TSTP Solution File: LAT268-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT268-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 06:26:36 EDT 2022
% Result : Timeout 300.02s 300.05s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT268-1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 01:57:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.16 ============================== Prover9 ===============================
% 1.93/2.16 Prover9 (32) version 2009-11A, November 2009.
% 1.93/2.16 Process 12205 was started by sandbox2 on n004.cluster.edu,
% 1.93/2.16 Wed Jun 29 01:57:24 2022
% 1.93/2.16 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12052_n004.cluster.edu".
% 1.93/2.16 ============================== end of head ===========================
% 1.93/2.16
% 1.93/2.16 ============================== INPUT =================================
% 1.93/2.16
% 1.93/2.16 % Reading from file /tmp/Prover9_12052_n004.cluster.edu
% 1.93/2.16
% 1.93/2.16 set(prolog_style_variables).
% 1.93/2.16 set(auto2).
% 1.93/2.16 % set(auto2) -> set(auto).
% 1.93/2.16 % set(auto) -> set(auto_inference).
% 1.93/2.16 % set(auto) -> set(auto_setup).
% 1.93/2.16 % set(auto_setup) -> set(predicate_elim).
% 1.93/2.16 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.93/2.16 % set(auto) -> set(auto_limits).
% 1.93/2.16 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.93/2.16 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.93/2.16 % set(auto) -> set(auto_denials).
% 1.93/2.16 % set(auto) -> set(auto_process).
% 1.93/2.16 % set(auto2) -> assign(new_constants, 1).
% 1.93/2.16 % set(auto2) -> assign(fold_denial_max, 3).
% 1.93/2.16 % set(auto2) -> assign(max_weight, "200.000").
% 1.93/2.16 % set(auto2) -> assign(max_hours, 1).
% 1.93/2.16 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.93/2.16 % set(auto2) -> assign(max_seconds, 0).
% 1.93/2.16 % set(auto2) -> assign(max_minutes, 5).
% 1.93/2.16 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.93/2.16 % set(auto2) -> set(sort_initial_sos).
% 1.93/2.16 % set(auto2) -> assign(sos_limit, -1).
% 1.93/2.16 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.93/2.16 % set(auto2) -> assign(max_megs, 400).
% 1.93/2.16 % set(auto2) -> assign(stats, some).
% 1.93/2.16 % set(auto2) -> clear(echo_input).
% 1.93/2.16 % set(auto2) -> set(quiet).
% 1.93/2.16 % set(auto2) -> clear(print_initial_clauses).
% 1.93/2.16 % set(auto2) -> clear(print_given).
% 1.93/2.16 assign(lrs_ticks,-1).
% 1.93/2.16 assign(sos_limit,10000).
% 1.93/2.16 assign(order,kbo).
% 1.93/2.16 set(lex_order_vars).
% 1.93/2.16 clear(print_given).
% 1.93/2.16
% 1.93/2.16 % formulas(sos). % not echoed (2752 formulas)
% 1.93/2.16
% 1.93/2.16 ============================== end of input ==========================
% 1.93/2.16
% 1.93/2.16 % From the command line: assign(max_seconds, 300).
% 1.93/2.16
% 1.93/2.16 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.93/2.16
% 1.93/2.16 % Formulas that are not ordinary clauses:
% 1.93/2.16
% 1.93/2.16 ============================== end of process non-clausal formulas ===
% 1.93/2.16
% 1.93/2.16 ============================== PROCESS INITIAL CLAUSES ===============
% 1.93/2.16
% 1.93/2.16 ============================== PREDICATE ELIMINATION =================
% 1.93/2.16 1 class_Orderings_Olinorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_35) # label(axiom). [assumption].
% 1.93/2.16 2 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset # label(cls_Finite__Set_OMax__ge_0) # label(axiom). [assumption].
% 1.93/2.16 3 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset # label(cls_Finite__Set_OMax__in_0) # label(axiom). [assumption].
% 1.93/2.16 4 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A) # label(cls_Finite__Set_OMax__insert_0) # label(axiom). [assumption].
% 1.93/2.16 5 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset # label(cls_Finite__Set_OMax__le__iff_0) # label(axiom). [assumption].
% 1.93/2.16 6 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__le__iff_1) # label(axiom). [assumption].
% 1.93/2.16 7 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__le__iff_2) # label(axiom). [assumption].
% 1.93/2.16 8 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset # label(cls_Finite__Set_OMax__less__iff_0) # label(axiom). [assumption].
% 1.93/2.16 9 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__less__iff_1) # label(axiom). [assumption].
% 1.93/2.16 10 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset # label(cls_Finite__Set_OMax__less__iff_2) # label(axiom). [assumption].
% 1.93/2.16 11 -class_Orderings_Olinorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B # label(cls_Finite__Set_OMax__singleton_0) # label(axiom). [assumption].
% 1.93/2.16 12 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset # label(cls_Finite__Set_OMin__ge__iff_0) # label(axiom). [assumption].
% 1.93/2.16 13 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__ge__iff_1) # label(axiom). [assumption].
% 1.93/2.16 14 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__ge__iff_2) # label(axiom). [assumption].
