TSTP Solution File: SWV364-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV364-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 21:12:24 EDT 2022
% Result : Unsatisfiable 5.95s 6.23s
% Output : Refutation 5.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV364-1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 21:04:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.95/1.37 ============================== Prover9 ===============================
% 0.95/1.37 Prover9 (32) version 2009-11A, November 2009.
% 0.95/1.37 Process 4358 was started by sandbox2 on n007.cluster.edu,
% 0.95/1.37 Tue Jun 14 21:04:11 2022
% 0.95/1.37 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4205_n007.cluster.edu".
% 0.95/1.37 ============================== end of head ===========================
% 0.95/1.37
% 0.95/1.37 ============================== INPUT =================================
% 0.95/1.37
% 0.95/1.37 % Reading from file /tmp/Prover9_4205_n007.cluster.edu
% 0.95/1.37
% 0.95/1.37 set(prolog_style_variables).
% 0.95/1.37 set(auto2).
% 0.95/1.37 % set(auto2) -> set(auto).
% 0.95/1.37 % set(auto) -> set(auto_inference).
% 0.95/1.37 % set(auto) -> set(auto_setup).
% 0.95/1.37 % set(auto_setup) -> set(predicate_elim).
% 0.95/1.37 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.95/1.37 % set(auto) -> set(auto_limits).
% 0.95/1.37 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.95/1.37 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.95/1.37 % set(auto) -> set(auto_denials).
% 0.95/1.37 % set(auto) -> set(auto_process).
% 0.95/1.37 % set(auto2) -> assign(new_constants, 1).
% 0.95/1.37 % set(auto2) -> assign(fold_denial_max, 3).
% 0.95/1.37 % set(auto2) -> assign(max_weight, "200.000").
% 0.95/1.37 % set(auto2) -> assign(max_hours, 1).
% 0.95/1.37 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.95/1.37 % set(auto2) -> assign(max_seconds, 0).
% 0.95/1.37 % set(auto2) -> assign(max_minutes, 5).
% 0.95/1.37 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.95/1.37 % set(auto2) -> set(sort_initial_sos).
% 0.95/1.37 % set(auto2) -> assign(sos_limit, -1).
% 0.95/1.37 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.95/1.37 % set(auto2) -> assign(max_megs, 400).
% 0.95/1.37 % set(auto2) -> assign(stats, some).
% 0.95/1.37 % set(auto2) -> clear(echo_input).
% 0.95/1.37 % set(auto2) -> set(quiet).
% 0.95/1.37 % set(auto2) -> clear(print_initial_clauses).
% 0.95/1.37 % set(auto2) -> clear(print_given).
% 0.95/1.37 assign(lrs_ticks,-1).
% 0.95/1.37 assign(sos_limit,10000).
% 0.95/1.37 assign(order,kbo).
% 0.95/1.37 set(lex_order_vars).
% 0.95/1.37 clear(print_given).
% 0.95/1.37
% 0.95/1.37 % formulas(sos). % not echoed (1473 formulas)
% 0.95/1.37
% 0.95/1.37 ============================== end of input ==========================
% 0.95/1.37
% 0.95/1.37 % From the command line: assign(max_seconds, 300).
% 0.95/1.37
% 0.95/1.37 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.95/1.37
% 0.95/1.37 % Formulas that are not ordinary clauses:
% 0.95/1.37
% 0.95/1.37 ============================== end of process non-clausal formulas ===
% 0.95/1.37
% 0.95/1.37 ============================== PROCESS INITIAL CLAUSES ===============
% 0.95/1.37
% 0.95/1.37 ============================== PREDICATE ELIMINATION =================
% 0.95/1.37 1 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom). [assumption].
% 0.95/1.37 2 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom). [assumption].
% 0.95/1.37 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1,a,2,a)].
% 0.95/1.37 3 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom). [assumption].
% 0.95/1.37 Derived: c_lessequals(A,A,tc_nat). [resolve(3,a,2,a)].
% 0.95/1.37 4 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom). [assumption].
% 0.95/1.37 Derived: c_lessequals(A,A,tc_set(B)). [resolve(4,a,2,a)].
% 0.95/1.37 5 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 0.95/1.37 Derived: -class_LOrder_Ojoin__semilorder(A) | c_lessequals(B,B,A). [resolve(5,b,2,a)].
% 0.95/1.37 6 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom). [assumption].
% 0.95/1.37 Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(6,b,2,a)].
% 0.95/1.37 7 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom). [assumption].
% 0.95/1.37 Derived: -class_LOrder_Omeet__semilorder(A) | c_lessequals(B,B,A). [resolve(7,b,2,a)].
% 0.95/1.37 8 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom). [assumption].
% 0.95/1.37 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(B,B,A). [resolve(8,b,2,a)].
% 0.95/1.37 9 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom). [assumption].
% 0.95/1.37 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(B,B,A). [resolve(9,b,2,a)].
% 0.95/1.38 10 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom). [assumption].
% 0.95/1.38 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(10,b,2,a)].
% 0.95/1.38 11 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom). [assumption].
% 0.95/1.38 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(11,b,2,a)].
% 0.95/1.38 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].
% 0.95/1.38 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(12,b,2,a)].
% 0.95/1.38 13 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom). [assumption].
% 0.95/1.38 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A). [resolve(13,b,2,a)].
% 0.95/1.38 14 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom). [assumption].
% 0.95/1.38 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(14,b,2,a)].
% 0.95/1.38 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].
% 0.95/1.38 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,B,A). [resolve(15,b,2,a)].
% 0.95/1.38 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].
% 0.95/1.38 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(16,b,2,a)].
% 0.95/1.38 17 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom). [assumption].
% 0.95/1.38 Derived: -class_Orderings_Olinorder(A) | c_lessequals(B,B,A). [resolve(17,b,2,a)].
% 0.95/1.38 18 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom). [assumption].
% 0.95/1.38 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(18,a,1,a)].
% 0.95/1.38 Derived: class_Orderings_Oord(tc_nat). [resolve(18,a,3,a)].
% 0.95/1.38 Derived: class_Orderings_Oord(tc_set(A)). [resolve(18,a,4,a)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_LOrder_Ojoin__semilorder(A). [resolve(18,a,5,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(18,a,6,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_LOrder_Omeet__semilorder(A). [resolve(18,a,7,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(18,a,8,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(18,a,9,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(18,a,10,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(18,a,11,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(18,a,12,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(18,a,13,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(18,a,14,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(18,a,15,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(18,a,16,b)].
% 0.95/1.38 Derived: class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(18,a,17,b)].
% 0.95/1.38 19 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom). [assumption].
% 0.95/1.40 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(19,b,2,a)].
% 0.95/1.40 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].
% 0.95/1.40 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(20,b,2,a)].
% 0.95/1.40 21 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom). [assumption].
% 0.95/1.40 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A). [resolve(21,b,2,a)].
% 0.95/1.40 22 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom). [assumption].
% 0.95/1.40 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(22,b,2,a)].
% 0.95/1.40 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].
% 0.95/1.40 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,B,A). [resolve(23,b,2,a)].
% 0.95/1.40 24 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom). [assumption].
% 0.95/1.40 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,B,A). [resolve(24,b,2,a)].
% 0.95/1.40 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].
% 0.95/1.40 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(25,b,2,a)].
% 0.95/1.40 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].
% 0.95/1.40 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(26,b,2,a)].
% 0.95/1.40 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].
% 0.95/1.40 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(27,b,2,a)].
% 0.95/1.40 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].
% 0.95/1.40 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A). [resolve(28,b,2,a)].
% 0.95/1.40 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].
% 0.95/1.40 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(29,b,2,a)].
% 0.95/1.40 30 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom). [assumption].
% 0.95/1.40 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(30,b,2,a)].
% 0.95/1.40 31 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom). [assumption].
% 0.95/1.40 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(31,b,2,a)].
% 0.95/1.40 32 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom). [assumption].
% 0.95/1.40 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(32,b,2,a)].
% 0.95/1.40 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(32,b,18,a)].
% 0.95/1.40 33 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl__iff1_0) # label(axiom). [assumption].
% 0.95/1.40 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(33,a,1,a)].
% 0.95/1.40 Derived: -c_less(A,A,tc_nat). [resolve(33,a,3,a)].
% 0.95/1.40 Derived: -c_less(A,A,tc_set(B)). [resolve(33,a,4,a)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(33,a,5,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(33,a,6,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_LOrder_Omeet__semilorder(B). [resolve(33,a,7,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(33,a,8,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(33,a,9,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(33,a,10,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(33,a,11,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(33,a,12,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(33,a,13,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(33,a,14,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(33,a,15,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(33,a,16,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(33,a,17,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(33,a,19,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(33,a,20,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(33,a,21,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(33,a,22,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(33,a,23,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(33,a,24,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(33,a,25,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(33,a,26,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(33,a,27,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(33,a,28,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(33,a,29,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(33,a,30,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(33,a,31,b)].
% 0.95/1.40 Derived: -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(33,a,32,b)].
% 0.95/1.40 34 -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__iff1_0) # label(axiom). [assumption].
% 0.95/1.40 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(34,a,1,a)].
% 0.95/1.40 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(34,a,3,a)].
% 0.95/1.40 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(34,a,4,a)].
% 0.95/1.40 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(34,a,5,b)].
% 0.95/1.40 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(34,a,6,b)].
% 0.95/1.40 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(34,a,7,b)].
% 0.95/1.40 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(34,a,8,b)].
% 0.95/1.40 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(34,a,9,b)].
% 0.95/1.40 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(34,a,10,b)].
% 0.95/1.40 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(34,a,11,b)].
% 0.95/1.40 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(34,a,12,b)].
% 0.95/1.40 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(34,a,13,b)].
% 0.95/1.40 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(34,a,14,b)].
% 0.95/1.40 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(34,a,15,b)].
% 0.95/1.40 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(34,a,16,b)].
% 0.95/1.40 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(34,a,17,b)].
% 0.95/1.40 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(34,a,19,b)].
% 0.95/1.40 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(34,a,20,b)].
% 0.95/1.40 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(34,a,21,b)].
% 0.95/1.40 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(34,a,22,b)].
% 0.95/1.40 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(34,a,23,b)].
% 0.95/1.40 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(34,a,24,b)].
% 0.95/1.40 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(34,a,25,b)].
% 0.95/1.40 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(34,a,26,b)].
% 0.95/1.40 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(34,a,27,b)].
% 0.95/1.40 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(34,a,28,b)].
% 0.95/1.40 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(34,a,29,b)].
% 0.95/1.40 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(34,a,30,b)].
% 0.95/1.40 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(34,a,31,b)].
% 0.95/1.40 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(34,a,32,b)].
% 0.95/1.40 35 -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__iff2_0) # label(axiom). [assumption].
% 0.95/1.40 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(35,a,1,a)].
% 0.95/1.40 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(35,a,3,a)].
% 0.95/1.40 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(35,a,4,a)].
% 0.95/1.40 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(35,a,5,b)].
% 0.95/1.40 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(35,a,6,b)].
% 0.95/1.40 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(35,a,7,b)].
% 0.95/1.40 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(35,a,8,b)].
% 0.95/1.40 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(35,a,9,b)].
% 0.95/1.40 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(35,a,10,b)].
% 0.95/1.40 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(35,a,11,b)].
% 0.95/1.40 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(35,a,12,b)].
% 0.95/1.40 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(35,a,13,b)].
% 0.95/1.40 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(35,a,14,b)].
% 0.95/1.40 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(35,a,15,b)].
% 0.95/1.40 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(35,a,16,b)].
% 0.95/1.40 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(35,a,17,b)].
% 0.95/1.40 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(35,a,19,b)].
% 0.95/1.40 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(35,a,20,b)].
% 0.95/1.40 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(35,a,21,b)].
% 0.95/1.40 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(35,a,22,b)].
% 0.95/1.40 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(35,a,23,b)].
% 0.95/1.41 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(35,a,24,b)].
% 0.95/1.41 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(35,a,25,b)].
% 0.95/1.41 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(35,a,26,b)].
% 0.95/1.41 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(35,a,27,b)].
% 0.95/1.41 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(35,a,28,b)].
% 0.95/1.41 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(35,a,29,b)].
% 0.95/1.41 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(35,a,30,b)].
% 0.95/1.41 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(35,a,31,b)].
% 0.95/1.41 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(35,a,32,b)].
% 0.95/1.41 36 -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__iff1_0) # label(axiom). [assumption].
% 0.95/1.41 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(36,a,1,a)].
% 0.95/1.41 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(36,a,3,a)].
% 0.95/1.41 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(36,a,4,a)].
% 0.95/1.41 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(36,a,5,b)].
% 0.95/1.41 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(36,a,6,b)].
% 0.95/1.41 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(36,a,7,b)].
% 0.95/1.41 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(36,a,8,b)].
% 0.95/1.41 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(36,a,9,b)].
% 0.95/1.41 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(36,a,10,b)].
% 0.95/1.41 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(36,a,11,b)].
% 0.95/1.41 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(36,a,12,b)].
% 0.95/1.41 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(36,a,13,b)].
% 0.95/1.41 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(36,a,14,b)].
% 0.95/1.41 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(36,a,15,b)].
% 0.95/1.41 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(36,a,16,b)].
% 0.95/1.41 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(36,a,17,b)].
% 0.95/1.41 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(36,a,19,b)].
% 0.95/1.41 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(36,a,20,b)].
% 0.95/1.41 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(36,a,21,b)].
% 0.95/1.41 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(36,a,22,b)].
% 0.95/1.41 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(36,a,23,b)].
% 0.95/1.41 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(36,a,24,b)].
% 0.95/1.41 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(36,a,25,b)].
% 0.95/1.41 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(36,a,26,b)].
% 0.95/1.41 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(36,a,27,b)].
% 0.95/1.41 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(36,a,28,b)].
% 0.95/1.41 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(36,a,29,b)].
% 0.95/1.41 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(36,a,30,b)].
% 0.95/1.41 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(36,a,31,b)].
% 0.95/1.41 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(36,a,32,b)].
% 0.95/1.41 37 -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__iff2_0) # label(axiom). [assumption].
% 0.95/1.41 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(37,a,1,a)].
% 0.95/1.41 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(37,a,3,a)].
% 0.95/1.41 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(37,a,4,a)].
% 0.95/1.41 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(37,a,5,b)].
% 0.95/1.41 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(37,a,6,b)].
% 0.95/1.41 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(37,a,7,b)].
% 0.95/1.41 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(37,a,8,b)].
% 0.95/1.41 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(37,a,9,b)].
% 0.95/1.41 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(37,a,10,b)].
% 0.95/1.41 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(37,a,11,b)].
% 0.95/1.41 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(37,a,12,b)].
% 0.95/1.41 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(37,a,13,b)].
% 0.95/1.41 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(37,a,14,b)].
% 0.95/1.41 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(37,a,15,b)].
% 0.95/1.41 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(37,a,16,b)].
% 0.95/1.41 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(37,a,17,b)].
% 0.95/1.41 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(37,a,19,b)].
% 0.95/1.41 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(37,a,20,b)].
% 0.95/1.41 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(37,a,21,b)].
% 0.95/1.41 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(37,a,22,b)].
% 0.95/1.41 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(37,a,23,b)].
% 0.95/1.41 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(37,a,24,b)].
% 0.95/1.41 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(37,a,25,b)].
% 0.95/1.41 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(37,a,26,b)].
% 0.95/1.41 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(37,a,27,b)].
% 0.95/1.41 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(37,a,28,b)].
% 0.95/1.57 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(37,a,29,b)].
% 0.95/1.57 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(37,a,30,b)].
% 0.95/1.57 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(37,a,31,b)].
% 0.95/1.57 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(37,a,32,b)].
% 0.95/1.57 38 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_0) # label(axiom). [assumption].
% 0.95/1.57 39 class_Ring__and__Field_Osemiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_10) # label(axiom). [assumption].
% 0.95/1.57 40 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat_18) # label(axiom). [assumption].
% 0.95/1.57 41 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom). [assumption].
% 0.95/1.57 42 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Power_Orecpower_10) # label(axiom). [assumption].
% 0.95/1.57 43 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_4) # label(axiom). [assumption].
% 0.95/1.57 44 -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].
% 0.95/1.57 45 -class_Ring__and__Field_Ocomm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_6) # label(axiom). [assumption].
% 0.95/1.57 46 -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].
% 0.95/1.57 47 -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].
% 0.95/1.57 48 -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].
% 0.95/1.57 49 -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].
% 0.95/1.57 50 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ofield_20) # label(axiom). [assumption].
% 0.95/1.57 51 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom). [assumption].
% 0.95/1.57 52 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_14) # label(axiom). [assumption].
% 0.95/1.57 53 -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].
% 0.95/1.57 54 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__field_23) # label(axiom). [assumption].
% 0.95/1.57 55 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__idom_20) # label(axiom). [assumption].
% 0.95/1.57 56 -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].
% 0.95/1.57 57 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_14) # label(axiom). [assumption].
% 0.95/1.57 58 -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].
% 0.95/1.57 59 -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].
% 0.95/1.57 60 -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].
% 0.95/1.57 61 -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].
% 0.95/1.57 62 -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].
% 0.95/1.57 63 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_7) # label(axiom). [assumption].
% 0.95/1.57 64 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__semiring_1) # label(axiom). [assumption].
% 0.95/1.57 65 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring_0) # label(axiom). [assumption].
% 0.95/1.57 66 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring__1_7) # label(axiom). [assumption].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(38,a,39,a)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(38,a,40,a)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(38,a,41,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(38,a,42,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(38,a,43,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(38,a,44,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(38,a,45,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(38,a,46,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(38,a,47,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(38,a,48,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(38,a,49,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(38,a,50,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(38,a,51,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(38,a,52,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(38,a,53,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(38,a,54,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(38,a,55,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(38,a,56,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(38,a,57,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(38,a,58,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(38,a,59,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(38,a,60,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(38,a,61,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(38,a,62,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(38,a,63,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(38,a,64,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(38,a,65,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(38,a,66,b)].
% 0.95/1.57 67 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring_1) # label(axiom). [assumption].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(67,a,39,a)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(67,a,40,a)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(67,a,41,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(67,a,42,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(67,a,43,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(67,a,44,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(67,a,45,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(67,a,46,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(67,a,47,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(67,a,48,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(67,a,49,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(67,a,50,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(67,a,51,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(67,a,52,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(67,a,53,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(67,a,54,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(67,a,55,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(67,a,56,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(67,a,57,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(67,a,58,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(67,a,59,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(67,a,60,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(67,a,61,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(67,a,62,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(67,a,63,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(67,a,64,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(67,a,65,b)].
% 0.95/1.57 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(67,a,66,b)].
% 0.95/1.58 68 -class_Ring__and__Field_Osemiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring_2) # label(axiom). [assumption].
% 0.95/1.58 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(68,a,39,a)].
% 0.95/1.58 Derived: class_HOL_Oplus(tc_nat). [resolve(68,a,40,a)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(68,a,41,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(68,a,42,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(68,a,43,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(68,a,44,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(68,a,45,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(68,a,46,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(68,a,47,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(68,a,48,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(68,a,49,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(68,a,50,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(68,a,51,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(68,a,52,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(68,a,53,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(68,a,54,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(68,a,55,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(68,a,56,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(68,a,57,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(68,a,58,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(68,a,59,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(68,a,60,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(68,a,61,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(68,a,62,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(68,a,63,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(68,a,64,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(68,a,65,b)].
% 0.95/1.58 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(68,a,66,b)].
% 0.95/1.58 69 -class_Ring__and__Field_Osemiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring_3) # label(axiom). [assumption].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(69,a,39,a)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(69,a,40,a)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(69,a,41,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(69,a,42,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(69,a,43,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(69,a,44,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(69,a,45,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(69,a,46,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(69,a,47,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(69,a,48,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(69,a,49,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(69,a,50,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(69,a,51,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(69,a,52,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(69,a,53,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(69,a,54,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(69,a,55,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(69,a,56,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(69,a,57,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(69,a,58,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(69,a,59,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(69,a,60,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(69,a,61,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(69,a,62,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(69,a,63,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(69,a,64,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(69,a,65,b)].
% 0.95/1.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(69,a,66,b)].
% 0.95/1.58 70 -class_Ring__and__Field_Osemiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring_4) # label(axiom). [assumption].
% 0.95/1.58 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(70,a,39,a)].
% 0.95/1.58 Derived: class_HOL_Otimes(tc_nat). [resolve(70,a,40,a)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(70,a,41,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(70,a,42,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(70,a,43,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(70,a,44,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(70,a,45,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(70,a,46,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(70,a,47,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(70,a,48,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(70,a,49,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(70,a,50,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(70,a,51,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(70,a,52,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(70,a,53,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(70,a,54,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(70,a,55,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(70,a,56,b)].
% 0.95/1.58 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(70,a,57,b)].
% 0.95/1.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(70,a,58,b)].
% 0.95/1.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(70,a,59,b)].
% 0.95/1.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(70,a,60,b)].
% 0.95/1.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(70,a,61,b)].
% 0.95/1.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(70,a,62,b)].
% 0.95/1.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(70,a,63,b)].
% 0.95/1.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(70,a,64,b)].
% 0.95/1.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(70,a,65,b)].
% 0.95/1.63 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(70,a,66,b)].
% 0.95/1.63 71 -class_Ring__and__Field_Osemiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0_0) # label(axiom). [assumption].
% 0.95/1.63 72 -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].
% 0.95/1.63 73 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1_4) # label(axiom). [assumption].
% 0.95/1.63 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(73,b,68,a)].
% 0.95/1.63 74 -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].
% 0.95/1.63 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(74,b,69,a)].
% 0.95/1.63 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(74,b,70,a)].
% 0.95/1.63 75 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_0) # label(axiom). [assumption].
% 0.95/1.63 76 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom). [assumption].
% 0.95/1.63 77 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom). [assumption].
% 0.95/1.63 78 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom). [assumption].
% 0.95/1.63 79 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom). [assumption].
% 0.95/1.63 80 -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].
% 0.95/1.63 81 -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].
% 0.95/1.63 82 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom). [assumption].
% 0.95/1.63 83 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom). [assumption].
% 0.95/1.63 84 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_3) # label(axiom). [assumption].
% 0.95/1.63 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(84,a,76,a)].
% 0.95/1.63 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(84,a,77,a)].
% 0.95/1.63 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(84,a,78,b)].
% 0.95/1.63 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Power_Orecpower(A). [resolve(84,a,79,b)].
% 0.95/1.63 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(84,a,80,b)].
% 0.95/1.63 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(84,a,81,b)].
% 1.42/1.66 85 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom). [assumption].
% 1.42/1.66 86 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom). [assumption].
% 1.42/1.66 87 -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].
% 1.42/1.66 88 -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].
% 1.42/1.66 89 -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].
% 1.42/1.66 90 -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].
% 1.42/1.66 91 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom). [assumption].
% 1.42/1.66 92 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom). [assumption].
% 1.42/1.66 93 -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].
% 1.42/1.66 94 -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].
% 1.42/1.66 95 -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].
% 1.42/1.66 96 -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].
% 1.42/1.66 97 -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].
% 1.42/1.66 98 -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].
% 1.42/1.66 99 -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].
% 1.42/1.66 100 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(38,a,45,b)].
% 1.42/1.66 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(100,b,76,a)].
% 1.42/1.66 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(100,b,77,a)].
% 1.42/1.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(100,b,78,b)].
% 1.42/1.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(100,b,79,b)].
% 1.42/1.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(100,b,80,b)].
% 1.42/1.66 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(100,b,81,b)].
% 1.42/1.66 101 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(67,a,45,b)].
% 1.42/1.66 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(101,b,76,a)].
% 1.42/1.66 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(101,b,77,a)].
% 1.42/1.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(101,b,78,b)].
% 1.42/1.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(101,b,79,b)].
% 1.42/1.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(101,b,80,b)].
% 1.42/1.66 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(101,b,81,b)].
% 1.45/1.68 102 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(68,a,45,b)].
% 1.45/1.68 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(102,b,76,a)].
% 1.45/1.68 Derived: class_HOL_Oplus(tc_nat). [resolve(102,b,77,a)].
% 1.45/1.68 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(102,b,78,b)].
% 1.45/1.68 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(102,b,79,b)].
% 1.45/1.68 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(102,b,80,b)].
% 1.45/1.68 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(102,b,81,b)].
% 1.45/1.68 103 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(69,a,45,b)].
% 1.45/1.68 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(103,b,76,a)].
% 1.45/1.68 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(103,b,77,a)].
% 1.45/1.68 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(103,b,78,b)].
% 1.45/1.68 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(103,b,79,b)].
% 1.45/1.68 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(103,b,80,b)].
% 1.45/1.68 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(103,b,81,b)].
% 1.45/1.68 104 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring(A). [resolve(70,a,45,b)].
% 1.45/1.68 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(104,b,76,a)].
% 1.45/1.68 Derived: class_HOL_Otimes(tc_nat). [resolve(104,b,77,a)].
% 1.45/1.68 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(104,b,78,b)].
% 1.45/1.68 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(104,b,79,b)].
% 1.45/1.68 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(104,b,80,b)].
% 1.45/1.68 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(104,b,81,b)].
% 1.45/1.68 105 -class_OrderedGroup_Ocomm__monoid__add(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_0) # label(axiom). [assumption].
% 1.45/1.68 106 class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_12) # label(axiom). [assumption].
% 1.45/1.68 107 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat_20) # label(axiom). [assumption].
% 1.45/1.68 108 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom). [assumption].
% 1.45/1.68 109 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Oab__group__add_1) # label(axiom). [assumption].
% 1.45/1.68 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(105,a,106,a)].
% 1.45/1.68 Derived: class_HOL_Ozero(tc_nat). [resolve(105,a,107,a)].
% 1.45/1.68 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(105,a,108,b)].
% 1.45/1.68 Derived: class_HOL_Ozero(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(105,a,109,b)].
% 1.45/1.68 110 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom). [assumption].
% 1.45/1.68 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(110,a,109,b)].
% 1.45/1.68 111 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_2) # label(axiom). [assumption].
% 1.45/1.68 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(111,a,109,b)].
% 1.45/1.68 112 -class_OrderedGroup_Ocomm__monoid__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_3) # label(axiom). [assumption].
% 1.45/1.68 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(112,a,109,b)].
% 1.45/1.68 113 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom). [assumption].
% 1.45/1.68 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(113,b,110,a)].
% 1.45/1.68 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(113,b,111,a)].
% 1.45/1.69 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A). [resolve(113,b,112,a)].
% 1.45/1.69 114 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_4) # label(axiom). [assumption].
% 1.45/1.69 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(114,b,110,a)].
% 1.45/1.69 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(114,b,111,a)].
% 1.45/1.69 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A). [resolve(114,b,112,a)].
% 1.45/1.69 115 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_3) # label(axiom). [assumption].
% 1.45/1.69 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(115,b,110,a)].
% 1.45/1.69 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(115,b,111,a)].
% 1.45/1.69 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A). [resolve(115,b,112,a)].
% 1.45/1.69 116 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_3) # label(axiom). [assumption].
% 1.45/1.69 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(116,b,110,a)].
% 1.45/1.69 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(116,b,111,a)].
% 1.45/1.69 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A). [resolve(116,b,112,a)].
% 1.45/1.69 117 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_2) # label(axiom). [assumption].
% 1.45/1.69 118 -class_Power_Orecpower(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Power_Orecpower_12) # label(axiom). [assumption].
% 1.45/1.69 Derived: -class_Power_Orecpower(A) | class_HOL_Ozero(A). [resolve(118,b,105,a)].
% 1.45/1.69 119 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_7) # label(axiom). [assumption].
% 1.45/1.69 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(119,b,105,a)].
% 1.45/1.69 120 -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].
% 1.45/1.69 121 -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].
% 1.45/1.69 122 -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].
% 1.45/1.69 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(122,b,105,a)].
% 1.45/1.69 123 -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].
% 1.45/1.69 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A). [resolve(123,b,105,a)].
% 1.45/1.69 124 -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].
% 1.45/1.69 Derived: -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Ozero(A). [resolve(124,b,105,a)].
% 1.45/1.69 125 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ofield_23) # label(axiom). [assumption].
% 1.45/1.69 126 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom). [assumption].
