble2=1. c_List_Onibble_ONibble3=1. c_List_Onibble_ONibble4=1. c_List_Onibble_ONibble5=1. c_List_Onibble_ONibble6=1. c_List_Onibble_ONibble7=1. c_List_Onibble_ONibble8=1. c_List_Onibble_ONibble9=1. c_List_Onibble_ONibbleA=1. c_List_Onibble_ONibbleB=1. c_List_Onibble_ONibbleC=1. c_List_Onibble_ONibbleD=1. c_List_Onibble_ONibbleE=1. c_List_Onibble_ONibbleF=1. c_Product__Type_OUnity=1. c_Public_Okeymode_OEncryption=1. c_Public_Okeymode_OSignature=1. v_B=1. c_Message_Oagent_OServer=1. tc_Extraction_Osumbool=1. tc_Numeral_Obit=1. tc_Product__Type_Ounit=1. tc_Public_Okeymode=1. v_A=1. tc_List_Ochar=1. tc_bool=1. v_KAB=1. v_NA=1. v_NB=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_Event_Oevent_OGets=1. c_Numeral_Obin__mult=1. c_Relation_Odiag=1. tc_sum=1. c_Binomial_Obinomial=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_Public_OshrK=1. c_Event_Oused=1. c_Message_Omsg_ONonce=1. c_IntDiv_OnegDivAlg=1. c_IntDiv_OposDivAlg=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. c_Main_OdiagE__1=1. c_Main_OInterI__1=1. c_Main_OInter__iff__1=1. c_Main_OUnionE__1=1. c_Main_OUnion__iff__1=1. c_Main_Oin__listsI__1=1. c_Main_OsubsetI__1=1. c_Datatype_Ounit_Ounit__case=1. c_Datatype_Ounit_Ounit__rec=1. c_List_Olexn=1. c_List_Oset__Cons=1. c_Main_Osurj__pair__1=1. c_Main_Osurj__pair__2=1. c_Pair=1. c_Relation_OImage=1. c_Datatype__Universe_Ontrunc=1. c_Datatype__Universe_OScons=1. c_List_Ozip=1. c_List_Olist__update=1. c_Datatype__Universe_Odsum=1. c_Datatype__Universe_Ousum=1. c_Sum__Type_OPlus=1. c_Datatype__Universe_Odprod=1. c_Datatype__Universe_Ouprod=1. c_Main_OPlusE__1=1. c_Main_OPlusE__2=1. c_Main_OdsumE__1=1. c_Main_OdsumE__2=1. c_Main_OdsumE__3=1. c_Main_OdsumE__4=1. c_Main_OusumE__1=1. c_Main_OusumE__2=1. c_Extraction_Osumbool_Osumbool__case=1. c_Extraction_Osumbool_Osumbool__rec=1. c_Main_OconverseE__1=1. c_Main_OconverseE__2=1. c_Numeral_Obit_Obit__case=1. c_Numeral_Obit_Obit__rec=1. c_Public_Okeymode_Okeymode__case=1. c_Public_Okeymode_Okeymode__rec=1. c_Wellfounded__Relations_Olex__prod=1. c_Main_ODomainE__1=1. c_Main_ORangeE__1=1. c_Map_Omap__of=1. c_Relation_Orel__comp=1. c_Main_OImageE__1=1. c_Main_OdprodE__1=1. c_Main_OdprodE__2=1. c_Main_OdprodE__3=1. c_Main_OdprodE__4=1. c_Main_Olistrel__Cons1__1=1. c_Main_Olistrel__Cons1__2=1. c_Main_Olistrel__Cons2__1=1. c_Main_Olistrel__Cons2__2=1. c_Main_OuprodE__1=1. c_Main_OuprodE__2=1. c_Main_Orel__compE__1=1. c_Main_Orel__compE__2=1. c_Main_Orel__compE__3=1. c_List_Onibble_Onibble__case=1. c_List_Onibble_Onibble__rec=1.
% 138.88/138.88
% 138.88/138.88 ============================== end of process initial clauses ========
% 138.88/138.88
% 138.88/138.88 ============================== CLAUSES FOR SEARCH ====================
% 138.88/138.88
% 138.88/138.88 ============================== end of clauses for search =============
% 138.88/138.88
% 138.88/138.88 ============================== SEARCH ================================
% 138.88/138.88
% 138.88/138.88 % Starting search at 31.25 seconds.