% 1.93/2.16 15 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset # label(cls_Finite__Set_OMin__gr__iff_0) # label(axiom). [assumption].
% 1.93/2.16 16 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__gr__iff_1) # label(axiom). [assumption].
% 1.93/2.16 17 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset # label(cls_Finite__Set_OMin__gr__iff_2) # label(axiom). [assumption].
% 1.93/2.16 18 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset # label(cls_Finite__Set_OMin__in_0) # label(axiom). [assumption].
% 1.93/2.16 19 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A) # label(cls_Finite__Set_OMin__insert_0) # label(axiom). [assumption].
% 1.93/2.16 20 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset # label(cls_Finite__Set_OMin__le_0) # label(axiom). [assumption].
% 1.93/2.16 21 -class_Orderings_Olinorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B # label(cls_Finite__Set_OMin__singleton_0) # label(axiom). [assumption].
% 1.93/2.16 22 -class_Orderings_Olinorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset # label(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) # label(axiom). [assumption].
% 1.93/2.16 23 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B # label(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) # label(axiom). [assumption].
% 1.93/2.16 24 -class_Orderings_Olinorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B # label(cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) # label(axiom). [assumption].
% 1.93/2.16 25 -class_OrderedGroup_Opordered__ab__group__add(A) | -class_Orderings_Olinorder(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) # label(cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 1.93/2.16 26 -class_OrderedGroup_Opordered__ab__group__add(A) | -class_Orderings_Olinorder(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) # label(cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 1.93/2.16 27 -class_Orderings_Olinorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A) # label(cls_Orderings_Omax__less__iff__conj_0) # label(axiom). [assumption].
% 1.93/2.16 28 -class_Orderings_Olinorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A) # label(cls_Orderings_Omax__less__iff__conj_1) # label(axiom). [assumption].
% 1.93/2.16 29 -class_Orderings_Olinorder(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A) # label(cls_Orderings_Omax__less__iff__conj_2) # label(axiom). [assumption].
% 1.93/2.16 30 -class_Orderings_Olinorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A) # label(cls_Orderings_Omin__less__iff__conj_0) # label(axiom). [assumption].
% 1.93/2.16 31 -class_Orderings_Olinorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A) # label(cls_Orderings_Omin__less__iff__conj_1) # label(axiom). [assumption].
% 1.93/2.16 32 -class_Orderings_Olinorder(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A) # label(cls_Orderings_Omin__less__iff__conj_2) # label(axiom). [assumption].
% 1.93/2.16 33 -class_Orderings_Olinorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A) # label(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) # label(axiom). [assumption].
% 1.93/2.16 34 -class_Orderings_Olinorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A) # label(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) # label(axiom). [assumption].
% 1.93/2.16 35 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A) # label(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) # label(axiom). [assumption].
% 1.93/2.16 36 -class_Orderings_Olinorder(A) | c_Orderings_Omin(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) # label(axiom). [assumption].
% 1.93/2.16 37 -class_Orderings_Olinorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A) # label(cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) # label(axiom). [assumption].
% 1.93/2.16 38 -class_Orderings_Olinorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) # label(axiom). [assumption].
% 1.93/2.16 39 -class_Orderings_Olinorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) # label(axiom). [assumption].
% 1.93/2.16 40 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A) # label(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) # label(axiom). [assumption].
% 1.93/2.16 41 -class_Orderings_Olinorder(A) | c_Orderings_Omax(B,B,A) = B # label(cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) # label(axiom). [assumption].
% 1.93/2.16 42 -class_Orderings_Olinorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A) # label(cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) # label(axiom). [assumption].
% 1.93/2.16 43 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A) # label(cls_SetInterval_OCompl__atLeast_0) # label(axiom). [assumption].
% 1.93/2.16 44 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A) # label(cls_SetInterval_OCompl__atMost_0) # label(axiom). [assumption].
% 1.93/2.16 45 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A) # label(cls_SetInterval_OCompl__greaterThan_0) # label(axiom). [assumption].
% 1.93/2.16 46 -class_Orderings_Olinorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A) # label(cls_SetInterval_OCompl__lessThan_0) # label(axiom). [assumption].
% 1.93/2.16 47 -class_Orderings_Olinorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C # label(cls_SetInterval_OatLeast__eq__iff_0) # label(axiom). [assumption].
% 1.93/2.16 48 -class_Orderings_Olinorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C # label(cls_SetInterval_OatMost__eq__iff_0) # label(axiom). [assumption].
% 1.93/2.16 49 -class_Orderings_Olinorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C # label(cls_SetInterval_OgreaterThan__eq__iff_0) # label(axiom). [assumption].
% 1.93/2.16 50 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A) # label(cls_SetInterval_OgreaterThan__subset__iff_0) # label(axiom). [assumption].
% 1.93/2.16 51 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)) # label(cls_SetInterval_OgreaterThan__subset__iff_1) # label(axiom). [assumption].
% 1.93/2.16 52 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A) # label(cls_SetInterval_Oivl__diff_0) # label(axiom). [assumption].