% 1.45/1.69 127 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_17) # label(axiom). [assumption].
% 1.50/1.74 128 -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].
% 1.50/1.74 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Ozero(A). [resolve(128,b,105,a)].
% 1.50/1.74 129 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__field_25) # label(axiom). [assumption].
% 1.50/1.74 130 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_23) # label(axiom). [assumption].
% 1.50/1.74 131 -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].
% 1.50/1.74 132 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_17) # label(axiom). [assumption].
% 1.50/1.74 133 -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].
% 1.50/1.74 134 -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].
% 1.50/1.74 135 -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].
% 1.50/1.74 136 -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].
% 1.50/1.74 137 -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].
% 1.50/1.74 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Ozero(A). [resolve(137,b,105,a)].
% 1.50/1.74 138 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_10) # label(axiom). [assumption].
% 1.50/1.74 139 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_4) # label(axiom). [assumption].
% 1.50/1.74 140 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom). [assumption].
% 1.50/1.74 141 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring__1_10) # label(axiom). [assumption].
% 1.50/1.74 142 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_6) # label(axiom). [assumption].
% 1.50/1.74 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(142,b,110,a)].
% 1.50/1.74 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(142,b,111,a)].
% 1.50/1.74 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A). [resolve(142,b,112,a)].
% 1.50/1.74 143 -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].
% 1.50/1.74 144 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_7) # label(axiom). [assumption].
% 1.50/1.74 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(144,b,105,a)].
% 1.50/1.74 145 -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].
% 1.50/1.74 146 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_1) # label(axiom). [assumption].
% 1.50/1.74 147 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom). [assumption].
% 1.50/1.74 148 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom). [assumption].
% 1.50/1.74 149 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom). [assumption].
% 1.50/1.74 150 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom). [assumption].
% 1.50/1.74 151 -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].
% 1.50/1.74 152 -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].
% 1.50/1.74 153 -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].
% 1.50/1.74 154 -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].
% 1.50/1.74 155 -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].
% 1.50/1.74 156 -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].
% 1.50/1.74 157 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom). [assumption].
% 1.50/1.74 158 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom). [assumption].
% 1.50/1.74 159 -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].
% 1.50/1.74 160 -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].
% 1.50/1.74 161 -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].
% 1.50/1.74 162 -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].
% 1.50/1.74 163 -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].
% 1.50/1.74 164 -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].
% 1.50/1.74 165 -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].
% 1.50/1.74 166 -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].
% 1.50/1.74 167 -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].
% 1.50/1.74 168 -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].
% 1.50/1.74 169 -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].
% 1.50/1.74 170 -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].
% 1.52/1.77 171 -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].
% 1.52/1.77 172 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom). [assumption].
% 1.52/1.77 173 -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].
% 1.52/1.77 174 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom). [assumption].
% 1.52/1.77 175 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom). [assumption].
% 1.52/1.77 176 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom). [assumption].
% 1.52/1.77 177 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom). [assumption].
% 1.52/1.77 178 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom). [assumption].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(178,a,152,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(178,a,153,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(178,a,157,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(178,a,158,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(178,a,159,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(178,a,161,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(178,a,162,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(178,a,163,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(178,a,164,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(178,a,165,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(178,a,166,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(178,a,167,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(178,a,168,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(178,a,170,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(178,a,171,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(178,a,172,b)].
% 1.52/1.77 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(178,a,173,b)].
% 1.52/1.77 179 -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].
% 1.52/1.77 180 -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].
% 1.52/1.77 181 -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].
% 1.52/1.77 182 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(142,b,110,a)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(182,a,147,a)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(182,a,148,a)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(182,a,149,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(182,a,150,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(182,a,151,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(182,a,152,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(182,a,153,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(182,a,154,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(182,a,155,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(182,a,156,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(182,a,157,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(182,a,158,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(182,a,159,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(182,a,160,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(182,a,161,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(182,a,162,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(182,a,163,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(182,a,164,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(182,a,165,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(182,a,166,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(182,a,167,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(182,a,168,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(182,a,169,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(182,a,170,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(182,a,171,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(182,a,172,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(182,a,173,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(182,a,179,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(182,a,180,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(182,a,181,b)].
% 1.52/1.77 183 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(142,b,111,a)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(183,a,147,a)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(183,a,148,a)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(183,a,149,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(183,a,150,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(183,a,151,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(183,a,152,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(183,a,153,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(183,a,154,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(183,a,155,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(183,a,156,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(183,a,157,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(183,a,158,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(183,a,159,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(183,a,160,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(183,a,161,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(183,a,162,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(183,a,163,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(183,a,164,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(183,a,165,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(183,a,166,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(183,a,167,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(183,a,168,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(183,a,169,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(183,a,170,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(183,a,171,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(183,a,172,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(183,a,173,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(183,a,179,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(183,a,180,b)].
% 1.52/1.77 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(183,a,181,b)].
% 1.52/1.77 184 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A). [resolve(142,b,112,a)].
% 1.52/1.77 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(184,a,147,a)].
% 1.52/1.77 Derived: class_HOL_Oplus(tc_nat). [resolve(184,a,148,a)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(184,a,149,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(184,a,150,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(184,a,151,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(184,a,152,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(184,a,153,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(184,a,154,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(184,a,155,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(184,a,156,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(184,a,157,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(184,a,158,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(184,a,159,b)].
% 1.52/1.77 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(184,a,160,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(184,a,161,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(184,a,162,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(184,a,163,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(184,a,164,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(184,a,165,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(184,a,166,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(184,a,167,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(184,a,168,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(184,a,169,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(184,a,170,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(184,a,171,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(184,a,172,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(184,a,173,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(184,a,179,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(184,a,180,b)].
% 1.52/1.80 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(184,a,181,b)].
% 1.52/1.80 185 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_1) # label(axiom). [assumption].
% 1.52/1.80 186 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom). [assumption].
% 1.52/1.80 187 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom). [assumption].
% 1.52/1.80 188 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom). [assumption].
% 1.52/1.80 189 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom). [assumption].
% 1.52/1.80 190 -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].
% 1.52/1.80 191 -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].
% 1.52/1.80 192 -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].
% 1.52/1.80 193 -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].
% 1.52/1.80 194 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_5) # label(axiom). [assumption].
% 1.52/1.80 195 -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].
% 1.52/1.80 196 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_7) # label(axiom). [assumption].
% 1.52/1.80 197 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_9) # label(axiom). [assumption].
% 1.52/1.80 198 -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].
% 1.52/1.80 199 -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].
% 1.52/1.80 200 -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].
% 1.58/1.83 201 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ofield_15) # label(axiom). [assumption].
% 1.58/1.83 202 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oidom_15) # label(axiom). [assumption].
% 1.58/1.83 203 -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].
% 1.58/1.83 204 -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].
% 1.58/1.83 205 -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].
% 1.58/1.83 206 -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].
% 1.58/1.83 Derived: -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(206,b,185,a)].
% 1.58/1.83 207 -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].
% 1.58/1.83 208 -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].
% 1.58/1.83 209 -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].
% 1.58/1.83 210 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(38,a,46,b)].
% 1.58/1.83 211 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(67,a,46,b)].
% 1.58/1.83 212 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(68,a,46,b)].
% 1.58/1.83 213 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(69,a,46,b)].
% 1.58/1.83 214 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(70,a,46,b)].
% 1.58/1.83 215 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(178,a,153,b)].
% 1.58/1.83 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(215,b,186,a)].
% 1.58/1.83 Derived: class_HOL_Ozero(tc_nat). [resolve(215,b,187,a)].
% 1.58/1.83 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(215,b,188,b)].
% 1.58/1.83 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(215,b,189,b)].
% 1.58/1.83 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(215,b,190,b)].
% 1.58/1.83 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(215,b,191,b)].
% 1.58/1.83 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(215,b,198,b)].
% 1.58/1.83 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(215,b,199,b)].
% 1.58/1.83 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(215,b,200,b)].
% 1.58/1.83 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(215,b,203,b)].
% 1.58/1.83 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(215,b,209,b)].
% 1.58/1.83 216 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(182,a,153,b)].
% 1.58/1.83 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(216,b,186,a)].
% 1.58/1.83 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(216,b,187,a)].
% 1.58/1.83 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(216,b,188,b)].
% 1.58/1.83 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(216,b,189,b)].
% 1.58/1.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(216,b,190,b)].
% 1.58/1.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(216,b,191,b)].
% 1.58/1.85 217 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(183,a,153,b)].
% 1.58/1.85 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(217,b,186,a)].
% 1.58/1.85 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(217,b,187,a)].
% 1.58/1.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(217,b,188,b)].
% 1.58/1.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(217,b,189,b)].
% 1.58/1.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(217,b,190,b)].
% 1.58/1.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(217,b,191,b)].
% 1.58/1.85 218 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(184,a,153,b)].
% 1.58/1.85 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(218,b,186,a)].
% 1.58/1.85 Derived: class_HOL_Oplus(tc_nat). [resolve(218,b,187,a)].
% 1.58/1.85 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(218,b,188,b)].
% 1.58/1.85 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(218,b,189,b)].
% 1.58/1.85 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(218,b,190,b)].
% 1.58/1.85 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(218,b,191,b)].
% 1.58/1.85 219 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom). [assumption].
% 1.58/1.85 220 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom). [assumption].
% 1.58/1.85 221 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom). [assumption].
% 1.58/1.85 222 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom). [assumption].
% 1.58/1.85 223 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom). [assumption].
% 1.58/1.85 224 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 1.58/1.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(219,a,224,b)].
% 1.58/1.85 225 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom). [assumption].
% 1.58/1.85 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(225,a,224,b)].
% 1.58/1.85 226 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom). [assumption].
% 1.58/1.85 227 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_11) # label(axiom). [assumption].
% 1.58/1.85 228 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_12) # label(axiom). [assumption].
% 1.58/1.85 229 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_12) # label(axiom). [assumption].
% 1.58/1.85 230 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) # label(axiom). [assumption].
% 1.58/1.85 231 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_6) # label(axiom). [assumption].
% 1.58/1.85 232 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) # label(axiom). [assumption].
% 1.58/1.85 233 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) # label(axiom). [assumption].
% 1.58/1.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(233,b,219,a)].
% 1.58/1.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(233,b,225,a)].
% 1.58/1.85 234 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom). [assumption].
% 1.58/1.85 235 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_15) # label(axiom). [assumption].
% 1.58/1.85 236 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_17) # label(axiom). [assumption].
% 1.58/1.85 237 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) # label(axiom). [assumption].
% 1.58/1.85 238 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) # label(axiom). [assumption].
% 1.58/1.85 239 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom). [assumption].
% 1.58/1.85 240 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom). [assumption].
% 1.58/1.85 241 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_21) # label(axiom). [assumption].
% 1.58/1.85 242 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) # label(axiom). [assumption].
% 1.58/1.85 243 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_28) # label(axiom). [assumption].
% 1.58/1.85 244 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_27) # label(axiom). [assumption].
% 1.58/1.85 245 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_5) # label(axiom). [assumption].
% 1.58/1.85 246 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_21) # label(axiom). [assumption].
% 1.58/1.85 247 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_20) # label(axiom). [assumption].
% 1.58/1.85 248 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) # label(axiom). [assumption].
% 1.58/1.85 249 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_14) # label(axiom). [assumption].
% 1.58/1.85 250 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_17) # label(axiom). [assumption].
% 1.58/1.85 251 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_5) # label(axiom). [assumption].
% 1.58/1.85 252 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom). [assumption].
% 1.62/1.89 253 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_5) # label(axiom). [assumption].
% 1.62/1.89 254 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_10) # label(axiom). [assumption].
% 1.62/1.89 255 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_14) # label(axiom). [assumption].
% 1.62/1.89 256 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) # label(axiom). [assumption].
% 1.62/1.89 257 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom). [assumption].
% 1.62/1.89 258 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom). [assumption].
% 1.62/1.89 259 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom). [assumption].
% 1.62/1.89 260 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom). [assumption].
% 1.62/1.89 261 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 1.62/1.89 262 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 1.62/1.89 263 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom). [assumption].
% 1.62/1.89 264 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_9) # label(axiom). [assumption].
% 1.62/1.89 265 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_10) # label(axiom). [assumption].
% 1.62/1.89 266 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_10) # label(axiom). [assumption].
% 1.62/1.89 267 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) # label(axiom). [assumption].
% 1.62/1.89 268 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_4) # label(axiom). [assumption].
% 1.62/1.89 269 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) # label(axiom). [assumption].
% 1.62/1.89 270 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) # label(axiom). [assumption].
% 1.62/1.89 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(270,b,256,a)].
% 1.62/1.89 271 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom). [assumption].
% 1.62/1.89 272 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_14) # label(axiom). [assumption].
% 1.62/1.89 273 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_15) # label(axiom). [assumption].
% 1.62/1.89 274 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) # label(axiom). [assumption].
% 1.62/1.92 275 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) # label(axiom). [assumption].
% 1.62/1.92 276 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom). [assumption].
% 1.62/1.92 277 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom). [assumption].
% 1.62/1.92 278 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_19) # label(axiom). [assumption].
% 1.62/1.92 279 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) # label(axiom). [assumption].
% 1.62/1.92 280 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_26) # label(axiom). [assumption].
% 1.62/1.92 281 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_25) # label(axiom). [assumption].
% 1.62/1.92 282 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_4) # label(axiom). [assumption].
% 1.62/1.92 283 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_19) # label(axiom). [assumption].
% 1.62/1.92 284 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_19) # label(axiom). [assumption].
% 1.62/1.92 285 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) # label(axiom). [assumption].
% 1.62/1.92 286 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_13) # label(axiom). [assumption].
% 1.62/1.92 287 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_15) # label(axiom). [assumption].
% 1.62/1.92 288 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_4) # label(axiom). [assumption].
% 1.62/1.92 289 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom). [assumption].
% 1.62/1.92 290 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_4) # label(axiom). [assumption].
% 1.62/1.92 291 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_9) # label(axiom). [assumption].
% 1.62/1.92 292 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_13) # label(axiom). [assumption].
% 1.62/1.92 293 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(219,a,224,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(293,b,257,a)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(293,b,258,a)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(293,b,259,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(293,b,260,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(293,b,263,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(293,b,264,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(293,b,265,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(293,b,266,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(293,b,267,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(293,b,268,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(293,b,269,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(293,b,271,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(293,b,272,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(293,b,273,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(293,b,274,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(293,b,275,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(293,b,276,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(293,b,277,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(293,b,278,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(293,b,279,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(293,b,280,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(293,b,281,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(293,b,282,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(293,b,283,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(293,b,284,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(293,b,285,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(293,b,286,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(293,b,287,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(293,b,288,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(293,b,289,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(293,b,290,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(293,b,291,b)].
% 1.62/1.92 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(293,b,292,b)].
% 1.62/1.92 294 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(225,a,224,b)].
% 1.62/1.92 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(294,b,257,a)].
% 1.62/1.92 Derived: class_HOL_Oplus(tc_nat). [resolve(294,b,258,a)].
% 1.62/1.92 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(294,b,259,b)].
% 1.62/1.92 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(294,b,260,b)].
% 1.62/1.92 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(294,b,263,b)].
% 1.62/1.92 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(294,b,264,b)].
% 1.62/1.92 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(294,b,265,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(294,b,266,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(294,b,267,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(294,b,268,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(294,b,269,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(294,b,271,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(294,b,272,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(294,b,273,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(294,b,274,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(294,b,275,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(294,b,276,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(294,b,277,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(294,b,278,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(294,b,279,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(294,b,280,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(294,b,281,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(294,b,282,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(294,b,283,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(294,b,284,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(294,b,285,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(294,b,286,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(294,b,287,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(294,b,288,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(294,b,289,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(294,b,290,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(294,b,291,b)].
% 1.71/1.94 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(294,b,292,b)].
% 1.71/1.94 295 -class_OrderedGroup_Oab__group__add(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Oab__group__add_2) # label(axiom). [assumption].
% 1.71/1.94 296 class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_17) # label(axiom). [assumption].
% 1.71/1.94 297 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Numeral_Onumber__ring_15) # label(axiom). [assumption].
% 1.71/1.94 298 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_3) # label(axiom). [assumption].
% 1.71/1.94 299 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_4) # label(axiom). [assumption].
% 1.71/1.94 300 -class_OrderedGroup_Oab__group__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Oab__group__add_5) # label(axiom). [assumption].
% 1.71/1.94 301 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom). [assumption].
% 1.71/1.94 302 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_2) # label(axiom). [assumption].
% 1.71/1.94 303 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_1) # label(axiom). [assumption].
% 1.71/1.94 304 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_1) # label(axiom). [assumption].
% 1.75/1.99 305 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_0) # label(axiom). [assumption].
% 1.75/1.99 306 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_12) # label(axiom). [assumption].
% 1.75/1.99 307 -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].
% 1.75/1.99 308 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ofield_4) # label(axiom). [assumption].
% 1.75/1.99 309 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom). [assumption].
% 1.75/1.99 310 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_3) # label(axiom). [assumption].
% 1.75/1.99 311 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__field_7) # label(axiom). [assumption].
% 1.75/1.99 312 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_4) # label(axiom). [assumption].
% 1.75/1.99 313 -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].
% 1.75/1.99 314 -class_Ring__and__Field_Opordered__comm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_2) # label(axiom). [assumption].
% 1.75/1.99 315 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_1) # label(axiom). [assumption].
% 1.75/1.99 316 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring_6) # label(axiom). [assumption].
% 1.75/1.99 317 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring__1_1) # label(axiom). [assumption].
% 1.75/1.99 318 class_HOL_Ozero(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(105,a,109,b)].
% 1.75/1.99 Derived: class_HOL_Ozero(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(318,b,301,b)].
% 1.75/1.99 Derived: class_HOL_Ozero(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(318,b,302,b)].
% 1.75/1.99 Derived: class_HOL_Ozero(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(318,b,303,b)].
% 1.75/1.99 Derived: class_HOL_Ozero(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(318,b,304,b)].
% 1.75/1.99 Derived: class_HOL_Ozero(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(318,b,305,b)].
% 1.75/1.99 319 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(110,a,109,b)].
% 1.75/1.99 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(319,b,305,b)].
% 1.75/1.99 320 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(111,a,109,b)].
% 1.75/1.99 321 class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(112,a,109,b)].
% 1.75/1.99 322 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(293,b,260,b)].
% 1.75/1.99 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(322,b,296,a)].
% 1.75/1.99 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(322,b,297,b)].
% 1.75/1.99 323 class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(294,b,260,b)].
% 1.75/1.99 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(323,b,296,a)].
% 1.75/1.99 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(323,b,297,b)].
% 1.75/1.99 324 -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].
% 1.75/1.99 325 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom). [assumption].
% 1.75/1.99 326 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom). [assumption].
% 1.75/1.99 327 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom). [assumption].
% 1.75/1.99 328 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom). [assumption].
% 1.75/1.99 329 -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].
% 1.75/1.99 330 -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].
% 1.75/1.99 331 -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].
% 1.75/1.99 332 -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].
% 1.75/1.99 333 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_18) # label(axiom). [assumption].
% 1.75/1.99 334 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_18) # label(axiom). [assumption].
% 1.75/1.99 335 -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].
% 1.75/1.99 336 -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].
% 1.75/1.99 337 -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].
% 1.75/1.99 338 -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].
% 1.75/1.99 339 -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].
% 1.75/1.99 340 -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].
% 1.75/1.99 341 -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].
% 1.75/1.99 342 -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].
% 1.75/1.99 343 -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].
% 1.75/1.99 344 -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].
% 1.75/1.99 345 -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].
% 1.75/1.99 346 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring_12) # label(axiom). [assumption].
% 1.75/1.99 347 -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].
% 1.75/1.99 348 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_3) # label(axiom). [assumption].
% 1.75/2.03 349 -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].
% 1.75/2.03 350 -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].
% 1.75/2.03 351 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_7) # label(axiom). [assumption].
% 1.75/2.03 352 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_8) # label(axiom). [assumption].
% 1.75/2.03 353 -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].
% 1.75/2.03 354 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(182,a,179,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(354,b,331,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(354,b,332,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(354,b,333,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(354,b,334,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(354,b,335,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(354,b,336,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(354,b,337,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(354,b,338,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(354,b,339,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(354,b,340,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(354,b,341,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(354,b,342,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(354,b,343,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(354,b,344,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(354,b,345,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(354,b,346,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(354,b,347,b)].
% 1.75/2.03 355 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(183,a,179,b)].
% 1.75/2.03 356 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(184,a,179,b)].
% 1.75/2.03 357 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(293,b,291,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(357,b,326,a)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(357,b,328,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(357,b,329,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(357,b,330,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(357,b,331,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(357,b,332,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(357,b,333,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(357,b,334,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(357,b,335,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(357,b,336,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(357,b,337,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(357,b,338,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(357,b,339,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(357,b,340,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(357,b,341,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(357,b,342,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(357,b,343,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(357,b,344,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(357,b,345,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(357,b,346,b)].
% 1.75/2.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(357,b,347,b)].
% 1.75/2.03 358 class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(294,b,291,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(tc_nat). [resolve(358,b,326,a)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(358,b,328,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(358,b,329,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(358,b,330,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(358,b,331,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(358,b,332,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(358,b,333,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(358,b,334,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(358,b,335,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(358,b,336,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(358,b,337,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(358,b,338,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(358,b,339,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(358,b,340,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(358,b,341,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(358,b,342,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(358,b,343,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(358,b,344,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(358,b,345,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(358,b,346,b)].
% 1.75/2.03 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring__1(A). [resolve(358,b,347,b)].
% 1.82/2.07 359 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_1) # label(axiom). [assumption].
% 1.82/2.07 360 class_Ring__and__Field_Oring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_19) # label(axiom). [assumption].
% 1.82/2.07 361 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom). [assumption].
% 1.82/2.07 362 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_16) # label(axiom). [assumption].
% 1.82/2.07 363 -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].
% 1.82/2.07 364 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ofield_3) # label(axiom). [assumption].
% 1.82/2.07 365 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom). [assumption].
% 1.82/2.07 366 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Olordered__ring_1) # label(axiom). [assumption].
% 1.82/2.07 367 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__field_6) # label(axiom). [assumption].
% 1.82/2.07 368 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oordered__idom_3) # label(axiom). [assumption].
% 1.82/2.07 369 -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].
% 1.82/2.07 370 -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].
% 1.82/2.07 371 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__ring_0) # label(axiom). [assumption].
% 1.82/2.07 372 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring_2) # label(axiom). [assumption].
% 1.82/2.07 373 -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oring_3) # label(axiom). [assumption].
% 1.82/2.07 374 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring_4) # label(axiom). [assumption].
% 1.82/2.07 375 -class_Ring__and__Field_Oring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring_5) # label(axiom). [assumption].
% 1.82/2.07 376 -class_Ring__and__Field_Oring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring_9) # label(axiom). [assumption].
% 1.82/2.07 377 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oring__1_0) # label(axiom). [assumption].
% 1.82/2.07 378 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(38,a,65,b)].
% 1.82/2.07 379 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(67,a,65,b)].
% 1.82/2.07 380 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(68,a,65,b)].
% 1.82/2.07 381 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(69,a,65,b)].
% 1.82/2.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(381,b,364,b)].
% 1.82/2.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(381,b,365,b)].
% 1.82/2.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(381,b,366,b)].
% 1.82/2.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(381,b,367,b)].
% 1.82/2.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(381,b,368,b)].
% 1.82/2.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(381,b,369,b)].
% 1.82/2.07 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(381,b,370,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(381,b,371,b)].
% 1.82/2.08 382 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(70,a,65,b)].
% 1.82/2.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(382,b,364,b)].
% 1.82/2.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(382,b,365,b)].
% 1.82/2.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(382,b,366,b)].
% 1.82/2.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(382,b,367,b)].
% 1.82/2.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(382,b,368,b)].
% 1.82/2.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(382,b,369,b)].
% 1.82/2.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(382,b,370,b)].
% 1.82/2.08 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(382,b,371,b)].
% 1.82/2.08 383 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(178,a,172,b)].
% 1.82/2.08 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(383,b,364,b)].
% 1.82/2.08 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(383,b,365,b)].
% 1.82/2.08 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(383,b,366,b)].
% 1.82/2.08 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(383,b,367,b)].
% 1.82/2.08 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(383,b,368,b)].
% 1.82/2.08 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(383,b,369,b)].
% 1.82/2.08 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(383,b,370,b)].
% 1.82/2.08 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(383,b,371,b)].
% 1.82/2.08 384 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(182,a,172,b)].
% 1.82/2.08 385 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(183,a,172,b)].
% 1.82/2.08 386 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(184,a,172,b)].
% 1.82/2.08 387 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(293,b,289,b)].
% 1.82/2.08 388 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(294,b,289,b)].
% 1.82/2.08 389 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(354,b,346,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(389,b,360,a)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(389,b,361,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(389,b,362,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(389,b,363,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(389,b,364,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(389,b,365,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(389,b,366,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(389,b,367,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(389,b,368,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(389,b,369,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(389,b,370,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(389,b,371,b)].
% 1.82/2.08 390 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(357,b,346,b)].
% 1.82/2.08 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(390,b,360,a)].
% 1.82/2.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(390,b,361,b)].
% 1.88/2.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(390,b,362,b)].
% 1.88/2.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(390,b,363,b)].
% 1.88/2.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(390,b,364,b)].
% 1.88/2.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(390,b,365,b)].
% 1.88/2.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(390,b,366,b)].
% 1.88/2.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(390,b,367,b)].
% 1.88/2.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(390,b,368,b)].
% 1.88/2.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(390,b,369,b)].
% 1.88/2.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(390,b,370,b)].
% 1.88/2.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(390,b,371,b)].
% 1.88/2.14 391 class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(358,b,346,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(391,b,360,a)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Numeral_Onumber__ring(A). [resolve(391,b,361,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(391,b,362,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(391,b,363,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(391,b,364,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(391,b,365,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(391,b,366,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(391,b,367,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(391,b,368,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(391,b,369,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(391,b,370,b)].
% 1.88/2.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(391,b,371,b)].
% 1.88/2.14 392 -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].
% 1.88/2.14 393 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom). [assumption].
% 1.88/2.14 394 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom). [assumption].
% 1.88/2.14 395 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom). [assumption].
% 1.88/2.14 396 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom). [assumption].
% 1.88/2.14 397 -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].
% 1.88/2.14 398 -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].
% 1.88/2.14 399 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) # label(axiom). [assumption].
% 1.88/2.14 400 -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].
% 1.88/2.14 401 -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].
% 1.93/2.18 402 -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].
% 1.93/2.18 403 -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].
% 1.93/2.18 404 -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].
% 1.93/2.18 405 -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].
% 1.93/2.18 406 -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].
% 1.93/2.18 407 -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].
% 1.93/2.18 408 -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].
% 1.93/2.18 409 -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].
% 1.93/2.18 410 -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].
% 1.93/2.18 411 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(38,a,47,b)].
% 1.93/2.18 412 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(67,a,47,b)].
% 1.93/2.18 413 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(69,a,47,b)].
% 1.93/2.18 414 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(70,a,47,b)].
% 1.93/2.18 415 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(122,b,105,a)].
% 1.93/2.18 416 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(182,a,154,b)].
% 1.93/2.18 417 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(183,a,154,b)].
% 1.93/2.18 418 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(215,b,198,b)].
% 1.93/2.18 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(418,b,393,a)].
% 1.93/2.18 Derived: class_HOL_Ozero(tc_nat). [resolve(418,b,394,a)].
% 1.93/2.18 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(418,b,395,b)].
% 1.93/2.18 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(418,b,396,b)].
% 1.93/2.18 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(418,b,397,b)].
% 1.93/2.18 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(418,b,398,b)].
% 1.93/2.18 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(418,b,409,b)].
% 1.93/2.18 419 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(293,b,274,b)].
% 1.93/2.18 420 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(354,b,331,b)].
% 1.93/2.18 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(420,b,394,a)].
% 1.93/2.18 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(420,b,396,b)].
% 1.93/2.18 421 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(357,b,331,b)].
% 1.93/2.18 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(421,b,394,a)].
% 1.93/2.18 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(421,b,396,b)].