% 138.88/138.88
% 138.88/138.88 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 107 (0.00 of 31.54 sec).
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=43.000, iters=3386
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=42.000, iters=3355
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=39.000, iters=3363
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=36.000, iters=3376
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=34.000, iters=3335
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=33.000, iters=3369
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=31.000, iters=3385
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=30.000, iters=3421
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=29.000, iters=3336
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=28.000, iters=3411
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=27.000, iters=3334
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=26.000, iters=3398
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=25.000, iters=3410
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=24.000, iters=3396
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=23.000, iters=3344
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=22.000, iters=3356
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=21.000, iters=3341
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=20.000, iters=3333
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=19.000, iters=3388
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=18.000, iters=3358
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=17.000, iters=3334
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=16.000, iters=3433
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=15.000, iters=3402
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=14.000, iters=3477
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=12.000, iters=3430
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=11.000, iters=3530
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=10.000, iters=3384
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=9.000, iters=3415
% 138.88/138.88
% 138.88/138.88 Low Water (keep): wt=8.000, iters=3337
% 138.88/138.88
% 138.88/138.88 Low Water (displace): id=18381, wt=43.000
% 138.88/138.88
% 138.88/138.88 Low Water (displace): id=19178, wt=7.000
% 138.88/138.88
% 138.88/138.88 ============================== PROOF =================================
% 138.88/138.88 % SZS status Unsatisfiable
% 138.88/138.88 % SZS output start Refutation
% 138.88/138.88
% 138.88/138.88 % Proof 1 at 133.31 (+ 4.06) seconds.
% 138.88/138.88 % Length of proof is 8.
% 138.88/138.88 % Level of proof is 5.
% 138.88/138.88 % Maximum clause weight is 10.000.
% 138.88/138.88 % Given clauses 29827.
% 138.88/138.88
% 138.88/138.88 6572 c_in(c_Message_Omsg_OKey(c_Public_OshrK(A)),c_Event_Oused(B),tc_Message_Omsg) # label(cls_Public_OshrK__in__used_0) # label(axiom). [assumption].
% 138.88/138.88 6595 -c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg) # label(cls_conjecture_6) # label(negated_conjecture). [assumption].
% 138.88/138.88 6598 v_K = c_Public_OshrK(v_B) | v_K = c_Public_OshrK(v_A) # label(cls_conjecture_8) # label(negated_conjecture). [assumption].
% 138.88/138.88 6599 c_Public_OshrK(v_B) = v_K | c_Public_OshrK(v_A) = v_K. [copy(6598),flip(a),flip(b)].
% 138.88/138.88 12724 c_Public_OshrK(v_B) = v_K | c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(A),tc_Message_Omsg). [para(6599(b,1),6572(a,1,1))].
% 138.88/138.88 84664 c_Public_OshrK(v_B) = v_K. [resolve(12724,b,6595,a)].
% 138.88/138.88 84668 c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(A),tc_Message_Omsg). [para(84664(a,1),6572(a,1,1))].
% 138.88/138.88 84669 $F. [resolve(84668,a,6595,a)].
% 138.88/138.88
% 138.88/138.88 % SZS output end Refutation
% 138.88/138.88 ============================== end of proof ==========================
% 138.88/138.88
% 138.88/138.88 ============================== STATISTICS ============================
% 138.88/138.88
% 138.88/138.88 Given=29827. Generated=8160079. Kept=78684. proofs=1.
% 138.88/138.88 Usable=28145. Sos=8506. Demods=1416. Limbo=3, Disabled=51960. Hints=0.
% 138.88/138.88 Megabytes=122.08.
% 138.88/138.88 User_CPU=133.31, System_CPU=4.06, Wall_clock=137.
% 138.88/138.88
% 138.88/138.88 ============================== end of statistics =====================
% 138.88/138.88
% 138.88/138.88 ============================== end of search =========================
% 138.88/138.88
% 138.88/138.88 THEOREM PROVED
% 138.88/138.88 % SZS status Unsatisfiable
% 138.88/138.88
% 138.88/138.88 Exiting with 1 proof.
% 138.88/138.88
% 138.88/138.88 Process 8904 exit (max_proofs) Wed Jun 15 11:32:12 2022
% 138.88/138.88 Prover9 interrupted
%------------------------------------------------------------------------------