% 1.93/2.18 422 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom). [assumption].
% 1.93/2.20 423 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom). [assumption].
% 1.93/2.20 424 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom). [assumption].
% 1.93/2.20 425 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_2) # label(axiom). [assumption].
% 1.93/2.20 426 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom). [assumption].
% 1.93/2.20 427 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom). [assumption].
% 1.93/2.20 428 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_8) # label(axiom). [assumption].
% 1.93/2.20 429 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom). [assumption].
% 1.93/2.20 430 -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].
% 1.93/2.20 431 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom). [assumption].
% 1.93/2.20 432 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom). [assumption].
% 1.93/2.20 433 -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].
% 1.93/2.20 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(433,b,425,a)].
% 1.93/2.20 434 -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].
% 1.93/2.20 435 -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].
% 1.93/2.20 436 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(38,a,43,b)].
% 1.93/2.20 437 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(67,a,43,b)].
% 1.93/2.20 438 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(69,a,43,b)].
% 1.93/2.20 439 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(70,a,43,b)].
% 1.93/2.20 440 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(84,a,80,b)].
% 1.93/2.20 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(440,b,423,a)].
% 1.93/2.20 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(440,b,424,b)].
% 1.93/2.20 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(440,b,431,b)].
% 1.93/2.20 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(440,b,432,b)].
% 1.93/2.20 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(440,b,434,b)].
% 1.93/2.20 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(440,b,435,b)].
% 1.93/2.20 441 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(100,b,80,b)].
% 1.93/2.20 442 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(101,b,80,b)].
% 1.93/2.20 443 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(103,b,80,b)].
% 1.93/2.20 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(443,b,423,a)].
% 1.93/2.20 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(443,b,424,b)].
% 1.93/2.20 444 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(104,b,80,b)].
% 1.93/2.20 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(444,b,423,a)].
% 1.93/2.20 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(444,b,424,b)].
% 1.93/2.22 445 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(119,b,105,a)].
% 1.93/2.22 446 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(182,a,151,b)].
% 1.93/2.22 447 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(183,a,151,b)].
% 1.93/2.22 448 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(215,b,190,b)].
% 1.93/2.22 449 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(216,b,190,b)].
% 1.93/2.22 450 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(217,b,190,b)].
% 1.93/2.22 451 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(293,b,272,b)].
% 1.93/2.22 452 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(357,b,329,b)].
% 1.93/2.22 453 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(389,b,362,b)].
% 1.93/2.22 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(453,b,423,a)].
% 1.93/2.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(453,b,424,b)].
% 1.93/2.22 454 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(390,b,362,b)].
% 1.93/2.22 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(454,b,423,a)].
% 1.93/2.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(454,b,424,b)].
% 1.93/2.22 455 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(418,b,397,b)].
% 1.93/2.22 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(455,b,423,a)].
% 1.93/2.22 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(455,b,424,b)].
% 1.93/2.22 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(455,b,431,b)].
% 1.93/2.22 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(455,b,432,b)].
% 1.93/2.22 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(455,b,433,b)].
% 1.93/2.22 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(455,b,434,b)].
% 1.93/2.22 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(455,b,435,b)].
% 1.93/2.22 456 -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].
% 1.93/2.22 457 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom). [assumption].
% 1.93/2.22 458 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom). [assumption].
% 1.93/2.22 459 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom). [assumption].
% 1.93/2.22 460 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom). [assumption].
% 1.93/2.22 461 -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].
% 1.93/2.22 462 -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].
% 1.93/2.22 463 -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].
% 1.93/2.22 464 -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].
% 1.93/2.22 465 -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].
% 1.93/2.22 466 -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].
% 1.93/2.22 467 -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].
% 2.02/2.29 468 -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].
% 2.02/2.29 469 -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].
% 2.02/2.29 470 -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].
% 2.02/2.29 471 -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].
% 2.02/2.29 472 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom). [assumption].
% 2.02/2.29 473 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom). [assumption].
% 2.02/2.29 474 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom). [assumption].
% 2.02/2.29 475 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom). [assumption].
% 2.02/2.29 476 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom). [assumption].
% 2.02/2.29 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(472,a,476,b)].
% 2.02/2.29 477 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom). [assumption].
% 2.02/2.29 Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(477,a,476,b)].
% 2.02/2.29 478 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom). [assumption].
% 2.02/2.29 479 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_24) # label(axiom). [assumption].
% 2.02/2.29 480 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_15) # label(axiom). [assumption].
% 2.02/2.29 481 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) # label(axiom). [assumption].
% 2.02/2.29 482 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom). [assumption].
% 2.02/2.29 483 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom). [assumption].
% 2.02/2.29 484 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom). [assumption].
% 2.02/2.29 485 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom). [assumption].
% 2.02/2.29 486 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom). [assumption].
% 2.02/2.29 487 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom). [assumption].
% 2.02/2.29 488 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom). [assumption].
% 2.02/2.29 489 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_9) # label(axiom). [assumption].
% 2.02/2.29 490 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom). [assumption].
% 2.02/2.29 491 class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_24) # label(axiom). [assumption].
% 2.02/2.29 492 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat_24) # label(axiom). [assumption].
% 2.06/2.32 493 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom). [assumption].
% 2.06/2.32 494 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_2) # label(axiom). [assumption].
% 2.06/2.32 495 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_3) # label(axiom). [assumption].
% 2.06/2.32 496 -class_Power_Orecpower(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Power_Orecpower_16) # label(axiom). [assumption].
% 2.06/2.32 497 -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].
% 2.06/2.32 498 -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].
% 2.06/2.32 499 -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].
% 2.06/2.32 500 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_8) # label(axiom). [assumption].
% 2.06/2.32 501 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom). [assumption].
% 2.06/2.32 502 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_11) # label(axiom). [assumption].
% 2.06/2.32 503 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_8) # label(axiom). [assumption].
% 2.06/2.32 504 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_2) # label(axiom). [assumption].
% 2.06/2.32 505 class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(472,a,476,b)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(505,b,491,a)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(505,b,492,a)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(505,b,493,b)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(505,b,496,b)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(505,b,497,b)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(505,b,498,b)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(505,b,499,b)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(505,b,500,b)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(505,b,501,b)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(505,b,502,b)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(505,b,503,b)].
% 2.06/2.32 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(505,b,504,b)].
% 2.06/2.32 506 class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(477,a,476,b)].
% 2.06/2.32 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(506,b,491,a)].
% 2.06/2.32 Derived: class_HOL_Otimes(tc_nat). [resolve(506,b,492,a)].
% 2.06/2.32 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(506,b,493,b)].
% 2.06/2.32 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(506,b,496,b)].
% 2.06/2.32 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(506,b,497,b)].
% 2.06/2.32 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(506,b,498,b)].
% 2.11/2.35 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(506,b,499,b)].
% 2.11/2.35 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(506,b,500,b)].
% 2.11/2.35 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(506,b,501,b)].
% 2.11/2.35 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(506,b,502,b)].
% 2.11/2.35 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(506,b,503,b)].
% 2.11/2.35 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(506,b,504,b)].
% 2.11/2.35 507 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom). [assumption].
% 2.11/2.35 508 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom). [assumption].
% 2.11/2.35 509 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom). [assumption].
% 2.11/2.35 510 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom). [assumption].
% 2.11/2.35 511 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom). [assumption].
% 2.11/2.35 512 -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].
% 2.11/2.35 513 -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].
% 2.11/2.35 514 -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].
% 2.11/2.35 515 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom). [assumption].
% 2.11/2.35 516 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom). [assumption].
% 2.11/2.35 517 -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].
% 2.11/2.35 518 -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].
% 2.11/2.35 519 -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].
% 2.11/2.35 520 -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].
% 2.11/2.35 521 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom). [assumption].
% 2.11/2.35 522 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom). [assumption].
% 2.11/2.35 523 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_8) # label(axiom). [assumption].
% 2.11/2.35 524 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom). [assumption].
% 2.11/2.35 525 -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].
% 2.11/2.35 526 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(144,b,105,a)].
% 2.11/2.35 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(526,a,525,b)].
% 2.11/2.35 527 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(182,a,180,b)].
% 2.11/2.35 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(527,b,513,b)].
% 2.11/2.35 528 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(183,a,180,b)].
% 2.11/2.40 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(528,b,513,b)].
% 2.11/2.40 529 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_1) # label(axiom). [assumption].
% 2.11/2.40 530 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom). [assumption].
% 2.11/2.40 531 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom). [assumption].
% 2.11/2.40 532 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom). [assumption].
% 2.11/2.40 533 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom). [assumption].
% 2.11/2.40 534 -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].
% 2.11/2.40 535 -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].
% 2.11/2.40 536 -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].
% 2.11/2.40 537 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_5) # label(axiom). [assumption].
% 2.11/2.40 538 -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].
% 2.11/2.40 539 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_9) # label(axiom). [assumption].
% 2.11/2.40 540 -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].
% 2.11/2.40 541 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ofield_7) # label(axiom). [assumption].
% 2.11/2.40 542 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oidom_7) # label(axiom). [assumption].
% 2.11/2.40 543 -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].
% 2.11/2.40 544 -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].
% 2.11/2.40 545 -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].
% 2.11/2.40 546 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(38,a,48,b)].
% 2.11/2.40 547 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(67,a,48,b)].
% 2.11/2.40 548 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(69,a,48,b)].
% 2.11/2.40 549 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(70,a,48,b)].
% 2.11/2.40 550 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A). [resolve(123,b,105,a)].
% 2.11/2.40 551 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(182,a,155,b)].
% 2.11/2.40 552 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(183,a,155,b)].
% 2.11/2.40 553 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(215,b,199,b)].
% 2.11/2.40 554 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(505,b,498,b)].
% 2.11/2.40 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(554,b,530,a)].
% 2.11/2.40 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(554,b,531,a)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(554,b,532,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(554,b,533,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(554,b,534,b)].
% 2.11/2.41 555 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(506,b,498,b)].
% 2.11/2.41 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(555,b,530,a)].
% 2.11/2.41 Derived: class_HOL_Otimes(tc_nat). [resolve(555,b,531,a)].
% 2.11/2.41 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(555,b,532,b)].
% 2.11/2.41 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(555,b,533,b)].
% 2.11/2.41 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(555,b,534,b)].
% 2.11/2.41 556 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(527,b,513,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(556,b,530,a)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(556,b,531,a)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(556,b,532,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(556,b,533,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(556,b,534,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(556,b,540,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(556,b,541,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(556,b,542,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(556,b,543,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(556,b,544,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(556,b,545,b)].
% 2.11/2.41 557 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(528,b,513,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(557,b,530,a)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(557,b,531,a)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(557,b,532,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(557,b,533,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(557,b,534,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(557,b,540,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(557,b,541,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(557,b,542,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(557,b,543,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(557,b,544,b)].
% 2.11/2.41 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(557,b,545,b)].
% 2.11/2.41 558 -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].
% 2.11/2.41 559 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom). [assumption].
% 2.11/2.41 560 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom). [assumption].
% 2.11/2.41 561 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom). [assumption].
% 2.11/2.41 562 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom). [assumption].
% 2.11/2.43 563 -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].
% 2.11/2.43 564 -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].
% 2.11/2.43 565 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_9) # label(axiom). [assumption].
% 2.11/2.43 566 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_9) # label(axiom). [assumption].
% 2.11/2.43 567 -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].
% 2.11/2.43 568 -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].
% 2.11/2.43 569 -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].
% 2.11/2.43 570 -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].
% 2.11/2.43 571 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_12) # label(axiom). [assumption].
% 2.11/2.43 572 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_5) # label(axiom). [assumption].
% 2.11/2.43 573 -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].
% 2.11/2.43 574 -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].
% 2.11/2.43 575 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(74,b,69,a)].
% 2.11/2.43 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(575,a,570,b)].
% 2.11/2.43 576 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(74,b,70,a)].
% 2.11/2.43 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(576,a,570,b)].
% 2.11/2.43 577 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(182,a,181,b)].
% 2.11/2.43 578 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(183,a,181,b)].
% 2.11/2.43 579 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(293,b,292,b)].
% 2.11/2.43 580 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(526,a,525,b)].
% 2.11/2.43 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(580,b,559,a)].
% 2.11/2.43 Derived: class_HOL_Ozero(tc_nat). [resolve(580,b,560,a)].
% 2.11/2.43 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(580,b,561,b)].
% 2.11/2.43 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(580,b,562,b)].
% 2.11/2.43 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(580,b,563,b)].
% 2.11/2.43 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(580,b,564,b)].
% 2.11/2.43 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(580,b,565,b)].
% 2.11/2.43 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(580,b,566,b)].
% 2.11/2.43 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(580,b,567,b)].
% 2.11/2.43 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(580,b,568,b)].
% 2.11/2.43 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(580,b,569,b)].
% 2.11/2.43 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(580,b,570,b)].
% 2.21/2.47 581 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_11) # label(axiom). [assumption].
% 2.21/2.47 582 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom). [assumption].
% 2.21/2.47 583 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom). [assumption].
% 2.21/2.47 584 -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].
% 2.21/2.47 585 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom). [assumption].
% 2.21/2.47 586 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom). [assumption].
% 2.21/2.47 587 -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].
% 2.21/2.47 588 -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].
% 2.21/2.47 589 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom). [assumption].
% 2.21/2.47 590 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom). [assumption].
% 2.21/2.47 591 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom). [assumption].
% 2.21/2.47 592 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom). [assumption].
% 2.21/2.47 593 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(38,a,66,b)].
% 2.21/2.47 594 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(67,a,66,b)].
% 2.21/2.47 595 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(69,a,66,b)].
% 2.21/2.47 596 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(70,a,66,b)].
% 2.21/2.47 597 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(178,a,173,b)].
% 2.21/2.47 598 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(182,a,173,b)].
% 2.21/2.47 599 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(183,a,173,b)].
% 2.21/2.47 600 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(293,b,290,b)].
% 2.21/2.47 601 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(354,b,347,b)].
% 2.21/2.47 602 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(357,b,347,b)].
% 2.21/2.47 603 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(575,a,570,b)].
% 2.21/2.47 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(603,b,582,a)].
% 2.21/2.47 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(603,b,583,b)].
% 2.21/2.47 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(603,b,584,b)].
% 2.21/2.47 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(603,b,585,b)].
% 2.21/2.47 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(603,b,586,b)].
% 2.21/2.47 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(603,b,587,b)].
% 2.21/2.47 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(603,b,588,b)].
% 2.21/2.47 604 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(576,a,570,b)].
% 2.21/2.47 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(604,b,582,a)].
% 2.21/2.47 Derived: class_HOL_Otimes(A) | -class_Numeral_Onumber__ring(A). [resolve(604,b,583,b)].
% 2.21/2.47 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(604,b,584,b)].
% 2.27/2.50 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(604,b,585,b)].
% 2.27/2.50 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(604,b,586,b)].
% 2.27/2.50 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(604,b,587,b)].
% 2.27/2.50 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(604,b,588,b)].
% 2.27/2.50 605 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(580,b,570,b)].
% 2.27/2.50 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(605,b,582,a)].
% 2.27/2.50 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(605,b,583,b)].
% 2.27/2.50 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(605,b,584,b)].
% 2.27/2.50 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(605,b,585,b)].
% 2.27/2.50 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(605,b,586,b)].
% 2.27/2.50 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(605,b,587,b)].
% 2.27/2.50 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(605,b,588,b)].
% 2.27/2.50 606 -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].
% 2.27/2.50 607 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom). [assumption].
% 2.27/2.50 608 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom). [assumption].
% 2.27/2.50 609 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom). [assumption].
% 2.27/2.50 610 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom). [assumption].
% 2.27/2.50 611 -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].
% 2.27/2.50 612 -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].
% 2.27/2.50 613 -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].
% 2.27/2.50 614 -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].
% 2.27/2.50 615 -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].
% 2.27/2.50 616 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) # label(axiom). [assumption].
% 2.27/2.50 617 -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].
% 2.27/2.50 618 -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].
% 2.27/2.50 619 -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].
% 2.27/2.50 620 -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].
% 2.27/2.50 621 -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].
% 2.27/2.50 622 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(38,a,49,b)].
% 2.27/2.50 623 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(67,a,49,b)].
% 2.27/2.55 624 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(69,a,49,b)].
% 2.27/2.55 625 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(70,a,49,b)].
% 2.27/2.55 626 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Ozero(A). [resolve(124,b,105,a)].
% 2.27/2.55 627 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(182,a,156,b)].
% 2.27/2.55 628 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(183,a,156,b)].
% 2.27/2.55 629 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(215,b,200,b)].
% 2.27/2.55 630 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(293,b,275,b)].
% 2.27/2.55 631 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(354,b,332,b)].
% 2.27/2.55 632 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(357,b,332,b)].
% 2.27/2.55 633 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(505,b,499,b)].
% 2.27/2.55 634 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(506,b,499,b)].
% 2.27/2.55 635 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(556,b,540,b)].
% 2.27/2.55 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(635,b,607,a)].
% 2.27/2.55 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(635,b,608,a)].
% 2.27/2.55 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(635,b,609,b)].
% 2.27/2.55 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(635,b,610,b)].
% 2.27/2.55 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(635,b,611,b)].
% 2.27/2.55 636 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(557,b,540,b)].
% 2.27/2.55 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(636,b,607,a)].
% 2.27/2.55 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(636,b,608,a)].
% 2.27/2.55 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(636,b,609,b)].
% 2.27/2.55 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(636,b,610,b)].
% 2.27/2.55 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(636,b,611,b)].
% 2.27/2.55 637 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1__cancel(A). [resolve(580,b,564,b)].
% 2.27/2.55 Derived: class_HOL_Ozero(tc_nat). [resolve(637,b,608,a)].
% 2.27/2.55 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(637,b,610,b)].
% 2.27/2.55 638 -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].
% 2.27/2.55 639 class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_30) # label(axiom). [assumption].
% 2.27/2.55 640 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom). [assumption].
% 2.27/2.55 641 -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_14) # label(axiom). [assumption].
% 2.27/2.55 642 -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].
% 2.27/2.55 643 -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].
% 2.27/2.55 644 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_7) # label(axiom). [assumption].
% 2.27/2.55 645 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Ofield_0) # label(axiom). [assumption].
% 2.27/2.55 646 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oidom_0) # label(axiom). [assumption].
% 2.33/2.58 647 -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].
% 2.33/2.58 648 -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].
% 2.33/2.58 649 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(38,a,44,b)].
% 2.33/2.58 650 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(67,a,44,b)].
% 2.33/2.58 651 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(69,a,44,b)].
% 2.33/2.58 652 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(84,a,81,b)].
% 2.33/2.58 653 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(100,b,81,b)].
% 2.33/2.58 654 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(101,b,81,b)].
% 2.33/2.58 655 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(103,b,81,b)].
% 2.33/2.58 656 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(178,a,152,b)].
% 2.33/2.58 657 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(182,a,152,b)].
% 2.33/2.58 658 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(183,a,152,b)].
% 2.33/2.58 659 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(215,b,191,b)].
% 2.33/2.58 660 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(216,b,191,b)].
% 2.33/2.58 661 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(217,b,191,b)].
% 2.33/2.58 662 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(293,b,273,b)].
% 2.33/2.58 663 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(357,b,330,b)].
% 2.33/2.58 664 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(389,b,363,b)].
% 2.33/2.58 665 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(390,b,363,b)].
% 2.33/2.58 666 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(418,b,398,b)].
% 2.33/2.58 667 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(505,b,497,b)].
% 2.33/2.58 668 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(554,b,534,b)].
% 2.33/2.58 669 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(556,b,534,b)].
% 2.33/2.58 670 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(557,b,534,b)].
% 2.33/2.58 671 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(580,b,563,b)].
% 2.33/2.58 672 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(603,b,584,b)].
% 2.33/2.58 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(672,b,639,a)].
% 2.33/2.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(672,b,640,b)].
% 2.33/2.58 673 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(605,b,584,b)].
% 2.33/2.58 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(673,b,639,a)].
% 2.33/2.58 Derived: class_HOL_Ozero(A) | -class_Numeral_Onumber__ring(A). [resolve(673,b,640,b)].
% 2.33/2.58 674 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(635,b,611,b)].
% 2.33/2.58 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(674,b,639,a)].
% 2.33/2.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(674,b,640,b)].
% 2.33/2.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(674,b,645,b)].
% 2.33/2.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(674,b,646,b)].
% 2.33/2.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(674,b,647,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(674,b,648,b)].
% 2.33/2.59 675 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring__1(A). [resolve(636,b,611,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(675,b,639,a)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(675,b,640,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(675,b,645,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(675,b,646,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(675,b,647,b)].
% 2.33/2.59 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(675,b,648,b)].
% 2.33/2.59 676 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom). [assumption].
% 2.33/2.59 677 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom). [assumption].
% 2.33/2.59 678 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom). [assumption].
% 2.33/2.59 679 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom). [assumption].
% 2.33/2.59 680 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom). [assumption].
% 2.33/2.59 681 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom). [assumption].
% 2.33/2.59 682 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom). [assumption].
% 2.33/2.59 683 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom). [assumption].
% 2.33/2.59 684 -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].
% 2.33/2.59 685 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom). [assumption].
% 2.33/2.59 686 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom). [assumption].
% 2.33/2.59 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(686,b,676,a)].
% 2.33/2.59 687 -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].
% 2.33/2.59 688 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom). [assumption].
% 2.33/2.59 689 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom). [assumption].
% 2.33/2.59 690 -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].
% 2.33/2.59 691 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom). [assumption].
% 2.33/2.59 692 -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].
% 2.33/2.59 693 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom). [assumption].
% 2.33/2.59 694 -class_LOrder_Omeet__semilorder(A) | c_lessequals(B,B,A). [resolve(7,b,2,a)].
% 2.38/2.60 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(694,a,677,a)].
% 2.38/2.60 Derived: c_lessequals(A,A,tc_nat). [resolve(694,a,678,a)].
% 2.38/2.60 Derived: c_lessequals(A,A,B) | -class_LOrder_Olorder(B). [resolve(694,a,679,b)].
% 2.38/2.60 695 class_Orderings_Oord(A) | -class_LOrder_Omeet__semilorder(A). [resolve(18,a,7,b)].
% 2.38/2.60 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(695,b,677,a)].
% 2.38/2.60 Derived: class_Orderings_Oord(tc_nat). [resolve(695,b,678,a)].
% 2.38/2.60 Derived: class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(695,b,679,b)].
% 2.38/2.60 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(695,b,687,b)].
% 2.38/2.60 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(695,b,688,b)].
% 2.38/2.60 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(695,b,689,b)].
% 2.38/2.60 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(695,b,690,b)].
% 2.38/2.60 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(695,b,691,b)].
% 2.38/2.60 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(695,b,692,b)].
% 2.38/2.60 696 -c_less(A,A,B) | -class_LOrder_Omeet__semilorder(B). [resolve(33,a,7,b)].
% 2.38/2.60 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(696,b,677,a)].
% 2.38/2.60 Derived: -c_less(A,A,tc_nat). [resolve(696,b,678,a)].
% 2.38/2.60 Derived: -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(696,b,679,b)].
% 2.38/2.60 697 -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(34,a,7,b)].
% 2.38/2.60 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(697,c,677,a)].
% 2.38/2.60 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(697,c,678,a)].
% 2.38/2.60 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(697,c,679,b)].
% 2.38/2.60 698 -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(35,a,7,b)].
% 2.38/2.60 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(698,c,677,a)].
% 2.38/2.60 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(698,c,678,a)].
% 2.38/2.60 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(698,c,679,b)].
% 2.38/2.60 699 -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(36,a,7,b)].
% 2.38/2.60 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(699,c,677,a)].
% 2.38/2.60 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(699,c,678,a)].
% 2.38/2.60 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(699,c,679,b)].
% 2.38/2.60 700 -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(37,a,7,b)].
% 2.38/2.60 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(700,c,677,a)].
% 2.38/2.60 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(700,c,678,a)].
% 2.38/2.60 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(700,c,679,b)].
% 2.42/2.65 701 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom). [assumption].
% 2.42/2.65 702 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom). [assumption].
% 2.42/2.65 703 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom). [assumption].
% 2.42/2.65 704 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom). [assumption].
% 2.42/2.65 705 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom). [assumption].
% 2.42/2.65 706 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom). [assumption].
% 2.42/2.65 707 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom). [assumption].
% 2.42/2.65 708 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom). [assumption].
% 2.42/2.65 709 -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].
% 2.42/2.65 710 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom). [assumption].
% 2.42/2.65 711 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom). [assumption].
% 2.42/2.65 712 -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].
% 2.42/2.65 713 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom). [assumption].
% 2.42/2.65 714 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 2.42/2.65 715 -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].
% 2.42/2.65 716 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom). [assumption].
% 2.42/2.65 717 -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].
% 2.42/2.65 718 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom). [assumption].
% 2.42/2.65 719 -class_LOrder_Ojoin__semilorder(A) | c_lessequals(B,B,A). [resolve(5,b,2,a)].
% 2.42/2.65 720 class_Orderings_Oord(A) | -class_LOrder_Ojoin__semilorder(A). [resolve(18,a,5,b)].
% 2.42/2.65 721 -c_less(A,A,B) | -class_LOrder_Ojoin__semilorder(B). [resolve(33,a,5,b)].
% 2.42/2.65 722 -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(34,a,5,b)].
% 2.42/2.65 723 -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(35,a,5,b)].
% 2.42/2.65 724 -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(36,a,5,b)].
% 2.42/2.65 725 -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(37,a,5,b)].
% 2.42/2.65 726 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom). [assumption].
% 2.42/2.65 727 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom). [assumption].
% 2.42/2.67 728 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom). [assumption].
% 2.42/2.67 729 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom). [assumption].
% 2.42/2.67 730 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom). [assumption].
% 2.42/2.67 731 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom). [assumption].
% 2.42/2.67 732 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom). [assumption].
% 2.42/2.67 733 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) # label(axiom). [assumption].
% 2.42/2.67 734 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom). [assumption].
% 2.42/2.67 735 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom). [assumption].
% 2.42/2.67 736 -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].
% 2.42/2.67 737 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom). [assumption].
% 2.42/2.67 738 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom). [assumption].
% 2.42/2.67 739 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_18) # label(axiom). [assumption].
% 2.42/2.67 740 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom). [assumption].
% 2.42/2.67 741 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_11) # label(axiom). [assumption].
% 2.42/2.67 742 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom). [assumption].
% 2.42/2.67 743 -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(6,b,2,a)].
% 2.42/2.67 744 class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(18,a,6,b)].
% 2.42/2.67 745 -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(33,a,6,b)].
% 2.42/2.67 746 -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(34,a,6,b)].
% 2.42/2.67 747 -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(35,a,6,b)].
% 2.42/2.67 748 -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(36,a,6,b)].
% 2.42/2.67 749 -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(37,a,6,b)].
% 2.42/2.67 750 c_lessequals(A,A,B) | -class_LOrder_Olorder(B). [resolve(694,a,679,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(750,b,727,a)].
% 2.42/2.67 Derived: c_lessequals(A,A,tc_nat). [resolve(750,b,728,a)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(750,b,729,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(750,b,730,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(750,b,731,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(750,b,732,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(750,b,733,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_Orderings_Olinorder(B). [resolve(750,b,734,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(750,b,735,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(750,b,736,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(750,b,737,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(750,b,738,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(750,b,739,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(750,b,740,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(750,b,741,b)].
% 2.42/2.67 Derived: c_lessequals(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(750,b,742,b)].
% 2.42/2.67 751 class_Orderings_Oord(A) | -class_LOrder_Olorder(A). [resolve(695,b,679,b)].
% 2.42/2.67 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(751,b,727,a)].
% 2.42/2.67 Derived: class_Orderings_Oord(tc_nat). [resolve(751,b,728,a)].
% 2.42/2.67 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(751,b,729,b)].
% 2.42/2.67 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(751,b,730,b)].
% 2.42/2.67 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(751,b,731,b)].
% 2.42/2.67 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(751,b,732,b)].
% 2.42/2.67 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(751,b,733,b)].
% 2.42/2.67 Derived: class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(751,b,734,b)].
% 2.42/2.67 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(751,b,735,b)].
% 2.42/2.67 Derived: class_Orderings_Oord(A) | -class_Wellfounded__Recursion_Owellorder(A). [resolve(751,b,742,b)].
% 2.42/2.67 752 -c_less(A,A,B) | -class_LOrder_Olorder(B). [resolve(696,b,679,b)].
% 2.42/2.67 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(752,b,727,a)].
% 2.42/2.67 Derived: -c_less(A,A,tc_nat). [resolve(752,b,728,a)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(752,b,729,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(752,b,730,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(752,b,731,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(752,b,732,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(752,b,733,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(752,b,734,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(752,b,735,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(752,b,736,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(752,b,737,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(752,b,738,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(752,b,739,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(752,b,740,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(752,b,741,b)].
% 2.42/2.67 Derived: -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(752,b,742,b)].
% 2.42/2.67 753 -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(697,c,679,b)].
% 2.42/2.67 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(753,c,727,a)].
% 2.42/2.67 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(753,c,728,a)].
% 2.42/2.67 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(753,c,729,b)].
% 2.42/2.67 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(753,c,730,b)].
% 2.42/2.67 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(753,c,731,b)].
% 2.42/2.67 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(753,c,732,b)].
% 2.42/2.67 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(753,c,733,b)].
% 2.42/2.67 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(753,c,734,b)].
% 2.42/2.67 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(753,c,735,b)].
% 2.42/2.67 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(753,c,736,b)].
% 2.42/2.67 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(753,c,737,b)].
% 2.42/2.67 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(753,c,738,b)].
% 2.42/2.67 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(753,c,739,b)].
% 2.42/2.67 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(753,c,740,b)].
% 2.42/2.67 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(753,c,741,b)].
% 2.42/2.67 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(753,c,742,b)].
% 2.42/2.67 754 -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(698,c,679,b)].
% 2.42/2.67 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(754,c,727,a)].
% 2.42/2.67 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(754,c,728,a)].
% 2.42/2.67 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(754,c,729,b)].
% 2.42/2.67 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(754,c,730,b)].
% 2.42/2.67 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(754,c,731,b)].
% 2.42/2.67 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(754,c,732,b)].
% 2.42/2.67 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(754,c,733,b)].
% 2.42/2.67 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(754,c,734,b)].
% 2.42/2.67 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(754,c,735,b)].
% 2.42/2.67 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(754,c,736,b)].
% 2.42/2.67 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(754,c,737,b)].
% 2.42/2.67 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(754,c,738,b)].
% 2.42/2.67 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(754,c,739,b)].
% 2.42/2.67 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(754,c,740,b)].
% 2.42/2.67 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(754,c,741,b)].
% 2.42/2.67 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(754,c,742,b)].
% 2.42/2.67 755 -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(699,c,679,b)].
% 2.42/2.67 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(755,c,727,a)].
% 2.42/2.67 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(755,c,728,a)].
% 2.42/2.67 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(755,c,729,b)].
% 2.42/2.67 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(755,c,730,b)].
% 2.42/2.67 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(755,c,731,b)].
% 2.42/2.67 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(755,c,732,b)].
% 2.42/2.67 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(755,c,733,b)].
% 2.42/2.67 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(755,c,734,b)].
% 2.42/2.67 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(755,c,735,b)].
% 2.42/2.67 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(755,c,736,b)].
% 2.42/2.67 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(755,c,737,b)].
% 2.42/2.67 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(755,c,738,b)].
% 2.42/2.67 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(755,c,739,b)].
% 2.42/2.68 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(755,c,740,b)].
% 2.42/2.68 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(755,c,741,b)].
% 2.42/2.68 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(755,c,742,b)].
% 2.42/2.68 756 -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(700,c,679,b)].
% 2.42/2.68 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(756,c,727,a)].
% 2.42/2.68 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(756,c,728,a)].
% 2.42/2.68 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(756,c,729,b)].
% 2.42/2.68 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(756,c,730,b)].
% 2.42/2.68 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(756,c,731,b)].
% 2.42/2.68 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(756,c,732,b)].
% 2.42/2.68 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(756,c,733,b)].
% 2.42/2.68 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(756,c,734,b)].
% 2.42/2.68 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(756,c,735,b)].
% 2.42/2.68 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(756,c,736,b)].
% 2.42/2.68 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(756,c,737,b)].
% 2.42/2.68 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(756,c,738,b)].
% 2.42/2.68 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(756,c,739,b)].
% 2.42/2.68 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(756,c,740,b)].
% 2.42/2.68 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(756,c,741,b)].
% 2.42/2.68 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(756,c,742,b)].
% 2.42/2.68 757 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom). [assumption].
% 2.42/2.68 758 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom). [assumption].
% 2.42/2.68 759 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom). [assumption].
% 2.42/2.68 760 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Olinorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) # label(axiom). [assumption].
% 2.42/2.69 761 -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].
% 2.42/2.69 762 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom). [assumption].
% 2.42/2.69 763 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 2.42/2.69 764 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_17) # label(axiom). [assumption].
% 2.42/2.69 765 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom). [assumption].
% 2.42/2.69 766 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_10) # label(axiom). [assumption].
% 2.42/2.69 767 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom). [assumption].
% 2.42/2.69 768 -class_Orderings_Olinorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C # label(cls_SetInterval_OatLeast__eq__iff__iff1_0) # label(axiom). [assumption].
% 2.42/2.69 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(768,a,758,a)].
% 2.42/2.69 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(768,a,759,a)].
% 2.42/2.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(768,a,760,b)].
% 2.42/2.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(768,a,761,b)].
% 2.42/2.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(768,a,762,b)].
% 2.42/2.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(768,a,763,b)].
% 2.42/2.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(768,a,764,b)].
% 2.42/2.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(768,a,765,b)].
% 2.42/2.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(768,a,766,b)].
% 2.42/2.69 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(768,a,767,b)].
% 2.42/2.69 769 -class_Orderings_Olinorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C # label(cls_SetInterval_OatMost__eq__iff__iff1_0) # label(axiom). [assumption].
% 2.42/2.69 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(769,a,758,a)].
% 2.42/2.69 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(769,a,759,a)].
% 2.42/2.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(769,a,760,b)].
% 2.42/2.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(769,a,761,b)].
% 2.42/2.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(769,a,762,b)].
% 2.42/2.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(769,a,763,b)].
% 2.42/2.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(769,a,764,b)].
% 2.42/2.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(769,a,765,b)].
% 2.42/2.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(769,a,766,b)].
% 2.42/2.69 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(769,a,767,b)].
% 2.42/2.69 770 -class_Orderings_Olinorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C # label(cls_SetInterval_OgreaterThan__eq__iff__iff1_0) # label(axiom). [assumption].
% 2.42/2.69 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(770,a,758,a)].
% 2.42/2.69 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(770,a,759,a)].
% 2.42/2.69 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(770,a,760,b)].
% 2.42/2.69 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(770,a,761,b)].
% 2.42/2.69 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(770,a,762,b)].
% 2.42/2.69 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(770,a,763,b)].
% 2.42/2.69 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(770,a,764,b)].
% 2.42/2.69 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(770,a,765,b)].
% 2.42/2.69 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(770,a,766,b)].
% 2.42/2.69 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(770,a,767,b)].
% 2.42/2.69 771 -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__iff1_0) # label(axiom). [assumption].
% 2.42/2.69 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(771,a,758,a)].
% 2.42/2.69 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(771,a,759,a)].
% 2.42/2.69 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(771,a,760,b)].
% 2.42/2.69 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(771,a,761,b)].
% 2.42/2.69 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(771,a,762,b)].
% 2.42/2.69 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(771,a,763,b)].
% 2.42/2.69 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(771,a,764,b)].
% 2.42/2.69 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(771,a,765,b)].
% 2.42/2.69 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(771,a,766,b)].
% 2.42/2.69 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(771,a,767,b)].
% 2.42/2.69 772 -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__iff2_0) # label(axiom). [assumption].
% 2.42/2.69 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(772,a,758,a)].
% 2.42/2.69 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(772,a,759,a)].
% 2.42/2.69 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(772,a,760,b)].
% 2.42/2.69 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(772,a,761,b)].
% 2.42/2.69 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(772,a,762,b)].
% 2.42/2.69 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(772,a,763,b)].
% 2.42/2.69 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(772,a,764,b)].
% 2.42/2.69 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(772,a,765,b)].
% 2.42/2.69 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(772,a,766,b)].
% 2.42/2.69 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(772,a,767,b)].
% 2.42/2.69 773 -class_Orderings_Olinorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C # label(cls_SetInterval_OlessThan__eq__iff__iff1_0) # label(axiom). [assumption].
% 2.42/2.69 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(773,a,758,a)].
% 2.42/2.69 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(773,a,759,a)].
% 2.42/2.69 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(773,a,760,b)].
% 2.42/2.69 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(773,a,761,b)].
% 2.42/2.69 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(773,a,762,b)].
% 2.42/2.69 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(773,a,763,b)].
% 2.42/2.69 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(773,a,764,b)].
% 2.42/2.69 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(773,a,765,b)].
% 2.42/2.69 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(773,a,766,b)].
% 2.42/2.69 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(773,a,767,b)].
% 2.42/2.70 774 -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__iff1_0) # label(axiom). [assumption].
% 2.42/2.70 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(774,a,758,a)].
% 2.42/2.70 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(774,a,759,a)].
% 2.42/2.70 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(774,a,760,b)].
% 2.42/2.70 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(774,a,761,b)].
% 2.42/2.70 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(774,a,762,b)].
% 2.42/2.70 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(774,a,763,b)].
% 2.42/2.70 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(774,a,764,b)].
% 2.42/2.70 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(774,a,765,b)].
% 2.42/2.70 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(774,a,766,b)].
% 2.42/2.70 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(774,a,767,b)].
% 2.42/2.70 775 -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__iff2_0) # label(axiom). [assumption].
% 2.42/2.70 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(775,a,758,a)].
% 2.42/2.70 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(775,a,759,a)].
% 2.42/2.70 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(775,a,760,b)].
% 2.42/2.70 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(775,a,761,b)].
% 2.42/2.70 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(775,a,762,b)].
% 2.42/2.70 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(775,a,763,b)].
% 2.42/2.70 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(775,a,764,b)].
% 2.42/2.70 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(775,a,765,b)].
% 2.42/2.70 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(775,a,766,b)].
% 2.42/2.72 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(775,a,767,b)].
% 2.42/2.72 776 -class_Orderings_Olinorder(A) | c_lessequals(B,B,A). [resolve(17,b,2,a)].
% 2.42/2.72 777 class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(18,a,17,b)].
% 2.42/2.72 778 -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(33,a,17,b)].
% 2.42/2.72 779 -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(34,a,17,b)].
% 2.42/2.72 780 -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(35,a,17,b)].
% 2.42/2.72 781 -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(36,a,17,b)].
% 2.42/2.72 782 -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(37,a,17,b)].
% 2.42/2.72 783 c_lessequals(A,A,B) | -class_Orderings_Olinorder(B). [resolve(750,b,734,b)].
% 2.42/2.72 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(783,b,758,a)].
% 2.42/2.72 Derived: c_lessequals(A,A,tc_nat). [resolve(783,b,759,a)].
% 2.42/2.72 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(783,b,760,b)].
% 2.42/2.72 784 class_Orderings_Oord(A) | -class_Orderings_Olinorder(A). [resolve(751,b,734,b)].
% 2.42/2.72 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(784,b,758,a)].
% 2.42/2.72 Derived: class_Orderings_Oord(tc_nat). [resolve(784,b,759,a)].
% 2.42/2.72 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(784,b,760,b)].
% 2.42/2.72 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(784,b,761,b)].
% 2.42/2.72 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(784,b,762,b)].
% 2.42/2.72 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(784,b,763,b)].
% 2.42/2.72 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(784,b,764,b)].
% 2.42/2.72 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(784,b,765,b)].
% 2.42/2.72 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(784,b,766,b)].
% 2.42/2.72 785 -c_less(A,A,B) | -class_Orderings_Olinorder(B). [resolve(752,b,734,b)].
% 2.42/2.72 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(785,b,758,a)].
% 2.42/2.72 Derived: -c_less(A,A,tc_nat). [resolve(785,b,759,a)].
% 2.42/2.72 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(785,b,760,b)].
% 2.42/2.72 786 -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(753,c,734,b)].
% 2.42/2.72 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(786,c,758,a)].
% 2.42/2.72 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(786,c,759,a)].
% 2.42/2.72 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(786,c,760,b)].
% 2.42/2.72 787 -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(754,c,734,b)].
% 2.42/2.72 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(787,c,758,a)].
% 2.42/2.72 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(787,c,759,a)].
% 2.42/2.72 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(787,c,760,b)].
% 2.52/2.74 788 -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(755,c,734,b)].
% 2.52/2.74 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(788,c,758,a)].
% 2.52/2.74 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(788,c,759,a)].
% 2.52/2.74 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(788,c,760,b)].
% 2.52/2.74 789 -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(756,c,734,b)].
% 2.52/2.74 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(789,c,758,a)].
% 2.52/2.74 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(789,c,759,a)].
% 2.52/2.74 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(789,c,760,b)].
% 2.52/2.74 790 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom). [assumption].
% 2.52/2.74 791 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom). [assumption].
% 2.52/2.74 792 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom). [assumption].
% 2.52/2.74 793 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom). [assumption].
% 2.52/2.74 794 -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].
% 2.52/2.74 795 -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].
% 2.52/2.74 796 -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].
% 2.52/2.74 797 -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].
% 2.52/2.74 798 -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].
% 2.52/2.74 799 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) # label(axiom). [assumption].
% 2.52/2.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(799,a,797,b)].
% 2.52/2.74 800 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom). [assumption].
% 2.52/2.74 801 -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].
% 2.52/2.74 802 -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].
% 2.52/2.74 803 -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].
% 2.52/2.75 804 -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].
% 2.52/2.75 805 -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].
% 2.52/2.75 806 -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].
% 2.52/2.75 807 -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].
% 2.52/2.75 808 -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].
% 2.52/2.75 809 -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].
% 2.52/2.75 810 -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].
% 2.52/2.75 811 -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].
% 2.52/2.75 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A). [resolve(811,b,790,a)].
% 2.52/2.75 812 -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].
% 2.52/2.75 813 -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].
% 2.52/2.75 814 -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].
% 2.52/2.75 815 -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].
% 2.52/2.75 Derived: -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A). [resolve(815,b,790,a)].
% 2.52/2.75 816 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(14,b,2,a)].
% 2.52/2.75 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(816,a,798,b)].
% 2.52/2.75 817 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(18,a,14,b)].
% 2.52/2.75 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(817,b,798,b)].
% 2.52/2.75 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(817,b,810,b)].
% 2.52/2.75 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(817,b,812,b)].
% 2.52/2.75 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(817,b,813,b)].
% 2.52/2.75 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(817,b,814,b)].
% 2.52/2.75 818 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add(B). [resolve(33,a,14,b)].
% 2.52/2.75 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(818,b,798,b)].
% 2.52/2.75 819 -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(34,a,14,b)].
% 2.52/2.75 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(819,c,798,b)].
% 2.52/2.78 820 -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(35,a,14,b)].
% 2.52/2.78 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(820,c,798,b)].
% 2.52/2.78 821 -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(36,a,14,b)].
% 2.52/2.78 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(821,c,798,b)].
% 2.52/2.78 822 -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(37,a,14,b)].
% 2.52/2.78 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(822,c,798,b)].
% 2.52/2.78 823 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 2.52/2.78 824 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom). [assumption].
% 2.52/2.78 825 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom). [assumption].
% 2.52/2.78 826 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_6) # label(axiom). [assumption].
% 2.52/2.78 827 -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].
% 2.52/2.78 828 -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].
% 2.52/2.78 829 -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].
% 2.52/2.78 830 -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].
% 2.52/2.78 831 -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].
% 2.52/2.78 832 -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].
% 2.52/2.78 833 -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].
% 2.52/2.78 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(833,a,832,b)].
% 2.52/2.78 834 -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].
% 2.52/2.78 835 -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].
% 2.52/2.78 836 -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].
% 2.52/2.80 837 -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].
% 2.52/2.80 838 -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].
% 2.52/2.80 839 -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].
% 2.52/2.80 840 -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].
% 2.52/2.80 841 -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].
% 2.52/2.80 842 -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].
% 2.52/2.80 843 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(16,b,2,a)].
% 2.52/2.80 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(843,a,832,b)].
% 2.52/2.80 844 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(18,a,16,b)].
% 2.52/2.80 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(844,b,832,b)].
% 2.52/2.80 845 -c_less(A,A,B) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(B). [resolve(33,a,16,b)].
% 2.52/2.80 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(845,b,832,b)].
% 2.52/2.80 846 -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(34,a,16,b)].
% 2.52/2.80 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(846,c,832,b)].
% 2.52/2.80 847 -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(35,a,16,b)].
% 2.52/2.80 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(847,c,832,b)].
% 2.52/2.80 848 -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(36,a,16,b)].
% 2.52/2.80 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(848,c,832,b)].
% 2.52/2.80 849 -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(37,a,16,b)].
% 2.52/2.80 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(849,c,832,b)].
% 2.52/2.80 850 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(233,b,219,a)].
% 2.52/2.80 851 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(270,b,256,a)].
% 2.52/2.80 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(851,a,826,b)].
% 2.52/2.80 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(851,a,827,b)].
% 2.52/2.80 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(851,a,828,b)].
% 2.59/2.83 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(851,a,829,b)].
% 2.59/2.83 852 -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].
% 2.59/2.83 853 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom). [assumption].
% 2.59/2.83 854 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom). [assumption].
% 2.59/2.83 855 -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].
% 2.59/2.83 856 -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].
% 2.59/2.83 857 -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].
% 2.59/2.83 858 -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].
% 2.59/2.83 859 -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].
% 2.59/2.83 860 -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].
% 2.59/2.83 861 -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].
% 2.59/2.83 862 -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].
% 2.59/2.83 863 -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].
% 2.59/2.83 864 -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].
% 2.59/2.83 865 -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].
% 2.59/2.83 866 -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].
% 2.59/2.83 867 -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].
% 2.59/2.83 868 -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].
% 2.59/2.83 869 -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].
% 2.59/2.83 870 -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].
% 2.59/2.83 871 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,B,A). [resolve(15,b,2,a)].
% 2.59/2.83 872 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(18,a,15,b)].
% 2.59/2.85 873 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(33,a,15,b)].
% 2.59/2.85 874 -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(34,a,15,b)].
% 2.59/2.85 875 -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(35,a,15,b)].
% 2.59/2.85 876 -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(36,a,15,b)].
% 2.59/2.85 877 -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(37,a,15,b)].
% 2.59/2.85 878 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(293,b,269,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(878,b,855,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(878,b,856,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(878,b,857,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(878,b,858,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(878,b,859,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(878,b,860,b)].
% 2.59/2.85 879 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(833,a,832,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(879,b,853,a)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(879,b,854,a)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(879,b,859,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(879,b,860,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(879,b,863,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(879,b,864,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(879,b,865,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(879,b,866,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(879,b,867,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(879,b,868,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(879,b,869,b)].
% 2.59/2.85 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(879,b,870,b)].
% 2.59/2.85 880 c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(843,a,832,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(880,b,853,a)].
% 2.59/2.85 Derived: c_lessequals(A,A,tc_nat). [resolve(880,b,854,a)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(880,b,855,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(880,b,856,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(880,b,857,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(880,b,858,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(880,b,859,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(880,b,860,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(880,b,863,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(880,b,864,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(880,b,865,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(880,b,866,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(880,b,867,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(880,b,868,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(880,b,869,b)].
% 2.59/2.85 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(880,b,870,b)].
% 2.59/2.85 881 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(844,b,832,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(881,b,853,a)].
% 2.59/2.85 Derived: class_Orderings_Oord(tc_nat). [resolve(881,b,854,a)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(881,b,855,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(881,b,856,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(881,b,857,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(881,b,858,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(881,b,859,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(881,b,860,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(881,b,863,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(881,b,864,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(881,b,865,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(881,b,866,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(881,b,867,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(881,b,868,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(881,b,869,b)].
% 2.59/2.85 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(881,b,870,b)].
% 2.59/2.85 882 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(B). [resolve(845,b,832,b)].
% 2.59/2.85 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(882,b,853,a)].
% 2.59/2.85 Derived: -c_less(A,A,tc_nat). [resolve(882,b,854,a)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(882,b,855,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(882,b,856,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(882,b,857,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(882,b,858,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(882,b,859,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(882,b,860,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(882,b,863,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(882,b,864,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(882,b,865,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(882,b,866,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(882,b,867,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(882,b,868,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(882,b,869,b)].
% 2.59/2.85 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(882,b,870,b)].
% 2.59/2.85 883 -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(846,c,832,b)].
% 2.59/2.85 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(883,c,853,a)].
% 2.59/2.85 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(883,c,854,a)].
% 2.59/2.85 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(883,c,855,b)].
% 2.59/2.85 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(883,c,856,b)].
% 2.59/2.85 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(883,c,857,b)].
% 2.59/2.85 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(883,c,858,b)].
% 2.59/2.85 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(883,c,859,b)].
% 2.59/2.85 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(883,c,860,b)].
% 2.59/2.85 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(883,c,863,b)].
% 2.59/2.85 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(883,c,864,b)].
% 2.59/2.85 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(883,c,865,b)].
% 2.59/2.85 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(883,c,866,b)].
% 2.59/2.85 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(883,c,867,b)].
% 2.59/2.85 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(883,c,868,b)].
% 2.59/2.85 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(883,c,869,b)].
% 2.59/2.85 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(883,c,870,b)].
% 2.59/2.85 884 -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(847,c,832,b)].
% 2.59/2.85 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(884,c,853,a)].
% 2.59/2.85 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(884,c,854,a)].
% 2.59/2.85 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(884,c,855,b)].
% 2.59/2.85 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(884,c,856,b)].
% 2.59/2.85 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(884,c,857,b)].
% 2.59/2.85 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(884,c,858,b)].
% 2.59/2.85 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(884,c,859,b)].
% 2.59/2.85 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(884,c,860,b)].
% 2.59/2.85 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(884,c,863,b)].
% 2.59/2.85 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(884,c,864,b)].
% 2.59/2.85 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(884,c,865,b)].
% 2.59/2.85 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(884,c,866,b)].
% 2.59/2.85 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(884,c,867,b)].
% 2.59/2.85 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(884,c,868,b)].
% 2.59/2.85 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(884,c,869,b)].
% 2.59/2.85 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(884,c,870,b)].
% 2.59/2.85 885 -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(848,c,832,b)].
% 2.59/2.85 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(885,c,853,a)].
% 2.59/2.85 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(885,c,854,a)].
% 2.59/2.85 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(885,c,855,b)].
% 2.59/2.85 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(885,c,856,b)].
% 2.59/2.85 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(885,c,857,b)].
% 2.59/2.85 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(885,c,858,b)].
% 2.59/2.85 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(885,c,859,b)].
% 2.59/2.86 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(885,c,860,b)].
% 2.59/2.86 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(885,c,863,b)].
% 2.59/2.86 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(885,c,864,b)].
% 2.59/2.86 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(885,c,865,b)].
% 2.59/2.86 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(885,c,866,b)].
% 2.59/2.86 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(885,c,867,b)].
% 2.59/2.86 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(885,c,868,b)].
% 2.59/2.86 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(885,c,869,b)].
% 2.59/2.86 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(885,c,870,b)].
% 2.59/2.86 886 -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(849,c,832,b)].
% 2.59/2.86 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(886,c,853,a)].
% 2.59/2.86 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(886,c,854,a)].
% 2.59/2.86 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(886,c,855,b)].
% 2.59/2.86 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(886,c,856,b)].
% 2.59/2.86 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(886,c,857,b)].
% 2.59/2.86 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(886,c,858,b)].
% 2.59/2.86 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(886,c,859,b)].
% 2.59/2.86 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(886,c,860,b)].
% 2.59/2.86 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(886,c,863,b)].
% 2.59/2.86 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(886,c,864,b)].
% 2.59/2.86 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(886,c,865,b)].
% 2.59/2.86 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(886,c,866,b)].
% 2.59/2.86 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(886,c,867,b)].
% 2.65/2.89 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(886,c,868,b)].
% 2.65/2.89 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(886,c,869,b)].
% 2.65/2.89 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(886,c,870,b)].
% 2.65/2.89 887 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 2.65/2.89 888 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom). [assumption].
% 2.65/2.89 889 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom). [assumption].
% 2.65/2.89 890 -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].
% 2.65/2.89 891 -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].
% 2.65/2.89 892 -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].
% 2.65/2.89 893 -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].
% 2.65/2.89 894 -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].
% 2.65/2.89 895 -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].
% 2.65/2.89 896 -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].
% 2.65/2.89 897 -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].
% 2.65/2.89 898 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(12,b,2,a)].
% 2.65/2.89 899 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(18,a,12,b)].
% 2.65/2.89 900 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(33,a,12,b)].
% 2.65/2.89 901 -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(34,a,12,b)].
% 2.65/2.89 902 -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(35,a,12,b)].
% 2.65/2.89 903 -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(36,a,12,b)].
% 2.65/2.89 904 -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(37,a,12,b)].
% 2.65/2.89 905 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(293,b,267,b)].
% 2.65/2.89 906 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(750,b,733,b)].
% 2.65/2.90 907 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(751,b,733,b)].
% 2.65/2.90 908 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(752,b,733,b)].
% 2.65/2.90 909 -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(753,c,733,b)].
% 2.65/2.90 910 -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(754,c,733,b)].
% 2.65/2.90 911 -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(755,c,733,b)].
% 2.65/2.90 912 -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(756,c,733,b)].
% 2.65/2.90 913 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(768,a,760,b)].
% 2.65/2.90 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(913,c,888,a)].
% 2.65/2.90 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(913,c,889,a)].
% 2.65/2.90 914 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(769,a,760,b)].
% 2.65/2.90 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(914,c,888,a)].
% 2.65/2.90 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(914,c,889,a)].
% 2.65/2.90 915 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(770,a,760,b)].
% 2.65/2.90 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(915,c,888,a)].
% 2.65/2.90 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(915,c,889,a)].
% 2.65/2.90 916 -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(771,a,760,b)].
% 2.65/2.90 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(916,c,888,a)].
% 2.65/2.90 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(916,c,889,a)].
% 2.65/2.90 917 -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(772,a,760,b)].
% 2.65/2.90 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(917,c,888,a)].
% 2.65/2.90 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(917,c,889,a)].
% 2.65/2.90 918 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(773,a,760,b)].
% 2.65/2.90 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(918,c,888,a)].
% 2.65/2.90 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(918,c,889,a)].
% 2.65/2.90 919 -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(774,a,760,b)].
% 2.65/2.90 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(919,c,888,a)].
% 2.70/2.90 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(919,c,889,a)].
% 2.70/2.90 920 -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(775,a,760,b)].
% 2.70/2.90 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(920,c,888,a)].
% 2.70/2.90 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(920,c,889,a)].
% 2.70/2.90 921 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(783,b,760,b)].
% 2.70/2.90 922 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(784,b,760,b)].
% 2.70/2.90 923 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(785,b,760,b)].
% 2.70/2.90 924 -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(786,c,760,b)].
% 2.70/2.90 925 -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(787,c,760,b)].
% 2.70/2.90 926 -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(788,c,760,b)].
% 2.70/2.90 927 -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(789,c,760,b)].
% 2.70/2.90 928 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(799,a,797,b)].
% 2.70/2.90 929 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(878,b,859,b)].
% 2.70/2.90 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(929,b,888,a)].
% 2.70/2.90 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(929,b,889,a)].
% 2.70/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(929,b,892,b)].
% 2.70/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(929,b,893,b)].
% 2.70/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(929,b,894,b)].
% 2.70/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(929,b,895,b)].
% 2.70/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(929,b,896,b)].
% 2.70/2.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(929,b,897,b)].
% 2.70/2.90 930 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(879,b,859,b)].
% 2.70/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(930,b,888,a)].
% 2.70/2.90 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(930,b,889,a)].
% 2.70/2.90 931 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(880,b,859,b)].
% 2.70/2.90 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(931,b,888,a)].
% 2.70/2.90 Derived: c_lessequals(A,A,tc_nat). [resolve(931,b,889,a)].
% 2.70/2.90 932 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(881,b,859,b)].
% 2.70/2.90 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(932,b,888,a)].
% 2.70/2.90 Derived: class_Orderings_Oord(tc_nat). [resolve(932,b,889,a)].
% 2.70/2.90 933 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(882,b,859,b)].
% 2.70/2.90 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(933,b,888,a)].
% 2.70/2.90 Derived: -c_less(A,A,tc_nat). [resolve(933,b,889,a)].
% 2.73/2.95 934 -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(883,c,859,b)].
% 2.73/2.95 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(934,c,888,a)].
% 2.73/2.95 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(934,c,889,a)].
% 2.73/2.95 935 -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(884,c,859,b)].
% 2.73/2.95 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(935,c,888,a)].
% 2.73/2.95 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(935,c,889,a)].
% 2.73/2.96 936 -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(885,c,859,b)].
% 2.73/2.96 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(936,c,888,a)].
% 2.73/2.96 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(936,c,889,a)].
% 2.73/2.96 937 -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(886,c,859,b)].
% 2.73/2.96 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(937,c,888,a)].
% 2.73/2.96 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(937,c,889,a)].
% 2.73/2.96 938 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom). [assumption].
% 2.73/2.96 939 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom). [assumption].
% 2.73/2.96 940 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom). [assumption].
% 2.73/2.96 941 -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].
% 2.73/2.96 942 -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].
% 2.73/2.96 943 -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].
% 2.73/2.96 944 -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].
% 2.73/2.96 945 -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].
% 2.73/2.96 946 -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].
% 2.73/2.96 947 -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].
% 2.73/2.96 948 -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].
% 2.73/2.97 949 -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].
% 2.73/2.97 950 -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].
% 2.73/2.97 951 -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].
% 2.73/2.97 952 -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].
% 2.73/2.97 953 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom). [assumption].
% 2.73/2.97 954 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_5) # label(axiom). [assumption].
% 2.73/2.97 955 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom). [assumption].
% 2.73/2.97 956 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(31,b,2,a)].
% 2.73/2.97 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(956,a,948,b)].
% 2.73/2.97 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(956,a,949,b)].
% 2.73/2.97 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(956,a,950,b)].
% 2.73/2.97 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(956,a,951,b)].
% 2.73/2.97 957 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__semiring(B). [resolve(33,a,31,b)].
% 2.73/2.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(957,b,948,b)].
% 2.73/2.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(957,b,949,b)].
% 2.73/2.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(957,b,950,b)].
% 2.73/2.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(957,b,951,b)].
% 2.73/2.97 958 -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(34,a,31,b)].
% 2.73/2.97 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(958,c,948,b)].
% 2.73/2.97 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(958,c,949,b)].
% 2.73/2.97 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(958,c,950,b)].
% 2.73/2.97 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(958,c,951,b)].
% 2.73/2.97 959 -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(35,a,31,b)].
% 2.73/2.97 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(959,c,948,b)].
% 2.73/2.97 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(959,c,949,b)].
% 2.73/2.97 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(959,c,950,b)].
% 2.73/3.00 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(959,c,951,b)].
% 2.73/3.00 960 -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(36,a,31,b)].
% 2.73/3.00 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(960,c,948,b)].
% 2.73/3.00 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(960,c,949,b)].
% 2.73/3.00 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(960,c,950,b)].
% 2.73/3.00 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(960,c,951,b)].
% 2.73/3.00 961 -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(37,a,31,b)].
% 2.73/3.00 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(961,c,948,b)].
% 2.73/3.00 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(961,c,949,b)].
% 2.73/3.00 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(961,c,950,b)].
% 2.73/3.00 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(961,c,951,b)].
% 2.73/3.00 962 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(38,a,64,b)].
% 2.73/3.00 963 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(67,a,64,b)].
% 2.73/3.00 964 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(69,a,64,b)].
% 2.73/3.00 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(964,b,942,b)].
% 2.73/3.00 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(964,b,947,b)].
% 2.73/3.00 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(964,b,948,b)].
% 2.73/3.00 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(964,b,949,b)].
% 2.73/3.00 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(964,b,951,b)].
% 2.73/3.00 965 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(182,a,171,b)].
% 2.73/3.00 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(965,b,951,b)].
% 2.73/3.00 966 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(183,a,171,b)].
% 2.73/3.00 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(966,b,951,b)].
% 2.73/3.00 967 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A). [resolve(815,b,790,a)].
% 2.73/3.00 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(967,a,949,b)].
% 2.73/3.00 968 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_12) # label(axiom). [assumption].
% 2.73/3.00 969 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom). [assumption].
% 2.73/3.01 970 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom). [assumption].
% 2.73/3.01 971 -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].
% 2.73/3.01 972 -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].
% 2.73/3.01 973 -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].
% 2.73/3.01 974 -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].
% 2.73/3.01 975 -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].
% 2.73/3.01 976 -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].
% 2.73/3.01 977 -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].
% 2.73/3.01 978 -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].
% 2.73/3.01 979 -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].
% 2.73/3.01 980 -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].
% 2.73/3.01 981 -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].
% 2.73/3.01 982 -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].
% 2.73/3.01 983 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(27,b,2,a)].
% 2.73/3.01 984 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(33,a,27,b)].
% 2.73/3.01 985 -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(34,a,27,b)].
% 2.73/3.01 986 -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(35,a,27,b)].
% 2.73/3.01 987 -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(36,a,27,b)].
% 2.73/3.01 988 -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(37,a,27,b)].
% 2.73/3.01 989 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(38,a,60,b)].
% 2.73/3.01 990 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(67,a,60,b)].
% 2.73/3.01 991 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(69,a,60,b)].
% 2.73/3.01 992 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(182,a,167,b)].
% 2.73/3.01 993 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(183,a,167,b)].
% 2.83/3.03 994 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(293,b,286,b)].
% 2.83/3.03 995 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(354,b,343,b)].
% 2.83/3.03 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(995,b,978,b)].
% 2.83/3.03 996 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(357,b,343,b)].
% 2.83/3.03 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(996,b,978,b)].
% 2.83/3.03 997 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A). [resolve(811,b,790,a)].
% 2.83/3.03 998 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(956,a,949,b)].
% 2.83/3.03 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(998,b,969,a)].
% 2.83/3.03 Derived: c_lessequals(A,A,tc_nat). [resolve(998,b,970,a)].
% 2.83/3.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(998,b,971,b)].
% 2.83/3.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(998,b,972,b)].
% 2.83/3.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(998,b,973,b)].
% 2.83/3.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(998,b,974,b)].
% 2.83/3.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(998,b,975,b)].
% 2.83/3.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(998,b,976,b)].
% 2.83/3.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(998,b,977,b)].
% 2.83/3.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(998,b,978,b)].
% 2.83/3.03 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(998,b,982,b)].
% 2.83/3.03 999 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(957,b,949,b)].
% 2.83/3.03 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(999,b,969,a)].
% 2.83/3.03 Derived: -c_less(A,A,tc_nat). [resolve(999,b,970,a)].
% 2.83/3.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(999,b,971,b)].
% 2.83/3.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(999,b,972,b)].
% 2.83/3.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(999,b,973,b)].
% 2.83/3.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(999,b,974,b)].
% 2.83/3.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(999,b,975,b)].
% 2.83/3.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(999,b,976,b)].
% 2.83/3.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(999,b,977,b)].
% 2.83/3.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(999,b,978,b)].
% 2.83/3.03 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(999,b,982,b)].
% 2.83/3.03 1000 -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(958,c,949,b)].
% 2.83/3.03 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(1000,c,969,a)].
% 2.83/3.03 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(1000,c,970,a)].
% 2.83/3.03 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(1000,c,971,b)].
% 2.83/3.03 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(1000,c,972,b)].
% 2.83/3.03 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(1000,c,973,b)].
% 2.83/3.03 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(1000,c,974,b)].
% 2.83/3.03 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(1000,c,975,b)].
% 2.83/3.03 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(1000,c,976,b)].
% 2.83/3.03 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(1000,c,977,b)].
% 2.83/3.03 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(1000,c,978,b)].
% 2.83/3.03 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(1000,c,982,b)].
% 2.83/3.03 1001 -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(959,c,949,b)].
% 2.83/3.03 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(1001,c,969,a)].
% 2.83/3.03 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(1001,c,970,a)].
% 2.83/3.03 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(1001,c,971,b)].
% 2.83/3.03 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_Oordered__comm__semiring__strict(C). [resolve(1001,c,972,b)].
% 2.83/3.03 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_Oordered__field(C). [resolve(1001,c,973,b)].
% 2.83/3.03 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_Oordered__idom(C). [resolve(1001,c,974,b)].
% 2.83/3.03 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_Oordered__ring__strict(C). [resolve(1001,c,975,b)].
% 2.83/3.03 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_Oordered__semidom(C). [resolve(1001,c,976,b)].
% 2.83/3.03 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_Oordered__semiring__strict(C). [resolve(1001,c,977,b)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1001,c,978,b)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1001,c,982,b)].
% 2.83/3.03 1002 -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(960,c,949,b)].
% 2.83/3.03 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(1002,c,969,a)].
% 2.83/3.03 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(1002,c,970,a)].
% 2.83/3.03 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1002,c,971,b)].
% 2.83/3.03 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1002,c,972,b)].
% 2.83/3.03 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1002,c,973,b)].
% 2.83/3.03 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1002,c,974,b)].
% 2.83/3.03 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1002,c,975,b)].
% 2.83/3.03 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1002,c,976,b)].
% 2.83/3.03 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1002,c,977,b)].
% 2.83/3.03 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1002,c,978,b)].
% 2.83/3.03 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1002,c,982,b)].
% 2.83/3.03 1003 -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(961,c,949,b)].
% 2.83/3.03 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(1003,c,969,a)].
% 2.83/3.03 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(1003,c,970,a)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1003,c,971,b)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1003,c,972,b)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1003,c,973,b)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1003,c,974,b)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1003,c,975,b)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1003,c,976,b)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1003,c,977,b)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1003,c,978,b)].
% 2.83/3.03 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1003,c,982,b)].
% 2.83/3.03 1004 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(964,b,949,b)].
% 2.83/3.03 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1004,b,969,a)].
% 2.83/3.03 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1004,b,970,a)].
% 2.83/3.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1004,b,971,b)].
% 2.83/3.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1004,b,972,b)].
% 2.83/3.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1004,b,973,b)].
% 2.83/3.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1004,b,974,b)].
% 2.83/3.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1004,b,975,b)].
% 2.83/3.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1004,b,976,b)].
% 2.83/3.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1004,b,977,b)].
% 2.83/3.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1004,b,978,b)].
% 2.83/3.05 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1004,b,982,b)].
% 2.83/3.05 1005 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(967,a,949,b)].
% 2.83/3.05 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1005,b,969,a)].
% 2.83/3.05 Derived: class_Orderings_Oord(tc_nat). [resolve(1005,b,970,a)].
% 2.83/3.05 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1005,b,971,b)].
% 2.83/3.05 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1005,b,972,b)].
% 2.83/3.05 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1005,b,973,b)].
% 2.83/3.05 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1005,b,974,b)].
% 2.83/3.05 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1005,b,975,b)].
% 2.83/3.05 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1005,b,976,b)].
% 2.83/3.05 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1005,b,977,b)].
% 2.83/3.05 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1005,b,978,b)].
% 2.83/3.05 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1005,b,982,b)].
% 2.83/3.05 1006 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_18) # label(axiom). [assumption].
% 2.83/3.05 1007 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom). [assumption].
% 2.83/3.05 1008 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom). [assumption].
% 2.83/3.05 1009 -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].
% 2.83/3.05 1010 -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].
% 2.83/3.05 1011 -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].
% 2.83/3.05 1012 -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].
% 2.83/3.05 1013 -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].
% 2.83/3.05 1014 -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].
% 2.83/3.05 1015 -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].
% 2.83/3.07 1016 -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].
% 2.83/3.07 1017 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(25,b,2,a)].
% 2.83/3.07 1018 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(33,a,25,b)].
% 2.83/3.07 1019 -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(34,a,25,b)].
% 2.83/3.07 1020 -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(35,a,25,b)].
% 2.83/3.07 1021 -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(36,a,25,b)].
% 2.83/3.07 1022 -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(37,a,25,b)].
% 2.83/3.07 1023 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(38,a,58,b)].
% 2.83/3.07 1024 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(67,a,58,b)].
% 2.83/3.07 1025 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(69,a,58,b)].
% 2.83/3.07 1026 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(182,a,165,b)].
% 2.83/3.07 1027 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(183,a,165,b)].
% 2.83/3.07 1028 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(293,b,284,b)].
% 2.83/3.07 1029 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(354,b,341,b)].
% 2.83/3.07 1030 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(357,b,341,b)].
% 2.83/3.07 1031 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(695,b,692,b)].
% 2.83/3.07 1032 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(750,b,741,b)].
% 2.83/3.07 1033 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(752,b,741,b)].
% 2.83/3.07 1034 -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(753,c,741,b)].
% 2.83/3.07 1035 -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(754,c,741,b)].
% 2.83/3.07 1036 -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(755,c,741,b)].
% 2.83/3.07 1037 -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(756,c,741,b)].
% 2.83/3.07 1038 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(768,a,766,b)].
% 2.83/3.07 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1038,c,1009,b)].
% 2.83/3.07 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1038,c,1010,b)].
% 2.83/3.07 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1038,c,1011,b)].
% 2.83/3.07 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1038,c,1012,b)].
% 2.83/3.07 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1038,c,1013,b)].
% 2.83/3.07 1039 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(769,a,766,b)].
% 2.83/3.07 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1039,c,1009,b)].
% 2.83/3.07 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1039,c,1010,b)].
% 2.83/3.07 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1039,c,1011,b)].
% 2.83/3.07 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1039,c,1012,b)].
% 2.83/3.07 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1039,c,1013,b)].
% 2.83/3.07 1040 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(770,a,766,b)].
% 2.83/3.07 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1040,c,1009,b)].
% 2.83/3.07 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1040,c,1010,b)].
% 2.83/3.07 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1040,c,1011,b)].
% 2.83/3.07 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1040,c,1012,b)].
% 2.83/3.07 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1040,c,1013,b)].
% 2.83/3.07 1041 -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(771,a,766,b)].
% 2.83/3.07 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(1041,c,1009,b)].
% 2.83/3.07 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(1041,c,1010,b)].
% 2.83/3.07 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(1041,c,1011,b)].
% 2.83/3.07 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(1041,c,1012,b)].
% 2.83/3.07 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(1041,c,1013,b)].
% 2.83/3.07 1042 -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(772,a,766,b)].
% 2.83/3.07 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(1042,c,1009,b)].
% 2.83/3.07 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(1042,c,1010,b)].
% 2.83/3.07 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(1042,c,1011,b)].
% 2.83/3.07 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(1042,c,1012,b)].
% 2.83/3.07 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(1042,c,1013,b)].
% 2.83/3.07 1043 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(773,a,766,b)].
% 2.83/3.07 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1043,c,1009,b)].
% 2.83/3.07 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1043,c,1010,b)].
% 2.83/3.07 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1043,c,1011,b)].
% 2.83/3.07 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1043,c,1012,b)].
% 2.83/3.07 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1043,c,1013,b)].
% 2.83/3.07 1044 -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(774,a,766,b)].
% 2.83/3.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1044,c,1009,b)].
% 2.83/3.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1044,c,1010,b)].
% 2.83/3.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1044,c,1011,b)].
% 2.83/3.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1044,c,1012,b)].
% 2.83/3.07 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1044,c,1013,b)].
% 2.83/3.07 1045 -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(775,a,766,b)].
% 2.83/3.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1045,c,1009,b)].
% 2.83/3.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1045,c,1010,b)].
% 2.83/3.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1045,c,1011,b)].
% 2.83/3.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1045,c,1012,b)].
% 2.83/3.07 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OlessThan(A,C),c_SetInterval_OlessThan(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1045,c,1013,b)].
% 2.83/3.07 1046 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(784,b,766,b)].
% 2.83/3.07 1047 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(879,b,869,b)].
% 2.83/3.07 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1047,b,1009,b)].
% 2.83/3.07 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1047,b,1010,b)].
% 2.83/3.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1047,b,1011,b)].
% 2.83/3.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1047,b,1012,b)].
% 2.83/3.08 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1047,b,1013,b)].
% 2.83/3.08 1048 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(880,b,869,b)].
% 2.83/3.08 1049 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(881,b,869,b)].
% 2.83/3.08 1050 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(882,b,869,b)].
% 2.83/3.08 1051 -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(883,c,869,b)].
% 2.83/3.08 1052 -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(884,c,869,b)].
% 2.83/3.08 1053 -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(885,c,869,b)].
% 2.83/3.08 1054 -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(886,c,869,b)].
% 2.83/3.08 1055 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(929,b,897,b)].
% 2.83/3.08 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1055,b,1007,a)].
% 2.83/3.08 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1055,b,1008,a)].
% 2.83/3.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1055,b,1009,b)].
% 2.83/3.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1055,b,1010,b)].
% 2.83/3.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1055,b,1011,b)].
% 2.83/3.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1055,b,1012,b)].
% 2.83/3.08 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1055,b,1013,b)].
% 2.83/3.08 1056 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(964,b,947,b)].
% 2.83/3.08 1057 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(998,b,977,b)].
% 2.83/3.08 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1057,b,1007,a)].
% 2.83/3.08 Derived: c_lessequals(A,A,tc_nat). [resolve(1057,b,1008,a)].
% 2.83/3.08 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1057,b,1009,b)].
% 2.83/3.08 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1057,b,1010,b)].
% 2.83/3.08 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1057,b,1011,b)].
% 2.83/3.08 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1057,b,1012,b)].
% 2.83/3.08 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1057,b,1013,b)].
% 2.83/3.08 1058 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(999,b,977,b)].
% 2.83/3.08 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1058,b,1007,a)].
% 2.83/3.08 Derived: -c_less(A,A,tc_nat). [resolve(1058,b,1008,a)].
% 2.83/3.08 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1058,b,1009,b)].
% 2.83/3.08 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1058,b,1010,b)].
% 2.83/3.08 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1058,b,1011,b)].
% 2.83/3.08 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1058,b,1012,b)].
% 2.83/3.08 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1058,b,1013,b)].
% 2.83/3.08 1059 -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(1000,c,977,b)].
% 2.83/3.08 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(1059,c,1007,a)].
% 2.83/3.08 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(1059,c,1008,a)].
% 2.83/3.08 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(1059,c,1009,b)].
% 2.83/3.08 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(1059,c,1010,b)].
% 2.83/3.08 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(1059,c,1011,b)].
% 2.83/3.08 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(1059,c,1012,b)].
% 2.83/3.08 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(1059,c,1013,b)].
% 2.83/3.08 1060 -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(1001,c,977,b)].
% 2.83/3.08 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(1060,c,1007,a)].
% 2.83/3.08 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(1060,c,1008,a)].
% 2.83/3.08 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(1060,c,1009,b)].
% 2.83/3.08 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(1060,c,1010,b)].
% 2.83/3.08 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(1060,c,1011,b)].
% 2.83/3.08 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(1060,c,1012,b)].
% 2.83/3.08 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(1060,c,1013,b)].
% 2.83/3.08 1061 -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(1002,c,977,b)].
% 2.83/3.08 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(1061,c,1007,a)].
% 2.83/3.08 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(1061,c,1008,a)].
% 2.83/3.08 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(1061,c,1009,b)].
% 2.83/3.08 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(1061,c,1010,b)].
% 2.83/3.08 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(1061,c,1011,b)].
% 2.83/3.08 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(1061,c,1012,b)].
% 2.90/3.10 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1061,c,1013,b)].
% 2.90/3.10 1062 -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(1003,c,977,b)].
% 2.90/3.10 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1062,c,1007,a)].
% 2.90/3.10 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatMost(A,tc_nat),c_SetInterval_OatMost(B,tc_nat),tc_set(tc_nat)). [resolve(1062,c,1008,a)].
% 2.90/3.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1062,c,1009,b)].
% 2.90/3.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(1062,c,1010,b)].
% 2.90/3.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1062,c,1011,b)].
% 2.90/3.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1062,c,1012,b)].
% 2.90/3.10 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1062,c,1013,b)].
% 2.90/3.10 1063 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1004,b,977,b)].
% 2.90/3.10 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1063,b,1007,a)].
% 2.90/3.10 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1063,b,1008,a)].
% 2.90/3.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1063,b,1009,b)].
% 2.90/3.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1063,b,1010,b)].
% 2.90/3.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1063,b,1011,b)].
% 2.90/3.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1063,b,1012,b)].
% 2.90/3.10 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1063,b,1013,b)].
% 2.90/3.10 1064 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1005,b,977,b)].
% 2.90/3.10 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1064,b,1007,a)].
% 2.90/3.10 Derived: class_Orderings_Oord(tc_nat). [resolve(1064,b,1008,a)].
% 2.90/3.10 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1064,b,1009,b)].
% 2.90/3.10 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1064,b,1010,b)].
% 2.90/3.10 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1064,b,1011,b)].
% 2.90/3.10 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1064,b,1012,b)].
% 2.90/3.10 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1064,b,1013,b)].
% 2.90/3.10 1065 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_14) # label(axiom). [assumption].
% 2.90/3.10 1066 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom). [assumption].
% 2.90/3.10 1067 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom). [assumption].
% 2.90/3.10 1068 -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].
% 2.90/3.13 1069 -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].
% 2.90/3.13 1070 -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].
% 2.90/3.13 1071 -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].
% 2.90/3.13 1072 -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].
% 2.90/3.13 1073 -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].
% 2.90/3.13 1074 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_2) # label(axiom). [assumption].
% 2.90/3.13 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1074,a,1068,b)].
% 2.90/3.13 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1074,a,1072,b)].
% 2.90/3.13 1075 -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].
% 2.90/3.13 1076 -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].
% 2.90/3.13 1077 -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].
% 2.90/3.13 1078 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(29,b,2,a)].
% 2.90/3.13 1079 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(33,a,29,b)].
% 2.90/3.13 1080 -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(34,a,29,b)].
% 2.90/3.13 1081 -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(35,a,29,b)].
% 2.90/3.13 1082 -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(36,a,29,b)].
% 2.90/3.13 1083 -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(37,a,29,b)].
% 2.90/3.13 1084 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(38,a,62,b)].
% 2.90/3.13 1085 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(67,a,62,b)].
% 2.90/3.13 1086 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(69,a,62,b)].
% 2.90/3.13 1087 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(182,a,169,b)].
% 2.90/3.13 1088 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(183,a,169,b)].
% 2.90/3.13 1089 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(817,b,813,b)].
% 2.90/3.13 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1089,b,1073,b)].
% 2.90/3.13 1090 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(956,a,951,b)].
% 2.90/3.13 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1090,b,1073,b)].
% 2.90/3.13 1091 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(957,b,951,b)].
% 2.90/3.15 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1091,b,1073,b)].
% 2.90/3.15 1092 -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(958,c,951,b)].
% 2.90/3.15 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__comm__ring(B). [resolve(1092,c,1073,b)].
% 2.90/3.15 1093 -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(959,c,951,b)].
% 2.90/3.15 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(1093,c,1073,b)].
% 2.90/3.15 1094 -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(960,c,951,b)].
% 2.90/3.15 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(1094,c,1073,b)].
% 2.90/3.15 1095 -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(961,c,951,b)].
% 2.90/3.15 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1095,c,1073,b)].
% 2.90/3.15 1096 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(964,b,951,b)].
% 2.90/3.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1096,b,1073,b)].
% 2.90/3.15 1097 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(965,b,951,b)].
% 2.90/3.15 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1097,b,1066,a)].
% 2.90/3.15 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1097,b,1067,a)].
% 2.90/3.15 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1097,b,1073,b)].
% 2.90/3.15 1098 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(966,b,951,b)].
% 2.90/3.15 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1098,b,1073,b)].
% 2.90/3.15 1099 -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].
% 2.90/3.15 1100 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom). [assumption].
% 2.90/3.15 1101 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom). [assumption].
% 2.90/3.15 1102 -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].
% 2.90/3.15 1103 -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].
% 2.90/3.15 1104 -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].
% 2.90/3.15 1105 -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].
% 2.90/3.15 1106 -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].
% 2.97/3.17 1107 -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].
% 2.97/3.17 1108 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) # label(axiom). [assumption].
% 2.97/3.17 1109 -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].
% 2.97/3.17 1110 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(26,b,2,a)].
% 2.97/3.17 1111 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(33,a,26,b)].
% 2.97/3.17 1112 -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(34,a,26,b)].
% 2.97/3.17 1113 -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(35,a,26,b)].
% 2.97/3.17 1114 -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(36,a,26,b)].
% 2.97/3.17 1115 -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(37,a,26,b)].
% 2.97/3.17 1116 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(38,a,59,b)].
% 2.97/3.17 1117 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(67,a,59,b)].
% 2.97/3.17 1118 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(69,a,59,b)].
% 2.97/3.17 1119 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(182,a,166,b)].
% 2.97/3.17 1120 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(183,a,166,b)].
% 2.97/3.17 1121 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(293,b,285,b)].
% 2.97/3.17 1122 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(354,b,342,b)].
% 2.97/3.17 1123 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(357,b,342,b)].
% 2.97/3.17 1124 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(817,b,810,b)].
% 2.97/3.17 1125 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(956,a,948,b)].
% 2.97/3.17 1126 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(957,b,948,b)].
% 2.97/3.17 1127 -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(958,c,948,b)].
% 2.97/3.17 1128 -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(959,c,948,b)].
% 2.97/3.17 1129 -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(960,c,948,b)].
% 2.97/3.17 1130 -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(961,c,948,b)].
% 2.97/3.17 1131 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(964,b,948,b)].
% 2.97/3.17 1132 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(995,b,978,b)].
% 2.97/3.19 1133 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(996,b,978,b)].
% 2.97/3.19 1134 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(998,b,978,b)].
% 2.97/3.19 1135 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(999,b,978,b)].
% 2.97/3.19 1136 -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(1000,c,978,b)].
% 2.97/3.19 1137 -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(1001,c,978,b)].
% 2.97/3.19 1138 -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(1002,c,978,b)].
% 2.97/3.19 1139 -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(1003,c,978,b)].
% 2.97/3.19 1140 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1004,b,978,b)].
% 2.97/3.19 1141 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1005,b,978,b)].
% 2.97/3.19 1142 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1074,a,1072,b)].
% 2.97/3.19 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(1142,b,1100,a)].
% 2.97/3.19 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(1142,b,1101,a)].
% 2.97/3.19 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1142,b,1102,b)].
% 2.97/3.19 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1142,b,1103,b)].
% 2.97/3.19 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1142,b,1104,b)].
% 2.97/3.19 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1142,b,1105,b)].
% 2.97/3.19 1143 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) # label(axiom). [assumption].
% 2.97/3.19 1144 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom). [assumption].
% 2.97/3.19 1145 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom). [assumption].
% 2.97/3.19 1146 -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].
% 2.97/3.19 1147 -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].
% 2.97/3.19 1148 -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].
% 2.97/3.19 1149 -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].
% 2.97/3.19 1150 -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].
% 2.97/3.19 1151 -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].
% 2.97/3.19 1152 -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].
% 3.00/3.21 1153 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(20,b,2,a)].
% 3.00/3.21 1154 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(33,a,20,b)].
% 3.00/3.21 1155 -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(34,a,20,b)].
% 3.00/3.21 1156 -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(35,a,20,b)].
% 3.00/3.21 1157 -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(36,a,20,b)].
% 3.00/3.21 1158 -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(37,a,20,b)].
% 3.00/3.21 1159 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(38,a,53,b)].
% 3.00/3.21 1160 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(67,a,53,b)].
% 3.00/3.21 1161 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(69,a,53,b)].
% 3.00/3.21 1162 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(182,a,160,b)].
% 3.00/3.21 1163 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(183,a,160,b)].
% 3.00/3.21 1164 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(293,b,279,b)].
% 3.00/3.21 1165 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(354,b,336,b)].
% 3.00/3.21 1166 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(357,b,336,b)].
% 3.00/3.21 1167 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(695,b,687,b)].
% 3.00/3.21 1168 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(750,b,736,b)].
% 3.00/3.21 1169 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(752,b,736,b)].
% 3.00/3.21 1170 -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(753,c,736,b)].
% 3.00/3.21 1171 -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(754,c,736,b)].
% 3.00/3.21 1172 -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(755,c,736,b)].
% 3.00/3.21 1173 -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(756,c,736,b)].
% 3.00/3.21 1174 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(768,a,761,b)].
% 3.00/3.21 1175 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(769,a,761,b)].
% 3.00/3.21 1176 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(770,a,761,b)].
% 3.00/3.21 1177 -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(771,a,761,b)].
% 3.00/3.21 1178 -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(772,a,761,b)].
% 3.00/3.21 1179 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(773,a,761,b)].
% 3.00/3.22 1180 -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(774,a,761,b)].
% 3.00/3.22 1181 -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(775,a,761,b)].
% 3.00/3.22 1182 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(784,b,761,b)].
% 3.00/3.22 1183 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(879,b,864,b)].
% 3.00/3.22 1184 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(880,b,864,b)].
% 3.00/3.22 1185 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(881,b,864,b)].
% 3.00/3.22 1186 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(882,b,864,b)].
% 3.00/3.22 1187 -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(883,c,864,b)].
% 3.00/3.22 1188 -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(884,c,864,b)].
% 3.00/3.22 1189 -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(885,c,864,b)].
% 3.00/3.22 1190 -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(886,c,864,b)].
% 3.00/3.22 1191 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(929,b,892,b)].
% 3.00/3.22 1192 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(964,b,942,b)].
% 3.00/3.22 1193 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(998,b,972,b)].
% 3.00/3.22 1194 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(999,b,972,b)].
% 3.00/3.22 1195 -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(1000,c,972,b)].
% 3.00/3.22 1196 -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(1001,c,972,b)].
% 3.00/3.22 1197 -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(1002,c,972,b)].
% 3.00/3.22 1198 -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(1003,c,972,b)].
% 3.00/3.22 1199 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1004,b,972,b)].
% 3.00/3.22 1200 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1005,b,972,b)].
% 3.00/3.22 1201 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1038,c,1009,b)].
% 3.00/3.22 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1201,c,1144,a)].
% 3.00/3.22 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(1201,c,1145,a)].
% 3.00/3.22 1202 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1039,c,1009,b)].
% 3.00/3.22 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1202,c,1144,a)].
% 3.02/3.22 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(1202,c,1145,a)].
% 3.02/3.22 1203 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1040,c,1009,b)].
% 3.02/3.22 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1203,c,1144,a)].
% 3.02/3.22 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(1203,c,1145,a)].
% 3.02/3.22 1204 -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(1041,c,1009,b)].
% 3.02/3.22 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(1204,c,1144,a)].
% 3.02/3.22 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(1204,c,1145,a)].
% 3.02/3.22 1205 -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(1042,c,1009,b)].
% 3.02/3.22 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(1205,c,1144,a)].
% 3.02/3.22 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(1205,c,1145,a)].
% 3.02/3.22 1206 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1043,c,1009,b)].
% 3.02/3.22 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1206,c,1144,a)].
% 3.02/3.22 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(1206,c,1145,a)].
% 3.02/3.22 1207 -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(1044,c,1009,b)].
% 3.02/3.22 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(1207,c,1144,a)].
% 3.02/3.22 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(1207,c,1145,a)].
% 3.02/3.22 1208 -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(1045,c,1009,b)].
% 3.02/3.22 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(1208,c,1144,a)].
% 3.02/3.22 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(1208,c,1145,a)].
% 3.02/3.22 1209 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1047,b,1009,b)].
% 3.02/3.22 1210 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1055,b,1009,b)].
% 3.02/3.22 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1210,b,1144,a)].
% 3.02/3.22 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1210,b,1145,a)].
% 3.02/3.22 1211 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1057,b,1009,b)].
% 3.02/3.22 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1211,b,1144,a)].
% 3.02/3.22 Derived: c_lessequals(A,A,tc_nat). [resolve(1211,b,1145,a)].
% 3.02/3.22 1212 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1058,b,1009,b)].
% 3.02/3.22 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1212,b,1144,a)].
% 3.02/3.22 Derived: -c_less(A,A,tc_nat). [resolve(1212,b,1145,a)].
% 3.02/3.27 1213 -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(1059,c,1009,b)].
% 3.02/3.27 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(1213,c,1144,a)].
% 3.02/3.27 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(1213,c,1145,a)].
% 3.02/3.27 1214 -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(1060,c,1009,b)].
% 3.02/3.27 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(1214,c,1144,a)].
% 3.02/3.27 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(1214,c,1145,a)].
% 3.02/3.27 1215 -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(1061,c,1009,b)].
% 3.02/3.27 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(1215,c,1144,a)].
% 3.02/3.27 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(1215,c,1145,a)].
% 3.02/3.27 1216 -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(1062,c,1009,b)].
% 3.02/3.27 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(1216,c,1144,a)].
% 3.02/3.27 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(1216,c,1145,a)].
% 3.02/3.27 1217 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1063,b,1009,b)].
% 3.02/3.27 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1217,b,1144,a)].
% 3.02/3.27 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1217,b,1145,a)].
% 3.02/3.27 1218 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1064,b,1009,b)].
% 3.02/3.27 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1218,b,1144,a)].
% 3.02/3.27 Derived: class_Orderings_Oord(tc_nat). [resolve(1218,b,1145,a)].
% 3.02/3.27 1219 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1074,a,1068,b)].
% 3.02/3.27 1220 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1142,b,1102,b)].
% 3.02/3.27 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(1220,b,1144,a)].
% 3.02/3.27 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(1220,b,1145,a)].
% 3.02/3.27 1221 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_1) # label(axiom). [assumption].
% 3.02/3.27 1222 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom). [assumption].
% 3.02/3.27 1223 -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].
% 3.02/3.27 1224 -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].
% 3.02/3.27 1225 -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].
% 3.02/3.27 1226 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom). [assumption].
% 3.02/3.29 1227 class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_47) # label(axiom). [assumption].
% 3.02/3.29 1228 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom). [assumption].
% 3.02/3.29 1229 -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].
% 3.02/3.29 1230 -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].
% 3.02/3.29 1231 -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].
% 3.02/3.29 1232 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_5) # label(axiom). [assumption].
% 3.02/3.29 1233 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_7) # label(axiom). [assumption].
% 3.02/3.29 1234 -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].
% 3.02/3.29 1235 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_Ring__and__Field_Oordered__field_54) # label(axiom). [assumption].
% 3.02/3.29 1236 -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].
% 3.02/3.29 1237 -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].
% 3.02/3.29 1238 -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].
% 3.02/3.29 1239 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A). [resolve(13,b,2,a)].
% 3.02/3.29 1240 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(18,a,13,b)].
% 3.02/3.29 1241 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(33,a,13,b)].
% 3.02/3.29 1242 -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(34,a,13,b)].
% 3.02/3.29 1243 -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(35,a,13,b)].
% 3.02/3.29 1244 -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(36,a,13,b)].
% 3.02/3.29 1245 -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(37,a,13,b)].
% 3.02/3.29 1246 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(293,b,268,b)].
% 3.02/3.29 1247 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(319,b,305,b)].
% 3.02/3.29 1248 c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(816,a,798,b)].
% 3.02/3.29 1249 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(817,b,798,b)].
% 3.02/3.29 1250 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(818,b,798,b)].
% 3.02/3.29 1251 -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(819,c,798,b)].
% 3.02/3.29 1252 -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(820,c,798,b)].
% 3.02/3.29 1253 -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(821,c,798,b)].
% 3.02/3.29 1254 -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(822,c,798,b)].
% 3.02/3.29 1255 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(878,b,860,b)].
% 3.02/3.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1255,b,1228,b)].
% 3.02/3.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1255,b,1229,b)].
% 3.02/3.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1255,b,1230,b)].
% 3.02/3.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1255,b,1231,b)].
% 3.02/3.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1255,b,1234,b)].
% 3.02/3.29 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1255,b,1238,b)].
% 3.02/3.29 1256 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(879,b,860,b)].
% 3.02/3.29 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1256,b,1228,b)].
% 3.02/3.29 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1256,b,1229,b)].
% 3.02/3.29 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1256,b,1230,b)].
% 3.02/3.29 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1256,b,1231,b)].
% 3.02/3.29 1257 c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(880,b,860,b)].
% 3.02/3.29 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1257,b,1228,b)].
% 3.02/3.29 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1257,b,1229,b)].
% 3.02/3.29 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1257,b,1230,b)].
% 3.02/3.29 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1257,b,1231,b)].
% 3.02/3.29 1258 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(881,b,860,b)].
% 3.02/3.29 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1258,b,1228,b)].
% 3.02/3.29 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1258,b,1229,b)].
% 3.02/3.29 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1258,b,1230,b)].
% 3.02/3.29 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1258,b,1231,b)].
% 3.02/3.29 1259 -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(882,b,860,b)].
% 3.02/3.29 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1259,b,1228,b)].
% 3.02/3.29 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1259,b,1229,b)].
% 3.02/3.29 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1259,b,1230,b)].
% 3.02/3.29 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1259,b,1231,b)].
% 3.02/3.29 1260 -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(883,c,860,b)].
% 3.02/3.29 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1260,c,1228,b)].
% 3.02/3.29 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1260,c,1229,b)].
% 3.02/3.32 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(1260,c,1230,b)].
% 3.02/3.32 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(1260,c,1231,b)].
% 3.02/3.32 1261 -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(884,c,860,b)].
% 3.02/3.32 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(1261,c,1228,b)].
% 3.02/3.32 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(1261,c,1229,b)].
% 3.02/3.32 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(1261,c,1230,b)].
% 3.02/3.32 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(1261,c,1231,b)].
% 3.02/3.32 1262 -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(885,c,860,b)].
% 3.02/3.32 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(1262,c,1228,b)].
% 3.02/3.32 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(1262,c,1229,b)].
% 3.02/3.32 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(1262,c,1230,b)].
% 3.02/3.32 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(1262,c,1231,b)].
% 3.02/3.32 1263 -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(886,c,860,b)].
% 3.02/3.32 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(1263,c,1228,b)].
% 3.02/3.32 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(1263,c,1229,b)].
% 3.02/3.32 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(1263,c,1230,b)].
% 3.02/3.32 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(1263,c,1231,b)].
% 3.02/3.32 1264 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom). [assumption].
% 3.02/3.32 1265 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom). [assumption].
% 3.02/3.32 1266 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom). [assumption].
% 3.02/3.32 1267 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom). [assumption].
% 3.02/3.32 1268 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_0) # label(axiom). [assumption].
% 3.02/3.33 1269 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_16) # label(axiom). [assumption].
% 3.02/3.33 1270 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_16) # label(axiom). [assumption].
% 3.02/3.33 1271 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Olordered__ring_25) # label(axiom). [assumption].
% 3.02/3.33 1272 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__field_50) # label(axiom). [assumption].
% 3.02/3.33 1273 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__idom_53) # label(axiom). [assumption].
% 3.02/3.33 1274 -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].
% 3.02/3.33 1275 -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(B,B,A). [resolve(8,b,2,a)].
% 3.02/3.33 1276 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(18,a,8,b)].
% 3.02/3.33 1277 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(33,a,8,b)].
% 3.02/3.33 1278 -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(34,a,8,b)].
% 3.02/3.33 1279 -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(35,a,8,b)].
% 3.02/3.33 1280 -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(36,a,8,b)].
% 3.02/3.33 1281 -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(37,a,8,b)].
% 3.02/3.33 1282 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(113,b,110,a)].
% 3.02/3.33 1283 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(113,b,111,a)].
% 3.02/3.33 1284 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(293,b,263,b)].
% 3.02/3.33 1285 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(750,b,729,b)].
% 3.02/3.33 1286 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(751,b,729,b)].
% 3.02/3.33 1287 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(752,b,729,b)].
% 3.02/3.33 1288 -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(753,c,729,b)].
% 3.02/3.33 1289 -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(754,c,729,b)].
% 3.02/3.33 1290 -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(755,c,729,b)].
% 3.02/3.33 1291 -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(756,c,729,b)].
% 3.02/3.33 1292 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(851,a,826,b)].
% 3.02/3.33 1293 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(878,b,855,b)].
% 3.02/3.33 1294 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(880,b,855,b)].
% 3.02/3.33 1295 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(881,b,855,b)].
% 3.02/3.33 1296 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(882,b,855,b)].
% 3.02/3.33 1297 -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(883,c,855,b)].
% 3.13/3.34 1298 -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(884,c,855,b)].
% 3.13/3.34 1299 -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(885,c,855,b)].
% 3.13/3.34 1300 -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(886,c,855,b)].
% 3.13/3.34 1301 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1255,b,1228,b)].
% 3.13/3.34 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1301,b,1265,a)].
% 3.13/3.34 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1301,b,1272,b)].
% 3.13/3.34 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1301,b,1273,b)].
% 3.13/3.34 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1301,b,1274,b)].
% 3.13/3.34 1302 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1256,b,1228,b)].
% 3.13/3.34 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1302,b,1265,a)].
% 3.13/3.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1302,b,1271,b)].
% 3.13/3.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1302,b,1272,b)].
% 3.13/3.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1302,b,1273,b)].
% 3.13/3.34 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1302,b,1274,b)].
% 3.13/3.34 1303 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1257,b,1228,b)].
% 3.13/3.34 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1303,b,1265,a)].
% 3.13/3.34 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1303,b,1271,b)].
% 3.13/3.34 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1303,b,1272,b)].
% 3.13/3.34 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1303,b,1273,b)].
% 3.13/3.34 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1303,b,1274,b)].
% 3.13/3.34 1304 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(1258,b,1228,b)].
% 3.13/3.34 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(1304,b,1265,a)].
% 3.13/3.34 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1304,b,1271,b)].
% 3.13/3.34 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1304,b,1272,b)].
% 3.13/3.34 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1304,b,1273,b)].
% 3.13/3.34 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1304,b,1274,b)].
% 3.13/3.34 1305 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group(B). [resolve(1259,b,1228,b)].
% 3.13/3.34 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1305,b,1265,a)].
% 3.13/3.34 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1305,b,1271,b)].
% 3.13/3.34 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1305,b,1272,b)].
% 3.13/3.34 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1305,b,1273,b)].
% 3.13/3.34 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1305,b,1274,b)].
% 3.13/3.34 1306 -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(1260,c,1228,b)].
% 3.13/3.34 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1306,c,1265,a)].
% 3.13/3.34 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1306,c,1271,b)].
% 3.13/3.36 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(1306,c,1272,b)].
% 3.13/3.36 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(1306,c,1273,b)].
% 3.13/3.36 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(1306,c,1274,b)].
% 3.13/3.36 1307 -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(1261,c,1228,b)].
% 3.13/3.36 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(1307,c,1265,a)].
% 3.13/3.36 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(1307,c,1271,b)].
% 3.13/3.36 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(1307,c,1272,b)].
% 3.13/3.36 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(1307,c,1273,b)].
% 3.13/3.36 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(1307,c,1274,b)].
% 3.13/3.36 1308 -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(1262,c,1228,b)].
% 3.13/3.36 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(1308,c,1265,a)].
% 3.13/3.36 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(1308,c,1271,b)].
% 3.13/3.36 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(1308,c,1272,b)].
% 3.13/3.36 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(1308,c,1273,b)].
% 3.13/3.36 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(1308,c,1274,b)].
% 3.13/3.36 1309 -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(1263,c,1228,b)].
% 3.13/3.36 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(1309,c,1265,a)].
% 3.13/3.36 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(1309,c,1271,b)].
% 3.13/3.36 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(1309,c,1272,b)].
% 3.13/3.36 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(1309,c,1273,b)].
% 3.13/3.36 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(1309,c,1274,b)].
% 3.13/3.36 1310 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_11) # label(axiom). [assumption].
% 3.13/3.37 1311 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom). [assumption].
% 3.13/3.37 1312 -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].
% 3.13/3.37 1313 -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].
% 3.13/3.37 1314 -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].
% 3.13/3.37 1315 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Ring__and__Field_Opordered__ring(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_32) # label(axiom). [assumption].
% 3.13/3.37 1316 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom). [assumption].
% 3.13/3.37 1317 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom). [assumption].
% 3.13/3.37 1318 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom). [assumption].
% 3.13/3.37 1319 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(30,b,2,a)].
% 3.13/3.37 1320 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(33,a,30,b)].
% 3.13/3.37 1321 -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(34,a,30,b)].
% 3.13/3.37 1322 -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(35,a,30,b)].
% 3.13/3.37 1323 -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(36,a,30,b)].
% 3.13/3.37 1324 -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(37,a,30,b)].
% 3.13/3.37 1325 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(38,a,63,b)].
% 3.13/3.37 1326 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(67,a,63,b)].
% 3.13/3.37 1327 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(69,a,63,b)].
% 3.13/3.37 1328 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(182,a,170,b)].
% 3.13/3.37 1329 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(183,a,170,b)].
% 3.13/3.37 1330 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(293,b,288,b)].
% 3.13/3.37 1331 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(354,b,345,b)].
% 3.13/3.37 1332 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(357,b,345,b)].
% 3.13/3.37 1333 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(381,b,371,b)].
% 3.13/3.37 1334 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(389,b,371,b)].
% 3.13/3.37 1335 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(390,b,371,b)].
% 3.13/3.37 1336 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(817,b,814,b)].
% 3.13/3.37 1337 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(879,b,870,b)].
% 3.13/3.37 1338 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(880,b,870,b)].
% 3.13/3.37 1339 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(881,b,870,b)].
% 3.13/3.37 1340 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(882,b,870,b)].
% 3.13/3.37 1341 -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(883,c,870,b)].
% 3.13/3.40 1342 -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(884,c,870,b)].
% 3.13/3.40 1343 -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(885,c,870,b)].
% 3.13/3.40 1344 -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(886,c,870,b)].
% 3.13/3.40 1345 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(998,b,982,b)].
% 3.13/3.40 1346 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(999,b,982,b)].
% 3.13/3.40 1347 -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(1000,c,982,b)].
% 3.13/3.40 1348 -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(1001,c,982,b)].
% 3.13/3.40 1349 -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(1002,c,982,b)].
% 3.13/3.40 1350 -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(1003,c,982,b)].
% 3.13/3.40 1351 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1004,b,982,b)].
% 3.13/3.40 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1351,b,1312,b)].
% 3.13/3.40 1352 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1005,b,982,b)].
% 3.13/3.40 1353 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1255,b,1238,b)].
% 3.13/3.40 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1353,b,1312,b)].
% 3.13/3.40 1354 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeast__iff__iff1_0) # label(axiom). [assumption].
% 3.13/3.40 1355 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom). [assumption].
% 3.13/3.40 1356 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom). [assumption].
% 3.13/3.40 1357 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom). [assumption].
% 3.13/3.40 1358 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom). [assumption].
% 3.13/3.40 1359 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom). [assumption].
% 3.13/3.40 1360 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom). [assumption].
% 3.13/3.40 1361 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom). [assumption].
% 3.13/3.40 1362 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom). [assumption].
% 3.13/3.40 1363 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom). [assumption].
% 3.13/3.40 1364 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_27) # label(axiom). [assumption].
% 3.13/3.40 1365 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom). [assumption].
% 3.13/3.40 1366 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_24) # label(axiom). [assumption].
% 3.13/3.40 1367 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom). [assumption].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1354,a,1355,a)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1354,a,1356,a)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_set(C)),tc_set(C)) | c_lessequals(B,A,tc_set(C)). [resolve(1354,a,1357,a)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1354,a,1358,b)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1354,a,1359,b)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1354,a,1360,b)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1354,a,1361,b)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1354,a,1362,b)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1354,a,1363,b)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1354,a,1364,b)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1354,a,1365,b)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1354,a,1366,b)].
% 3.13/3.40 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1354,a,1367,b)].
% 3.13/3.40 1368 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A) # label(cls_SetInterval_OatLeast__iff__iff2_0) # label(axiom). [assumption].
% 3.13/3.40 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1368,a,1355,a)].
% 3.13/3.40 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1368,a,1356,a)].
% 3.13/3.40 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(B,c_SetInterval_OatLeast(A,tc_set(C)),tc_set(C)). [resolve(1368,a,1357,a)].
% 3.13/3.40 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1368,a,1358,b)].
% 3.13/3.40 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1368,a,1359,b)].
% 3.13/3.40 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1368,a,1360,b)].
% 3.13/3.40 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1368,a,1361,b)].
% 3.13/3.40 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1368,a,1362,b)].
% 3.13/3.40 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1368,a,1363,b)].
% 3.13/3.40 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1368,a,1364,b)].
% 3.13/3.40 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1368,a,1365,b)].
% 3.13/3.40 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1368,a,1366,b)].
% 3.13/3.40 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1368,a,1367,b)].
% 3.13/3.40 1369 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A) # label(cls_SetInterval_OatMost__iff__iff1_0) # label(axiom). [assumption].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1369,a,1355,a)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1369,a,1356,a)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)) | c_lessequals(A,B,tc_set(C)). [resolve(1369,a,1357,a)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1369,a,1358,b)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1369,a,1359,b)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1369,a,1360,b)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1369,a,1361,b)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1369,a,1362,b)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1369,a,1363,b)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1369,a,1364,b)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1369,a,1365,b)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1369,a,1366,b)].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1369,a,1367,b)].
% 3.13/3.41 1370 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A) # label(cls_SetInterval_OatMost__iff__iff2_0) # label(axiom). [assumption].
% 3.13/3.41 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1370,a,1355,a)].
% 3.13/3.41 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1370,a,1356,a)].
% 3.13/3.41 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)). [resolve(1370,a,1357,a)].
% 3.13/3.41 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1370,a,1358,b)].
% 3.13/3.41 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1370,a,1359,b)].
% 3.13/3.41 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1370,a,1360,b)].
% 3.13/3.41 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1370,a,1361,b)].
% 3.13/3.41 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1370,a,1362,b)].
% 3.13/3.41 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1370,a,1363,b)].
% 3.13/3.41 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1370,a,1364,b)].
% 3.13/3.41 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1370,a,1365,b)].
% 3.13/3.41 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1370,a,1366,b)].
% 3.13/3.41 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1370,a,1367,b)].
% 3.13/3.41 1371 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThan__iff__iff1_0) # label(axiom). [assumption].
% 3.13/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1371,a,1355,a)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1371,a,1356,a)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_set(C)),tc_set(C)) | c_less(B,A,tc_set(C)). [resolve(1371,a,1357,a)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1371,a,1358,b)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1371,a,1359,b)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1371,a,1360,b)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1371,a,1361,b)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1371,a,1362,b)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1371,a,1363,b)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1371,a,1364,b)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1371,a,1365,b)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1371,a,1366,b)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1371,a,1367,b)].
% 3.22/3.41 1372 -class_Orderings_Oord(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A) # label(cls_SetInterval_OgreaterThan__iff__iff2_0) # label(axiom). [assumption].
% 3.22/3.41 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1372,a,1355,a)].
% 3.22/3.41 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1372,a,1356,a)].
% 3.22/3.41 Derived: -c_less(A,B,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThan(A,tc_set(C)),tc_set(C)). [resolve(1372,a,1357,a)].
% 3.22/3.41 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1372,a,1358,b)].
% 3.22/3.41 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1372,a,1359,b)].
% 3.22/3.41 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1372,a,1360,b)].
% 3.22/3.41 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1372,a,1361,b)].
% 3.22/3.41 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1372,a,1362,b)].
% 3.22/3.41 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1372,a,1363,b)].
% 3.22/3.41 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1372,a,1364,b)].
% 3.22/3.41 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1372,a,1365,b)].
% 3.22/3.41 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1372,a,1366,b)].
% 3.22/3.41 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1372,a,1367,b)].
% 3.22/3.41 1373 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A) # label(cls_SetInterval_OlessThan__iff__iff1_0) # label(axiom). [assumption].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1373,a,1355,a)].
% 3.22/3.41 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1373,a,1356,a)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)) | c_less(A,B,tc_set(C)). [resolve(1373,a,1357,a)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1373,a,1358,b)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1373,a,1359,b)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1373,a,1360,b)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1373,a,1361,b)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1373,a,1362,b)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1373,a,1363,b)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1373,a,1364,b)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1373,a,1365,b)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1373,a,1366,b)].
% 3.22/3.42 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1373,a,1367,b)].
% 3.22/3.42 1374 -class_Orderings_Oord(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A) # label(cls_SetInterval_OlessThan__iff__iff2_0) # label(axiom). [assumption].
% 3.22/3.42 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1374,a,1355,a)].
% 3.22/3.42 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1374,a,1356,a)].
% 3.22/3.42 Derived: -c_less(A,B,tc_set(C)) | c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)). [resolve(1374,a,1357,a)].
% 3.22/3.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1374,a,1358,b)].
% 3.22/3.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1374,a,1359,b)].
% 3.22/3.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1374,a,1360,b)].
% 3.22/3.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1374,a,1361,b)].
% 3.22/3.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1374,a,1362,b)].
% 3.22/3.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1374,a,1363,b)].
% 3.22/3.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1374,a,1364,b)].
% 3.22/3.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1374,a,1365,b)].
% 3.22/3.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1374,a,1366,b)].
% 3.22/3.42 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1374,a,1367,b)].
% 3.22/3.42 1375 class_Orderings_Oord(tc_IntDef_Oint). [resolve(18,a,1,a)].
% 3.22/3.42 1376 class_Orderings_Oord(tc_nat). [resolve(18,a,3,a)].
% 3.22/3.42 1377 class_Orderings_Oord(tc_set(A)). [resolve(18,a,4,a)].
% 3.22/3.42 1378 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(18,a,9,b)].
% 3.22/3.42 1379 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(18,a,10,b)].
% 3.22/3.42 1380 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(18,a,11,b)].
% 3.22/3.42 1381 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(32,b,18,a)].
% 3.22/3.46 1382 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(686,b,676,a)].
% 3.22/3.46 1383 class_Orderings_Oord(tc_IntDef_Oint). [resolve(695,b,677,a)].
% 3.22/3.46 1384 class_Orderings_Oord(tc_nat). [resolve(695,b,678,a)].
% 3.22/3.46 1385 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(695,b,688,b)].
% 3.22/3.46 1386 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(695,b,689,b)].
% 3.22/3.46 1387 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(695,b,690,b)].
% 3.22/3.46 1388 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(695,b,691,b)].
% 3.22/3.46 1389 class_Orderings_Oord(tc_IntDef_Oint). [resolve(751,b,727,a)].
% 3.22/3.46 1390 class_Orderings_Oord(tc_nat). [resolve(751,b,728,a)].
% 3.22/3.46 1391 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(751,b,730,b)].
% 3.22/3.46 1392 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(751,b,731,b)].
% 3.22/3.46 1393 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(751,b,732,b)].
% 3.22/3.46 1394 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(751,b,735,b)].
% 3.22/3.46 1395 class_Orderings_Oord(A) | -class_Wellfounded__Recursion_Owellorder(A). [resolve(751,b,742,b)].
% 3.22/3.46 1396 class_Orderings_Oord(tc_IntDef_Oint). [resolve(784,b,758,a)].
% 3.22/3.46 1397 class_Orderings_Oord(tc_nat). [resolve(784,b,759,a)].
% 3.22/3.46 1398 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(784,b,762,b)].
% 3.22/3.46 1399 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(784,b,763,b)].
% 3.22/3.46 1400 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(784,b,764,b)].
% 3.22/3.46 1401 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(784,b,765,b)].
% 3.22/3.46 1402 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(817,b,812,b)].
% 3.22/3.46 1403 class_Orderings_Oord(tc_IntDef_Oint). [resolve(881,b,853,a)].
% 3.22/3.46 1404 class_Orderings_Oord(tc_nat). [resolve(881,b,854,a)].
% 3.22/3.46 1405 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(881,b,856,b)].
% 3.22/3.46 1406 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(881,b,857,b)].
% 3.22/3.46 1407 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(881,b,858,b)].
% 3.22/3.46 1408 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(881,b,863,b)].
% 3.22/3.46 1409 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(881,b,865,b)].
% 3.22/3.46 1410 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(881,b,866,b)].
% 3.22/3.46 1411 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(881,b,867,b)].
% 3.22/3.46 1412 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(881,b,868,b)].
% 3.22/3.46 1413 class_Orderings_Oord(tc_IntDef_Oint). [resolve(932,b,888,a)].
% 3.22/3.46 1414 class_Orderings_Oord(tc_nat). [resolve(932,b,889,a)].
% 3.22/3.46 1415 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1005,b,969,a)].
% 3.22/3.46 1416 class_Orderings_Oord(tc_nat). [resolve(1005,b,970,a)].
% 3.22/3.46 1417 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1005,b,971,b)].
% 3.22/3.46 1418 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1005,b,973,b)].
% 3.22/3.46 1419 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1005,b,974,b)].
% 3.22/3.46 1420 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1005,b,975,b)].
% 3.22/3.46 1421 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1005,b,976,b)].
% 3.22/3.46 1422 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1064,b,1007,a)].
% 3.22/3.46 1423 class_Orderings_Oord(tc_nat). [resolve(1064,b,1008,a)].
% 3.22/3.46 1424 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1064,b,1010,b)].
% 3.22/3.46 1425 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1064,b,1011,b)].
% 3.22/3.46 1426 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1064,b,1012,b)].
% 3.29/3.49 1427 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1064,b,1013,b)].
% 3.29/3.49 1428 class_Orderings_Oord(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1089,b,1073,b)].
% 3.29/3.49 1429 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1218,b,1144,a)].
% 3.29/3.49 1430 class_Orderings_Oord(tc_nat). [resolve(1218,b,1145,a)].
% 3.29/3.49 1431 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1258,b,1229,b)].
% 3.29/3.49 1432 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1258,b,1230,b)].
% 3.29/3.49 1433 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1258,b,1231,b)].
% 3.29/3.49 1434 class_Orderings_Oord(tc_IntDef_Oint). [resolve(1304,b,1265,a)].
% 3.29/3.49 1435 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1304,b,1271,b)].
% 3.29/3.49 1436 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1304,b,1272,b)].
% 3.29/3.49 1437 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1304,b,1273,b)].
% 3.29/3.49 1438 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1304,b,1274,b)].
% 3.29/3.49 1439 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_10) # label(axiom). [assumption].
% 3.29/3.49 1440 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom). [assumption].
% 3.29/3.49 1441 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom). [assumption].
% 3.29/3.49 1442 -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].
% 3.29/3.49 1443 -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].
% 3.29/3.49 1444 -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].
% 3.29/3.49 1445 -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].
% 3.29/3.49 1446 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(B,B,A). [resolve(9,b,2,a)].
% 3.29/3.49 1447 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(33,a,9,b)].
% 3.29/3.49 1448 -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(34,a,9,b)].
% 3.29/3.49 1449 -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(35,a,9,b)].
% 3.29/3.49 1450 -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(36,a,9,b)].
% 3.29/3.49 1451 -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(37,a,9,b)].
% 3.29/3.49 1452 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(114,b,110,a)].
% 3.29/3.49 1453 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(114,b,111,a)].
% 3.29/3.49 1454 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(293,b,264,b)].
% 3.29/3.49 1455 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(750,b,730,b)].
% 3.29/3.49 1456 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(752,b,730,b)].
% 3.29/3.49 1457 -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(753,c,730,b)].
% 3.29/3.51 1458 -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(754,c,730,b)].
% 3.29/3.51 1459 -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(755,c,730,b)].
% 3.29/3.51 1460 -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(756,c,730,b)].
% 3.29/3.51 1461 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(851,a,827,b)].
% 3.29/3.51 1462 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(878,b,856,b)].
% 3.29/3.51 1463 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(880,b,856,b)].
% 3.29/3.51 1464 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(882,b,856,b)].
% 3.29/3.51 1465 -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(883,c,856,b)].
% 3.29/3.51 1466 -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(884,c,856,b)].
% 3.29/3.51 1467 -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(885,c,856,b)].
% 3.29/3.51 1468 -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(886,c,856,b)].
% 3.29/3.51 1469 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1255,b,1229,b)].
% 3.29/3.51 1470 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__abs(A). [resolve(1256,b,1229,b)].
% 3.29/3.51 1471 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1257,b,1229,b)].
% 3.29/3.51 1472 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__abs(B). [resolve(1259,b,1229,b)].
% 3.29/3.51 1473 -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(1260,c,1229,b)].
% 3.29/3.51 1474 -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(1261,c,1229,b)].
% 3.29/3.51 1475 -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(1262,c,1229,b)].
% 3.29/3.51 1476 -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(1263,c,1229,b)].
% 3.29/3.51 1477 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1354,a,1358,b)].
% 3.29/3.51 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1477,c,1440,a)].
% 3.29/3.51 1478 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1368,a,1358,b)].
% 3.29/3.51 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1478,c,1440,a)].
% 3.29/3.51 1479 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1369,a,1358,b)].
% 3.29/3.51 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1479,c,1440,a)].
% 3.29/3.51 1480 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1370,a,1358,b)].
% 3.29/3.51 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1480,c,1440,a)].
% 3.29/3.51 1481 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1371,a,1358,b)].
% 3.29/3.53 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1481,c,1440,a)].
% 3.29/3.53 1482 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1372,a,1358,b)].
% 3.29/3.53 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1482,c,1440,a)].
% 3.29/3.53 1483 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1373,a,1358,b)].
% 3.29/3.53 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1483,c,1440,a)].
% 3.29/3.53 1484 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__abs(C). [resolve(1374,a,1358,b)].
% 3.29/3.53 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1484,c,1440,a)].
% 3.29/3.53 1485 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_11) # label(axiom). [assumption].
% 3.29/3.53 1486 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom). [assumption].
% 3.29/3.53 1487 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom). [assumption].
% 3.29/3.53 1488 -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].
% 3.29/3.53 1489 -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].
% 3.29/3.53 1490 -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].
% 3.29/3.53 1491 -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].
% 3.29/3.53 1492 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(11,b,2,a)].
% 3.29/3.53 1493 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(33,a,11,b)].
% 3.29/3.53 1494 -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(34,a,11,b)].
% 3.29/3.53 1495 -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(35,a,11,b)].
% 3.29/3.53 1496 -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(36,a,11,b)].
% 3.29/3.53 1497 -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(37,a,11,b)].
% 3.29/3.53 1498 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(116,b,110,a)].
% 3.29/3.53 1499 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(116,b,111,a)].
% 3.29/3.53 1500 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(293,b,266,b)].
% 3.29/3.53 1501 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(750,b,732,b)].
% 3.29/3.53 1502 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(752,b,732,b)].
% 3.29/3.53 1503 -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(753,c,732,b)].
% 3.29/3.53 1504 -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(754,c,732,b)].
% 3.29/3.55 1505 -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(755,c,732,b)].
% 3.29/3.55 1506 -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(756,c,732,b)].
% 3.29/3.55 1507 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(851,a,829,b)].
% 3.29/3.55 1508 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(878,b,858,b)].
% 3.29/3.55 1509 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(880,b,858,b)].
% 3.29/3.55 1510 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(882,b,858,b)].
% 3.29/3.55 1511 -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(883,c,858,b)].
% 3.29/3.55 1512 -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(884,c,858,b)].
% 3.29/3.55 1513 -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(885,c,858,b)].
% 3.29/3.55 1514 -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(886,c,858,b)].
% 3.29/3.55 1515 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1255,b,1231,b)].
% 3.29/3.55 1516 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(1256,b,1231,b)].
% 3.29/3.55 1517 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1257,b,1231,b)].
% 3.29/3.55 1518 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1259,b,1231,b)].
% 3.29/3.55 1519 -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(1260,c,1231,b)].
% 3.29/3.55 1520 -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(1261,c,1231,b)].
% 3.29/3.55 1521 -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(1262,c,1231,b)].
% 3.29/3.55 1522 -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(1263,c,1231,b)].
% 3.29/3.55 1523 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1354,a,1360,b)].
% 3.29/3.55 1524 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1368,a,1360,b)].
% 3.29/3.55 1525 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1369,a,1360,b)].
% 3.29/3.55 1526 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1370,a,1360,b)].
% 3.29/3.55 1527 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1371,a,1360,b)].
% 3.29/3.55 1528 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1372,a,1360,b)].
% 3.29/3.55 1529 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1373,a,1360,b)].
% 3.29/3.55 1530 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1374,a,1360,b)].
% 3.29/3.55 1531 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_11) # label(axiom). [assumption].
% 3.29/3.56 1532 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom). [assumption].
% 3.29/3.56 1533 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom). [assumption].
% 3.29/3.56 1534 -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].
% 3.29/3.56 1535 -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].
% 3.29/3.56 1536 -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].
% 3.29/3.56 1537 -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].
% 3.29/3.56 1538 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(10,b,2,a)].
% 3.29/3.56 1539 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(33,a,10,b)].
% 3.29/3.56 1540 -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(34,a,10,b)].
% 3.29/3.56 1541 -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(35,a,10,b)].
% 3.29/3.56 1542 -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(36,a,10,b)].
% 3.29/3.56 1543 -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(37,a,10,b)].
% 3.29/3.56 1544 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(115,b,110,a)].
% 3.29/3.56 1545 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(115,b,111,a)].
% 3.29/3.56 1546 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(293,b,265,b)].
% 3.29/3.56 1547 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(750,b,731,b)].
% 3.29/3.56 1548 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(752,b,731,b)].
% 3.29/3.56 1549 -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(753,c,731,b)].
% 3.29/3.56 1550 -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(754,c,731,b)].
% 3.29/3.56 1551 -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(755,c,731,b)].
% 3.29/3.56 1552 -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(756,c,731,b)].
% 3.29/3.56 1553 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(851,a,828,b)].
% 3.29/3.56 1554 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(878,b,857,b)].
% 3.29/3.56 1555 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(880,b,857,b)].
% 3.29/3.56 1556 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(882,b,857,b)].
% 3.29/3.56 1557 -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(883,c,857,b)].
% 3.29/3.56 1558 -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(884,c,857,b)].
% 3.39/3.59 1559 -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(885,c,857,b)].
% 3.39/3.59 1560 -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(886,c,857,b)].
% 3.39/3.59 1561 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1255,b,1230,b)].
% 3.39/3.59 1562 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(1256,b,1230,b)].
% 3.39/3.59 1563 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1257,b,1230,b)].
% 3.39/3.59 1564 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1259,b,1230,b)].
% 3.39/3.59 1565 -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(1260,c,1230,b)].
% 3.39/3.59 1566 -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(1261,c,1230,b)].
% 3.39/3.59 1567 -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(1262,c,1230,b)].
% 3.39/3.59 1568 -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(1263,c,1230,b)].
% 3.39/3.59 1569 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1354,a,1359,b)].
% 3.39/3.59 1570 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1368,a,1359,b)].
% 3.39/3.59 1571 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1369,a,1359,b)].
% 3.39/3.59 1572 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1370,a,1359,b)].
% 3.39/3.59 1573 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1371,a,1359,b)].
% 3.39/3.59 1574 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1372,a,1359,b)].
% 3.39/3.59 1575 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1373,a,1359,b)].
% 3.39/3.59 1576 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1374,a,1359,b)].
% 3.39/3.59 1577 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom). [assumption].
% 3.39/3.59 1578 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom). [assumption].
% 3.39/3.59 1579 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_20) # label(axiom). [assumption].
% 3.39/3.59 1580 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom). [assumption].
% 3.39/3.59 1581 -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].
% 3.39/3.59 1582 -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].
% 3.39/3.59 1583 -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].
% 3.39/3.59 1584 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(19,b,2,a)].
% 3.39/3.60 1585 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(33,a,19,b)].
% 3.39/3.60 1586 -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(34,a,19,b)].
% 3.39/3.60 1587 -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(35,a,19,b)].
% 3.39/3.60 1588 -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(36,a,19,b)].
% 3.39/3.60 1589 -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(37,a,19,b)].
% 3.39/3.60 1590 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(38,a,52,b)].
% 3.39/3.60 1591 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(67,a,52,b)].
% 3.39/3.60 1592 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(69,a,52,b)].
% 3.39/3.60 1593 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(182,a,159,b)].
% 3.39/3.60 1594 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(183,a,159,b)].
% 3.39/3.60 1595 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(293,b,278,b)].
% 3.39/3.60 1596 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(354,b,335,b)].
% 3.39/3.60 1597 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(357,b,335,b)].
% 3.39/3.60 1598 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(381,b,366,b)].
% 3.39/3.60 1599 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(389,b,366,b)].
% 3.39/3.60 1600 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(390,b,366,b)].
% 3.39/3.60 1601 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(750,b,735,b)].
% 3.39/3.60 1602 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(752,b,735,b)].
% 3.39/3.60 1603 -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(753,c,735,b)].
% 3.39/3.60 1604 -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(754,c,735,b)].
% 3.39/3.60 1605 -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(755,c,735,b)].
% 3.39/3.60 1606 -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(756,c,735,b)].
% 3.39/3.60 1607 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(879,b,863,b)].
% 3.39/3.60 1608 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(880,b,863,b)].
% 3.39/3.60 1609 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(882,b,863,b)].
% 3.39/3.60 1610 -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(883,c,863,b)].
% 3.39/3.60 1611 -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(884,c,863,b)].
% 3.39/3.60 1612 -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(885,c,863,b)].
% 3.39/3.60 1613 -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(886,c,863,b)].
% 3.39/3.60 1614 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(998,b,971,b)].
% 3.39/3.60 1615 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(999,b,971,b)].
% 3.39/3.61 1616 -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(1000,c,971,b)].
% 3.39/3.61 1617 -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(1001,c,971,b)].
% 3.39/3.61 1618 -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(1002,c,971,b)].
% 3.39/3.61 1619 -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(1003,c,971,b)].
% 3.39/3.61 1620 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1004,b,971,b)].
% 3.39/3.61 1621 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1255,b,1234,b)].
% 3.39/3.61 1622 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1302,b,1271,b)].
% 3.39/3.61 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1622,b,1578,a)].
% 3.39/3.61 1623 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1303,b,1271,b)].
% 3.39/3.61 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1623,b,1578,a)].
% 3.39/3.61 1624 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1305,b,1271,b)].
% 3.39/3.61 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1624,b,1578,a)].
% 3.39/3.61 1625 -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(1306,c,1271,b)].
% 3.39/3.61 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(1625,c,1578,a)].
% 3.39/3.61 1626 -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(1307,c,1271,b)].
% 3.39/3.61 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(1626,c,1578,a)].
% 3.39/3.61 1627 -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(1308,c,1271,b)].
% 3.39/3.61 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(1627,c,1578,a)].
% 3.39/3.61 1628 -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(1309,c,1271,b)].
% 3.39/3.61 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(1628,c,1578,a)].
% 3.39/3.61 1629 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1351,b,1312,b)].
% 3.39/3.61 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1629,b,1578,a)].
% 3.39/3.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1629,b,1581,b)].
% 3.39/3.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1629,b,1582,b)].
% 3.39/3.61 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1629,b,1583,b)].
% 3.39/3.61 1630 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1353,b,1312,b)].
% 3.39/3.61 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1630,b,1578,a)].
% 3.39/3.61 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1630,b,1581,b)].
% 3.39/3.61 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1630,b,1582,b)].
% 3.39/3.61 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1630,b,1583,b)].
% 3.43/3.65 1631 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1354,a,1361,b)].
% 3.43/3.65 1632 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1368,a,1361,b)].
% 3.43/3.65 1633 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1369,a,1361,b)].
% 3.43/3.65 1634 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1370,a,1361,b)].
% 3.43/3.65 1635 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1371,a,1361,b)].
% 3.43/3.65 1636 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1372,a,1361,b)].
% 3.43/3.65 1637 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1373,a,1361,b)].
% 3.43/3.65 1638 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1374,a,1361,b)].
% 3.43/3.65 1639 -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].
% 3.43/3.65 1640 class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_55) # label(axiom). [assumption].
% 3.43/3.65 1641 -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].
% 3.43/3.65 1642 -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].
% 3.43/3.65 1643 -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].
% 3.43/3.65 1644 -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].
% 3.43/3.65 1645 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,B,A). [resolve(23,b,2,a)].
% 3.43/3.65 1646 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(33,a,23,b)].
% 3.43/3.65 1647 -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(34,a,23,b)].
% 3.43/3.65 1648 -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(35,a,23,b)].
% 3.43/3.65 1649 -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(36,a,23,b)].
% 3.43/3.65 1650 -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(37,a,23,b)].
% 3.43/3.65 1651 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(38,a,56,b)].
% 3.43/3.65 1652 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(67,a,56,b)].
% 3.43/3.65 1653 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(69,a,56,b)].
% 3.43/3.65 1654 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(182,a,163,b)].
% 3.43/3.65 1655 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(183,a,163,b)].
% 3.43/3.65 1656 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(293,b,282,b)].
% 3.43/3.65 1657 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(354,b,339,b)].
% 3.43/3.65 1658 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(357,b,339,b)].
% 3.43/3.66 1659 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(381,b,369,b)].
% 3.43/3.66 1660 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(389,b,369,b)].
% 3.43/3.66 1661 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(390,b,369,b)].
% 3.43/3.66 1662 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(750,b,739,b)].
% 3.43/3.66 1663 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(752,b,739,b)].
% 3.43/3.66 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__ring__strict(B). [resolve(753,c,739,b)].
% 3.43/3.66 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__ring__strict(C). [resolve(754,c,739,b)].
% 3.43/3.66 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__ring__strict(B). [resolve(755,c,739,b)].
% 3.43/3.66 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__ring__strict(C). [resolve(756,c,739,b)].
% 3.43/3.66 1668 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(768,a,764,b)].
% 3.43/3.66 1669 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(769,a,764,b)].
% 3.43/3.66 1670 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(770,a,764,b)].
% 3.43/3.66 1671 -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(771,a,764,b)].
% 3.43/3.66 1672 -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(772,a,764,b)].
% 3.43/3.66 1673 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(773,a,764,b)].
% 3.43/3.66 1674 -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(774,a,764,b)].
% 3.43/3.66 1675 -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(775,a,764,b)].
% 3.43/3.66 1676 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(879,b,867,b)].
% 3.43/3.66 1677 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(880,b,867,b)].
% 3.43/3.66 1678 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(882,b,867,b)].
% 3.43/3.66 1679 -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(883,c,867,b)].
% 3.43/3.66 1680 -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(884,c,867,b)].
% 3.43/3.66 1681 -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(885,c,867,b)].
% 3.43/3.66 1682 -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(886,c,867,b)].
% 3.43/3.66 1683 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(929,b,895,b)].
% 3.43/3.66 1684 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(998,b,975,b)].
% 3.43/3.66 1685 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(999,b,975,b)].
% 3.43/3.66 1686 -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(1000,c,975,b)].
% 3.43/3.66 1687 -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(1001,c,975,b)].
% 3.43/3.66 1688 -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(1002,c,975,b)].
% 3.43/3.66 1689 -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(1003,c,975,b)].
% 3.43/3.66 1690 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1004,b,975,b)].
% 3.43/3.66 1691 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1038,c,1012,b)].
% 3.43/3.66 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1691,c,1641,b)].
% 3.43/3.66 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1691,c,1642,b)].
% 3.43/3.66 1692 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1039,c,1012,b)].
% 3.43/3.66 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1692,c,1641,b)].
% 3.43/3.66 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1692,c,1642,b)].
% 3.43/3.66 1693 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1040,c,1012,b)].
% 3.43/3.66 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1693,c,1641,b)].
% 3.43/3.66 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1693,c,1642,b)].
% 3.43/3.66 1694 -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(1041,c,1012,b)].
% 3.43/3.66 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(1694,c,1641,b)].
% 3.43/3.66 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(1694,c,1642,b)].
% 3.43/3.66 1695 -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(1042,c,1012,b)].
% 3.43/3.66 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(1695,c,1641,b)].
% 3.43/3.66 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(1695,c,1642,b)].
% 3.43/3.66 1696 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1043,c,1012,b)].
% 3.43/3.66 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1696,c,1641,b)].
% 3.43/3.66 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1696,c,1642,b)].
% 3.43/3.66 1697 -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(1044,c,1012,b)].
% 3.43/3.66 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(1697,c,1641,b)].
% 3.43/3.67 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(1697,c,1642,b)].
% 3.43/3.67 1698 -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(1045,c,1012,b)].
% 3.43/3.67 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(1698,c,1641,b)].
% 3.43/3.67 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(1698,c,1642,b)].
% 3.43/3.67 1699 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1047,b,1012,b)].
% 3.43/3.67 1700 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1055,b,1012,b)].
% 3.43/3.67 1701 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1057,b,1012,b)].
% 3.43/3.67 1702 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1058,b,1012,b)].
% 3.43/3.67 1703 -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(1059,c,1012,b)].
% 3.43/3.67 1704 -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(1060,c,1012,b)].
% 3.43/3.67 1705 -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(1061,c,1012,b)].
% 3.43/3.67 1706 -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(1062,c,1012,b)].
% 3.43/3.67 1707 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1063,b,1012,b)].
% 3.43/3.67 1708 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1301,b,1274,b)].
% 3.43/3.67 1709 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1302,b,1274,b)].
% 3.43/3.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1709,b,1641,b)].
% 3.43/3.67 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1709,b,1642,b)].
% 3.43/3.67 1710 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1303,b,1274,b)].
% 3.43/3.67 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1710,b,1641,b)].
% 3.43/3.67 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1710,b,1642,b)].
% 3.43/3.67 1711 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1305,b,1274,b)].
% 3.43/3.67 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1711,b,1641,b)].
% 3.43/3.67 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1711,b,1642,b)].
% 3.43/3.67 1712 -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(1306,c,1274,b)].
% 3.43/3.67 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(1712,c,1641,b)].
% 3.43/3.67 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(1712,c,1642,b)].
% 3.43/3.67 1713 -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(1307,c,1274,b)].
% 3.43/3.67 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(1713,c,1641,b)].
% 3.43/3.67 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(1713,c,1642,b)].
% 3.43/3.67 1714 -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(1308,c,1274,b)].
% 3.43/3.67 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(1714,c,1641,b)].
% 3.43/3.67 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(1714,c,1642,b)].
% 3.43/3.67 1715 -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(1309,c,1274,b)].
% 3.43/3.67 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(1715,c,1641,b)].
% 3.43/3.67 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(1715,c,1642,b)].
% 3.43/3.67 1716 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1354,a,1364,b)].
% 3.43/3.67 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1716,c,1641,b)].
% 3.43/3.67 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1716,c,1642,b)].
% 3.43/3.67 1717 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1368,a,1364,b)].
% 3.43/3.67 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1717,c,1641,b)].
% 3.43/3.67 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1717,c,1642,b)].
% 3.43/3.67 1718 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1369,a,1364,b)].
% 3.43/3.67 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1718,c,1641,b)].
% 3.43/3.67 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1718,c,1642,b)].
% 3.43/3.67 1719 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1370,a,1364,b)].
% 3.43/3.67 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1719,c,1641,b)].
% 3.43/3.67 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1719,c,1642,b)].
% 3.43/3.67 1720 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1371,a,1364,b)].
% 3.43/3.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1720,c,1641,b)].
% 3.43/3.67 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1720,c,1642,b)].
% 3.43/3.67 1721 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1372,a,1364,b)].
% 3.43/3.67 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1721,c,1641,b)].
% 3.43/3.67 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1721,c,1642,b)].
% 3.43/3.67 1722 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1373,a,1364,b)].
% 3.43/3.68 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1722,c,1641,b)].
% 3.43/3.68 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1722,c,1642,b)].
% 3.43/3.68 1723 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1374,a,1364,b)].
% 3.43/3.68 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1723,c,1641,b)].
% 3.43/3.68 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1723,c,1642,b)].
% 3.43/3.68 1724 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1629,b,1583,b)].
% 3.43/3.68 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1724,b,1640,a)].
% 3.43/3.68 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1724,b,1641,b)].
% 3.43/3.68 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1724,b,1642,b)].
% 3.43/3.68 1725 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1630,b,1583,b)].
% 3.43/3.68 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1725,b,1640,a)].
% 3.43/3.68 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1725,b,1641,b)].
% 3.43/3.68 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1725,b,1642,b)].
% 3.43/3.68 1726 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_11) # label(axiom). [assumption].
% 3.43/3.68 1727 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom). [assumption].
% 3.43/3.68 1728 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom). [assumption].
% 3.43/3.68 1729 -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].
% 3.43/3.68 1730 -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].
% 3.43/3.68 1731 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom). [assumption].
% 3.43/3.68 1732 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_20) # label(axiom). [assumption].
% 3.43/3.68 1733 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom). [assumption].
% 3.43/3.68 1734 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,B,A). [resolve(24,b,2,a)].
% 3.43/3.68 1735 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(33,a,24,b)].
% 3.43/3.68 1736 -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(34,a,24,b)].
% 3.43/3.68 1737 -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(35,a,24,b)].
% 3.43/3.68 1738 -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(36,a,24,b)].
% 3.43/3.68 1739 -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(37,a,24,b)].
% 3.43/3.68 1740 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(38,a,57,b)].
% 3.43/3.68 1741 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(67,a,57,b)].
% 3.43/3.68 1742 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(69,a,57,b)].
% 3.43/3.69 1743 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(182,a,164,b)].
% 3.43/3.69 1744 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(183,a,164,b)].
% 3.43/3.69 1745 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(206,b,185,a)].
% 3.43/3.69 1746 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(293,b,283,b)].
% 3.43/3.69 1747 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(354,b,340,b)].
% 3.43/3.69 1748 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(357,b,340,b)].
% 3.43/3.69 1749 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(505,b,504,b)].
% 3.43/3.69 1750 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(556,b,545,b)].
% 3.43/3.69 1751 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(557,b,545,b)].
% 3.43/3.69 1752 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(750,b,740,b)].
% 3.43/3.69 1753 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(752,b,740,b)].
% 3.43/3.69 1754 -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(753,c,740,b)].
% 3.43/3.69 1755 -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(754,c,740,b)].
% 3.43/3.69 1756 -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(755,c,740,b)].
% 3.43/3.69 1757 -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(756,c,740,b)].
% 3.43/3.69 1758 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(768,a,765,b)].
% 3.43/3.69 1759 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(769,a,765,b)].
% 3.43/3.69 1760 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(770,a,765,b)].
% 3.43/3.69 1761 -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(771,a,765,b)].
% 3.43/3.69 1762 -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(772,a,765,b)].
% 3.43/3.69 1763 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(773,a,765,b)].
% 3.43/3.69 1764 -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(774,a,765,b)].
% 3.43/3.69 1765 -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(775,a,765,b)].
% 3.43/3.69 1766 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(879,b,868,b)].
% 3.43/3.69 1767 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(880,b,868,b)].
% 3.43/3.69 1768 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(882,b,868,b)].
% 3.43/3.69 1769 -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(883,c,868,b)].
% 3.43/3.69 1770 -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(884,c,868,b)].
% 3.43/3.69 1771 -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(885,c,868,b)].
% 3.43/3.70 1772 -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(886,c,868,b)].
% 3.43/3.70 1773 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(929,b,896,b)].
% 3.43/3.70 1774 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(998,b,976,b)].
% 3.43/3.70 1775 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(999,b,976,b)].
% 3.43/3.70 1776 -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(1000,c,976,b)].
% 3.43/3.70 1777 -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(1001,c,976,b)].
% 3.43/3.70 1778 -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(1002,c,976,b)].
% 3.43/3.70 1779 -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(1003,c,976,b)].
% 3.43/3.70 1780 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1004,b,976,b)].
% 3.43/3.70 1781 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1038,c,1013,b)].
% 3.43/3.70 1782 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1039,c,1013,b)].
% 3.43/3.70 1783 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1040,c,1013,b)].
% 3.43/3.70 1784 -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(1041,c,1013,b)].
% 3.43/3.70 1785 -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(1042,c,1013,b)].
% 3.43/3.70 1786 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1043,c,1013,b)].
% 3.43/3.70 1787 -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(1044,c,1013,b)].
% 3.43/3.70 1788 -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(1045,c,1013,b)].
% 3.43/3.70 1789 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1047,b,1013,b)].
% 3.43/3.70 1790 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1055,b,1013,b)].
% 3.43/3.70 1791 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1057,b,1013,b)].
% 3.43/3.70 1792 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semidom(B). [resolve(1058,b,1013,b)].
% 3.43/3.70 1793 -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(1059,c,1013,b)].
% 3.43/3.70 1794 -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(1060,c,1013,b)].
% 3.43/3.70 1795 -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(1061,c,1013,b)].
% 3.43/3.70 1796 -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(1062,c,1013,b)].
% 3.43/3.70 1797 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1063,b,1013,b)].
% 3.52/3.71 1798 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__semidom(A). [resolve(1142,b,1105,b)].
% 3.52/3.71 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1798,b,1729,b)].
% 3.52/3.71 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1798,b,1730,b)].
% 3.52/3.71 1799 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1354,a,1365,b)].
% 3.52/3.71 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1799,c,1728,a)].
% 3.52/3.71 1800 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1368,a,1365,b)].
% 3.52/3.71 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1800,c,1728,a)].
% 3.52/3.71 1801 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1369,a,1365,b)].
% 3.52/3.71 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1801,c,1728,a)].
% 3.52/3.71 1802 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1370,a,1365,b)].
% 3.52/3.71 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1802,c,1728,a)].
% 3.52/3.71 1803 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1371,a,1365,b)].
% 3.52/3.71 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1803,c,1728,a)].
% 3.52/3.71 1804 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1372,a,1365,b)].
% 3.52/3.71 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1804,c,1728,a)].
% 3.52/3.71 1805 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1373,a,1365,b)].
% 3.52/3.71 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1805,c,1728,a)].
% 3.52/3.71 1806 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semidom(C). [resolve(1374,a,1365,b)].
% 3.52/3.71 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1806,c,1728,a)].
% 3.52/3.71 1807 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom). [assumption].
% 3.52/3.71 1808 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom). [assumption].
% 3.52/3.71 1809 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom). [assumption].
% 3.52/3.71 1810 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom). [assumption].
% 3.52/3.71 1811 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom). [assumption].
% 3.52/3.71 1812 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom). [assumption].
% 3.52/3.71 1813 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__field_2) # label(axiom). [assumption].
% 3.52/3.71 1814 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__idom_57) # label(axiom). [assumption].
% 3.52/3.71 1815 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(38,a,51,b)].
% 3.52/3.71 1816 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(67,a,51,b)].
% 3.52/3.71 1817 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(69,a,51,b)].
% 3.52/3.71 1818 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(182,a,158,b)].
% 3.52/3.71 1819 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(183,a,158,b)].
% 3.52/3.74 1820 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(293,b,277,b)].
% 3.52/3.74 1821 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(354,b,334,b)].
% 3.52/3.74 1822 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(357,b,334,b)].
% 3.52/3.74 1823 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(381,b,365,b)].
% 3.52/3.74 1824 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(389,b,365,b)].
% 3.52/3.74 1825 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(390,b,365,b)].
% 3.52/3.74 1826 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(440,b,432,b)].
% 3.52/3.74 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(1826,b,1809,b)].
% 3.52/3.74 1827 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(505,b,501,b)].
% 3.52/3.74 1828 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(556,b,542,b)].
% 3.52/3.74 1829 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(557,b,542,b)].
% 3.52/3.74 1830 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(603,b,586,b)].
% 3.52/3.74 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(1830,b,1809,b)].
% 3.52/3.74 1831 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(674,b,646,b)].
% 3.52/3.74 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1831,b,1809,b)].
% 3.52/3.74 1832 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(675,b,646,b)].
% 3.52/3.74 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1832,b,1809,b)].
% 3.52/3.74 1833 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_17) # label(axiom). [assumption].
% 3.52/3.74 1834 class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_58) # label(axiom). [assumption].
% 3.52/3.74 1835 -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].
% 3.52/3.74 1836 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_21) # label(axiom). [assumption].
% 3.52/3.74 1837 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_26) # label(axiom). [assumption].
% 3.52/3.74 1838 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_28) # label(axiom). [assumption].
% 3.52/3.74 1839 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(22,b,2,a)].
% 3.52/3.74 1840 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(33,a,22,b)].
% 3.52/3.74 1841 -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(34,a,22,b)].
% 3.52/3.74 1842 -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(35,a,22,b)].
% 3.52/3.74 1843 -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(36,a,22,b)].
% 3.52/3.74 1844 -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(37,a,22,b)].
% 3.52/3.74 1845 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(38,a,55,b)].
% 3.52/3.74 1846 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(67,a,55,b)].
% 3.52/3.74 1847 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(69,a,55,b)].
% 3.52/3.74 1848 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(182,a,162,b)].
% 3.52/3.74 1849 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(183,a,162,b)].
% 3.52/3.74 1850 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(293,b,281,b)].
% 3.52/3.74 1851 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(354,b,338,b)].
% 3.52/3.74 1852 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(357,b,338,b)].
% 3.52/3.74 1853 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(381,b,368,b)].
% 3.52/3.74 1854 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(389,b,368,b)].
% 3.52/3.74 1855 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(390,b,368,b)].
% 3.52/3.74 1856 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(440,b,434,b)].
% 3.52/3.74 1857 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(505,b,503,b)].
% 3.52/3.74 1858 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(556,b,544,b)].
% 3.52/3.74 1859 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(557,b,544,b)].
% 3.52/3.74 1860 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(603,b,588,b)].
% 3.52/3.74 1861 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(674,b,648,b)].
% 3.52/3.74 1862 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(675,b,648,b)].
% 3.52/3.74 1863 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(750,b,738,b)].
% 3.52/3.74 1864 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(752,b,738,b)].
% 3.52/3.74 1865 -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(753,c,738,b)].
% 3.52/3.74 1866 -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(754,c,738,b)].
% 3.52/3.74 1867 -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(755,c,738,b)].
% 3.52/3.74 1868 -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(756,c,738,b)].
% 3.52/3.74 1869 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(768,a,763,b)].
% 3.52/3.74 1870 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(769,a,763,b)].
% 3.52/3.74 1871 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(770,a,763,b)].
% 3.52/3.74 1872 -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(771,a,763,b)].
% 3.52/3.74 1873 -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(772,a,763,b)].
% 3.52/3.74 1874 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(773,a,763,b)].
% 3.52/3.74 1875 -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(774,a,763,b)].
% 3.52/3.74 1876 -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(775,a,763,b)].
% 3.52/3.74 1877 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(879,b,866,b)].
% 3.52/3.74 1878 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(880,b,866,b)].
% 3.52/3.74 1879 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(882,b,866,b)].
% 3.52/3.75 1880 -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(883,c,866,b)].
% 3.52/3.75 1881 -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(884,c,866,b)].
% 3.52/3.75 1882 -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(885,c,866,b)].
% 3.52/3.75 1883 -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(886,c,866,b)].
% 3.52/3.75 1884 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(929,b,894,b)].
% 3.52/3.75 1885 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(998,b,974,b)].
% 3.52/3.75 1886 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(999,b,974,b)].
% 3.52/3.75 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_Oordered__idom(B). [resolve(1000,c,974,b)].
% 3.52/3.75 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_Oordered__idom(C). [resolve(1001,c,974,b)].
% 3.52/3.75 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_Oordered__idom(B). [resolve(1002,c,974,b)].
% 3.52/3.75 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_Oordered__idom(C). [resolve(1003,c,974,b)].
% 3.52/3.75 1891 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1004,b,974,b)].
% 3.52/3.75 1892 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1038,c,1011,b)].
% 3.52/3.75 1893 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1039,c,1011,b)].
% 3.52/3.75 1894 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1040,c,1011,b)].
% 3.52/3.75 1895 -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(1041,c,1011,b)].
% 3.52/3.75 1896 -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(1042,c,1011,b)].
% 3.52/3.75 1897 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1043,c,1011,b)].
% 3.52/3.75 1898 -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(1044,c,1011,b)].
% 3.52/3.75 1899 -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(1045,c,1011,b)].
% 3.52/3.75 1900 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1047,b,1011,b)].
% 3.52/3.75 1901 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1055,b,1011,b)].
% 3.52/3.75 1902 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1057,b,1011,b)].
% 3.52/3.75 1903 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1058,b,1011,b)].
% 3.52/3.75 1904 -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(1059,c,1011,b)].
% 3.52/3.75 1905 -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(1060,c,1011,b)].
% 3.52/3.75 1906 -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(1061,c,1011,b)].
% 3.52/3.75 1907 -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(1062,c,1011,b)].
% 3.52/3.75 1908 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1063,b,1011,b)].
% 3.52/3.75 1909 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1142,b,1104,b)].
% 3.52/3.75 1910 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1301,b,1273,b)].
% 3.52/3.75 1911 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1302,b,1273,b)].
% 3.52/3.75 1912 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1303,b,1273,b)].
% 3.52/3.75 1913 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1305,b,1273,b)].
% 3.52/3.75 1914 -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(1306,c,1273,b)].
% 3.52/3.75 1915 -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(1307,c,1273,b)].
% 3.52/3.75 1916 -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(1308,c,1273,b)].
% 3.52/3.75 1917 -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(1309,c,1273,b)].
% 3.52/3.75 1918 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1354,a,1363,b)].
% 3.52/3.75 1919 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1368,a,1363,b)].
% 3.52/3.75 1920 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1369,a,1363,b)].
% 3.52/3.75 1921 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1370,a,1363,b)].
% 3.52/3.75 1922 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1371,a,1363,b)].
% 3.52/3.75 1923 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1372,a,1363,b)].
% 3.52/3.75 1924 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1373,a,1363,b)].
% 3.52/3.75 1925 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1374,a,1363,b)].
% 3.52/3.75 1926 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1629,b,1582,b)].
% 3.52/3.75 1927 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1630,b,1582,b)].
% 3.52/3.75 1928 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1691,c,1642,b)].
% 3.52/3.75 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1928,c,1834,a)].
% 3.52/3.75 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1928,c,1835,b)].
% 3.52/3.75 1929 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1692,c,1642,b)].
% 3.52/3.75 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1929,c,1834,a)].
% 3.52/3.75 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1929,c,1835,b)].
% 3.52/3.75 1930 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1693,c,1642,b)].
% 3.52/3.75 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1930,c,1834,a)].
% 3.52/3.75 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1930,c,1835,b)].
% 3.52/3.75 1931 -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(1694,c,1642,b)].
% 3.52/3.75 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(1931,c,1834,a)].
% 3.52/3.75 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(1931,c,1835,b)].
% 3.52/3.75 1932 -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(1695,c,1642,b)].
% 3.52/3.75 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1932,c,1834,a)].
% 3.52/3.75 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(1932,c,1835,b)].
% 3.52/3.75 1933 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(1696,c,1642,b)].
% 3.52/3.75 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1933,c,1834,a)].
% 3.52/3.75 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(1933,c,1835,b)].
% 3.52/3.75 1934 -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(1697,c,1642,b)].
% 3.52/3.75 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1934,c,1834,a)].
% 3.52/3.75 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(1934,c,1835,b)].
% 3.52/3.75 1935 -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(1698,c,1642,b)].
% 3.52/3.75 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OlessThan(A,tc_IntDef_Oint),c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1935,c,1834,a)].
% 3.52/3.75 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(1935,c,1835,b)].
% 3.52/3.75 1936 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1709,b,1642,b)].
% 3.52/3.75 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1936,b,1834,a)].
% 3.52/3.75 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1936,b,1835,b)].
% 3.52/3.75 1937 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1710,b,1642,b)].
% 3.52/3.75 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1937,b,1834,a)].
% 3.52/3.75 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1937,b,1835,b)].
% 3.52/3.75 1938 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1711,b,1642,b)].
% 3.52/3.75 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1938,b,1834,a)].
% 3.52/3.75 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1938,b,1835,b)].
% 3.52/3.75 1939 -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(1712,c,1642,b)].
% 3.52/3.75 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(1939,c,1834,a)].
% 3.52/3.75 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(1939,c,1835,b)].
% 3.52/3.75 1940 -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(1713,c,1642,b)].
% 3.52/3.75 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(1940,c,1834,a)].
% 3.52/3.75 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(1940,c,1835,b)].
% 3.52/3.75 1941 -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(1714,c,1642,b)].
% 3.52/3.75 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(1941,c,1834,a)].
% 3.52/3.75 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(1941,c,1835,b)].
% 3.52/3.75 1942 -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(1715,c,1642,b)].
% 3.52/3.75 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(1942,c,1834,a)].
% 3.52/3.75 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(1942,c,1835,b)].
% 3.52/3.75 1943 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1716,c,1642,b)].
% 3.52/3.75 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1943,c,1834,a)].
% 3.52/3.75 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1943,c,1835,b)].
% 3.52/3.75 1944 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1717,c,1642,b)].
% 3.52/3.75 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1944,c,1834,a)].
% 3.52/3.75 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1944,c,1835,b)].
% 3.52/3.75 1945 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1718,c,1642,b)].
% 3.52/3.75 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1945,c,1834,a)].
% 3.52/3.75 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1945,c,1835,b)].
% 3.52/3.75 1946 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1719,c,1642,b)].
% 3.52/3.75 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1946,c,1834,a)].
% 3.52/3.75 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1946,c,1835,b)].
% 3.52/3.75 1947 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1720,c,1642,b)].
% 3.52/3.75 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1947,c,1834,a)].
% 3.52/3.75 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1947,c,1835,b)].
% 3.52/3.75 1948 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1721,c,1642,b)].
% 3.52/3.75 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1948,c,1834,a)].
% 3.59/3.80 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1948,c,1835,b)].
% 3.59/3.80 1949 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1722,c,1642,b)].
% 3.59/3.80 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1949,c,1834,a)].
% 3.59/3.80 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1949,c,1835,b)].
% 3.59/3.80 1950 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1723,c,1642,b)].
% 3.59/3.80 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1950,c,1834,a)].
% 3.59/3.80 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1950,c,1835,b)].
% 3.59/3.80 1951 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1724,b,1642,b)].
% 3.59/3.80 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1951,b,1834,a)].
% 3.59/3.80 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1951,b,1835,b)].
% 3.59/3.80 1952 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1725,b,1642,b)].
% 3.59/3.80 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1952,b,1834,a)].
% 3.59/3.80 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1952,b,1835,b)].
% 3.59/3.80 1953 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1798,b,1730,b)].
% 3.59/3.80 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(1953,b,1834,a)].
% 3.59/3.80 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1953,b,1835,b)].
% 3.59/3.80 1954 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_2) # label(axiom). [assumption].
% 3.59/3.80 1955 class_Numeral_Onumber__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_60) # label(axiom). [assumption].
% 3.59/3.80 1956 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_4) # label(axiom). [assumption].
% 3.59/3.80 1957 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_5) # label(axiom). [assumption].
% 3.59/3.80 1958 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(38,a,41,b)].
% 3.59/3.80 1959 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(69,a,41,b)].
% 3.59/3.80 1960 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(84,a,78,b)].
% 3.59/3.80 1961 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(100,b,78,b)].
% 3.59/3.80 1962 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(103,b,78,b)].
% 3.59/3.80 1963 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(182,a,149,b)].
% 3.59/3.80 1964 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(216,b,188,b)].
% 3.59/3.80 1965 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(389,b,361,b)].
% 3.59/3.80 1966 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(440,b,424,b)].
% 3.59/3.80 1967 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(443,b,424,b)].
% 3.59/3.80 1968 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(453,b,424,b)].
% 3.59/3.80 1969 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(505,b,493,b)].
% 3.59/3.80 1970 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(554,b,532,b)].
% 3.59/3.80 1971 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(556,b,532,b)].
% 3.69/3.92 1972 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(603,b,583,b)].
% 3.69/3.92 1973 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(635,b,609,b)].
% 3.69/3.92 1974 class_OrderedGroup_Osemigroup__mult(A) | -class_Numeral_Onumber__ring(A). [resolve(672,b,640,b)].
% 3.69/3.92 1975 class_OrderedGroup_Oab__semigroup__add(A) | -class_Numeral_Onumber__ring(A). [resolve(674,b,640,b)].
% 3.69/3.92 1976 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Power_Orecpower_6) # label(axiom). [assumption].
% 3.69/3.92 1977 class_Power_Orecpower(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_63) # label(axiom). [assumption].
% 3.69/3.92 1978 class_Power_Orecpower(tc_nat) # label(clsarity_nat_45) # label(axiom). [assumption].
% 3.69/3.92 1979 -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Power_Orecpower_8) # label(axiom). [assumption].
% 3.69/3.92 1980 -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Power_Orecpower_9) # label(axiom). [assumption].
% 3.69/3.92 1981 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(38,a,42,b)].
% 3.69/3.92 1982 class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(69,a,42,b)].
% 3.69/3.92 1983 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Power_Orecpower(A). [resolve(84,a,79,b)].
% 3.69/3.92 1984 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(100,b,79,b)].
% 3.69/3.92 1985 class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(103,b,79,b)].
% 3.69/3.92 1986 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(182,a,150,b)].
% 3.69/3.92 1987 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(216,b,189,b)].
% 3.69/3.92 1988 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(420,b,396,b)].
% 3.69/3.92 1989 class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(505,b,496,b)].
% 3.69/3.92 1990 class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(554,b,533,b)].
% 3.69/3.92 1991 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(556,b,533,b)].
% 3.69/3.92 1992 class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(635,b,610,b)].
% 3.69/3.92 1993 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(32,b,2,a)].
% 3.69/3.92 1994 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom). [assumption].
% 3.69/3.92 1995 -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(33,a,32,b)].
% 3.69/3.92 1996 -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(34,a,32,b)].
% 3.69/3.92 1997 -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(35,a,32,b)].
% 3.69/3.92 1998 -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(36,a,32,b)].
% 3.69/3.92 1999 -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(37,a,32,b)].
% 3.69/3.92 2000 c_lessequals(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(750,b,742,b)].
% 3.69/3.92 2001 -c_less(A,A,B) | -class_Wellfounded__Recursion_Owellorder(B). [resolve(752,b,742,b)].
% 3.69/3.92 2002 -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(753,c,742,b)].
% 3.69/3.92 2003 -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(754,c,742,b)].
% 3.69/3.92 2004 -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(755,c,742,b)].
% 3.69/3.92 2005 -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(756,c,742,b)].
% 3.75/4.02 2006 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(768,a,767,b)].
% 3.75/4.02 2007 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(769,a,767,b)].
% 3.75/4.02 2008 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(770,a,767,b)].
% 3.75/4.02 2009 -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(771,a,767,b)].
% 3.75/4.02 2010 -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(772,a,767,b)].
% 3.75/4.02 2011 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Wellfounded__Recursion_Owellorder(B). [resolve(773,a,767,b)].
% 3.75/4.02 2012 -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(774,a,767,b)].
% 3.75/4.02 2013 -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(775,a,767,b)].
% 3.75/4.02 2014 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1354,a,1367,b)].
% 3.75/4.02 2015 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1368,a,1367,b)].
% 3.75/4.02 2016 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1369,a,1367,b)].
% 3.75/4.02 2017 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1370,a,1367,b)].
% 3.75/4.02 2018 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1371,a,1367,b)].
% 3.75/4.02 2019 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1372,a,1367,b)].
% 3.75/4.02 2020 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1373,a,1367,b)].
% 3.75/4.02 2021 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Wellfounded__Recursion_Owellorder(C). [resolve(1374,a,1367,b)].
% 3.75/4.02 2022 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ofield(A) # label(clsrel_Ring__and__Field_Oordered__field_0) # label(axiom). [assumption].
% 3.75/4.02 2023 -class_Ring__and__Field_Ofield(A) | class_HOL_Oinverse(A) # label(clsrel_Ring__and__Field_Ofield_30) # label(axiom). [assumption].
% 3.75/4.02
% 3.75/4.02 ============================== end predicate elimination =============
% 3.75/4.02
% 3.75/4.02 Auto_denials: (non-Horn, no changes).
% 3.75/4.02
% 3.75/4.02 Term ordering decisions:
% 3.75/4.02 Function symbol KB weights: tc_IntDef_Oint=1. tc_nat=1. tc_Message_Omsg=1. c_List_Olist_ONil=1. c_0=1. c_Finite__Set_OFinites=1. c_emptyset=1. c_Message_Oagent_OSpy=1. tc_Event_Oevent=1. c_Message_OsymKeys=1. c_Wellfounded__Relations_Oless__than=1. c_1=1. c_Event_Obad=1. c_Relation_OId=1. tc_Message_Oagent=1. c_Datatype_Ooption_ONone=1. c_Yahalom_Oyahalom=1. v_A=1. v_evs=1. c_UNIV=1. tc_Product__Type_Ounit=1. tc_bool=1. v_X=1. v_Y=1. c_Extraction_Osumbool_OLeft=1. c_Extraction_Osumbool_ORight=1. c_Message_Oagent_OServer=1. c_Numeral_Obit_OB0=1. c_Numeral_Obit_OB1=1. c_Public_Okeymode_OEncryption=1. c_Public_Okeymode_OSignature=1. c_SetInterval_OatMost=1. c_SetInterval_OatLeast=1. tc_Datatype__Universe_Onode=1. tc_prod=1. c_SetInterval_OlessThan=1. c_SetInterval_OgreaterThan=1. c_Message_Omsg_OMPair=1. c_List_Olists=1. c_uminus=1. c_Message_Omsg_OCrypt=1. c_Public_OpublicKey=1. c_List_Olistrel=1. c_List_Orev=1. c_List_Oset=1. c_Message_OHPair=1. c_Nat_Osize=1. c_Event_Oknows=1. tc_sum=1. c_Datatype_Ooption_OSome=1. c_Event_Oevent_OGets=1. c_List_Oremdups=1. c_Transitive__Closure_Ortrancl=1. c_Union=1. c_Event_Oevent_ONotes=1. c_List_Ochar_OChar=1. c_Pow=1. c_Inter=1. c_Relation_Odiag=1. c_Datatype_Oo2s=1. c_Main_OIdE__1=1. c_Main_Ofinite__Union__1=1. c_Transitive__Closure_Otrancl=1. c_List_Olenlex=1. c_List_Olex=1. c_Main_Omod__eq__0D__dest__1=1. c_Main_Onot__None__eq__iff1__1=1. c_Main_Onot__Some__eq__iff1__1=1. c_Main_Ozmod__eq__0D__dest__1=1. tc_fun=1. tc_set=1. tc_List_Olist=1. c_Message_Osynth=1. c_Message_Oanalz=1. c_Message_Omsg_OKey=1. c_Message_Oparts=1. c_Suc=1. c_Message_Omsg_OHash=1. c_Event_Oused=1. c_Public_OshrK=1. c_IntDef_Oint=1. c_Message_OinvKey=1. c_GCD_Ogcd=1. c_Message_Omsg_ONonce=1. c_Event_OinitState=1. c_Message_Omsg_OAgent=1. c_Message_Omsg_ONumber=1. c_Message_Oagent_OFriend=1. tc_Datatype_Ooption=1. c_insert=1. c_append=1. c_List_Olist_OCons=1. c_Datatype__Universe_OIn0=1. c_Datatype__Universe_OIn1=1. c_union=1. c_Relation_Oconverse=1. c_Event_Oevent_OSays=1. c_minus=1. c_plus=1. c_times=1. c_Sum__Type_OInl=1. c_Sum__Type_OInr=1. c_inter=1. c_Equiv__Relations_Oquotient=1. c_Main_OdiagE__1=1. c_Datatype__Universe_OAtom=1. c_Datatype__Universe_OLeaf=1. c_Datatype__Universe_ONumb=1. c_Divides_Oop_Amod=1. c_Main_OInterI__1=1. c_Main_OUnionE__1=1. c_Main_Oin__listsI__1=1. c_Main_OsubsetI__1=1. c_Relation_ODomain=1. c_Relation_ORange=1. c_SetInterval_OatLeastAtMost=1. c_SetInterval_OatLeastLessThan=1. c_SetInterval_OgreaterThanAtMost=1. c_SetInterval_OgreaterThanLessThan=1. c_Pair=1. c_Datatype__Universe_OScons=1. c_Datatype__Universe_Odsum=1. c_Datatype__Universe_Ousum=1. c_Sum__Type_OPlus=1. c_Relation_OImage=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_Main_OconverseE__1=1. c_Main_OconverseE__2=1. c_Wellfounded__Relations_Olex__prod=1. c_Main_ODomainE__1=1. c_Main_ORangeE__1=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.
% 5.95/6.23
% 5.95/6.23 ============================== end of process initial clauses ========
% 5.95/6.23
% 5.95/6.23 ============================== CLAUSES FOR SEARCH ====================
% 5.95/6.23
% 5.95/6.23 ============================== end of clauses for search =============
% 5.95/6.23
% 5.95/6.23 ============================== SEARCH ================================
% 5.95/6.23
% 5.95/6.23 % Starting search at 2.84 seconds.
% 5.95/6.23
% 5.95/6.23 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 83 (0.00 of 3.09 sec).
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=29.000, iters=3354
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=28.000, iters=3333
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=26.000, iters=3338
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=22.000, iters=3375
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=20.000, iters=3368
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=19.000, iters=3363
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=18.000, iters=3520
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=15.000, iters=3361
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=14.000, iters=3379
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=12.000, iters=3337
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=10.000, iters=3343
% 5.95/6.23
% 5.95/6.23 Low Water (keep): wt=8.000, iters=3333
% 5.95/6.23
% 5.95/6.23 Low Water (displace): id=3517, wt=94.000
% 5.95/6.23
% 5.95/6.23 Low Water (displace): id=6811, wt=91.000
% 5.95/6.23
% 5.95/6.23 Low Water (displace): id=13469, wt=7.000
% 5.95/6.23
% 5.95/6.23 ============================== PROOF =================================
% 5.95/6.23 % SZS status Unsatisfiable
% 5.95/6.23 % SZS output start Refutation
% 5.95/6.23
% 5.95/6.23 % Proof 1 at 4.96 (+ 0.10) seconds.
% 5.95/6.23 % Length of proof is 7.
% 5.95/6.23 % Level of proof is 2.
% 5.95/6.23 % Maximum clause weight is 20.000.
% 5.95/6.23 % Given clauses 4332.
% 5.95/6.23
% 5.95/6.23 2421 -c_in(c_Message_Omsg_OMPair(A,B),c_Message_Oanalz(C),tc_Message_Omsg) | c_in(B,c_Message_Oanalz(C),tc_Message_Omsg) # label(cls_Message_OMPair__analz_0) # label(axiom). [assumption].
% 5.95/6.23 2498 -c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) | -c_in(c_Event_Oevent_OGets(B,C),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent) | c_in(C,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg) # label(cls_Yahalom_OGets__imp__analz__Spy__dest_0) # label(axiom). [assumption].
% 5.95/6.23 2499 c_in(c_Event_Oevent_OGets(v_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),v_Y),v_X)),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 5.95/6.23 2500 c_in(v_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 5.95/6.23 2501 -c_in(v_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 5.95/6.23 3430 c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),v_Y),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg). [resolve(2499,a,2498,b),unit_del(a,2500)].
% 5.95/6.23 15375 $F. [resolve(3430,a,2421,a),unit_del(a,2501)].
% 5.95/6.23
% 5.95/6.23 % SZS output end Refutation
% 5.95/6.23 ============================== end of proof ==========================
% 5.95/6.23
% 5.95/6.23 ============================== STATISTICS ============================
% 5.95/6.23
% 5.95/6.23 Given=4332. Generated=182811. Kept=13249. proofs=1.
% 5.95/6.23 Usable=4330. Sos=8810. Demods=31. Limbo=0, Disabled=3534. Hints=0.
% 5.95/6.23 Megabytes=19.25.
% 5.95/6.23 User_CPU=4.96, System_CPU=0.10, Wall_clock=5.
% 5.95/6.23
% 5.95/6.23 ============================== end of statistics =====================
% 5.95/6.23
% 5.95/6.23 ============================== end of search =========================
% 5.95/6.23
% 5.95/6.23 THEOREM PROVED
% 5.95/6.23 % SZS status Unsatisfiable
% 5.95/6.23
% 5.95/6.23 Exiting with 1 proof.
% 5.95/6.23
% 5.95/6.23 Process 4358 exit (max_proofs) Tue Jun 14 21:04:16 2022
% 5.95/6.23 Prover9 interrupted
%------------------------------------------------------------------------------