% 1.93/2.16 53 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A) # label(cls_SetInterval_Oivl__subset_0) # label(axiom). [assumption].
% 1.93/2.16 54 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A) # label(cls_SetInterval_Oivl__subset_1) # label(axiom). [assumption].
% 1.93/2.16 55 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) # label(cls_SetInterval_Oivl__subset_2) # label(axiom). [assumption].
% 1.93/2.16 56 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)) # label(cls_SetInterval_Oivl__subset_3) # label(axiom). [assumption].
% 1.93/2.16 57 -class_Orderings_Olinorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C # label(cls_SetInterval_OlessThan__eq__iff_0) # label(axiom). [assumption].
% 1.93/2.16 58 -class_Orderings_Olinorder(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A) # label(cls_SetInterval_OlessThan__subset__iff_0) # label(axiom). [assumption].
% 1.93/2.16 59 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) # label(cls_SetInterval_OlessThan__subset__iff_1) # label(axiom). [assumption].
% 1.93/2.16 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) | B = c_emptyset. [resolve(1,a,2,a)].
% 1.93/2.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMax(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,3,a)].
% 1.93/2.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1,a,4,a)].
% 1.93/2.16 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(1,a,5,a)].
% 1.93/2.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,6,a)].
% 1.93/2.16 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,7,a)].
% 1.93/2.16 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(1,a,8,a)].
% 1.93/2.17 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,9,a)].
% 1.93/2.17 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,10,a)].
% 1.93/2.17 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1,a,11,a)].
% 1.93/2.17 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1,a,12,a)].
% 1.93/2.17 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,13,a)].
% 1.93/2.17 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,14,a)].
% 1.93/2.17 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1,a,15,a)].
% 1.93/2.17 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,16,a)].
% 1.93/2.17 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,17,a)].
% 1.93/2.17 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,18,a)].
% 1.93/2.17 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1,a,19,a)].
% 1.93/2.17 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(1,a,20,a)].
% 1.93/2.17 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1,a,21,a)].
% 1.93/2.17 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(1,a,22,a)].
% 1.93/2.17 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1,a,23,a)].
% 1.93/2.17 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(1,a,24,a)].
% 1.93/2.17 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint). [resolve(1,a,25,b)].
% 1.93/2.17 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(1,a,26,b)].
% 1.93/2.17 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1,a,27,a)].
% 1.93/2.17 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(1,a,28,a)].
% 1.93/2.17 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(1,a,29,a)].
% 1.93/2.17 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1,a,30,a)].
% 1.93/2.17 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1,a,31,a)].
% 1.93/2.17 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1,a,32,a)].
% 1.93/2.17 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1,a,33,a)].
% 1.93/2.17 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1,a,34,a)].
% 1.93/2.17 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1,a,35,a)].
% 1.93/2.17 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(1,a,36,a)].
% 1.93/2.17 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(A,B,tc_IntDef_Oint). [resolve(1,a,37,a)].
% 1.93/2.17 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1,a,38,a)].
% 1.93/2.17 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(1,a,39,a)].
% 1.93/2.17 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(1,a,40,a)].
% 1.93/2.17 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(1,a,41,a)].
% 1.93/2.17 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint). [resolve(1,a,42,a)].
% 1.93/2.17 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(1,a,43,a)].
% 1.93/2.17 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(1,a,44,a)].
% 1.93/2.17 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(1,a,45,a)].
% 1.93/2.17 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(1,a,46,a)].
% 1.93/2.17 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(1,a,47,a)].
% 1.93/2.17 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(1,a,48,a)].
% 1.93/2.17 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(1,a,49,a)].
% 1.93/2.17 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(1,a,50,a)].
% 1.93/2.17 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(1,a,51,a)].
% 1.93/2.17 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint). [resolve(1,a,52,a)].
% 1.93/2.17 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1,a,53,a)].
% 1.93/2.17 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,D,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1,a,54,a)].
% 1.93/2.17 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1,a,55,a)].
% 1.93/2.18 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1,a,56,a)].
% 1.93/2.18 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(1,a,57,a)].
% 1.93/2.18 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(1,a,58,a)].
% 1.93/2.18 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(1,a,59,a)].
% 1.93/2.18 60 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat_7) # label(axiom). [assumption].
% 1.93/2.18 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset. [resolve(60,a,2,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(60,a,3,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat). [resolve(60,a,4,a)].
% 1.93/2.18 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset. [resolve(60,a,5,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(60,a,6,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(60,a,7,a)].
% 1.93/2.18 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat) | B = c_emptyset. [resolve(60,a,8,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_nat),A,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(60,a,9,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_nat),B,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(60,a,10,a)].
% 1.93/2.18 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(60,a,11,a)].
% 1.93/2.18 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset. [resolve(60,a,12,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(60,a,13,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(60,a,14,a)].
% 1.93/2.18 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(60,a,15,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(60,a,16,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(60,a,17,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(60,a,18,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_nat),tc_nat). [resolve(60,a,19,a)].
% 1.93/2.18 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset. [resolve(60,a,20,a)].
% 1.93/2.18 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(60,a,21,a)].
% 1.93/2.18 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(A,tc_nat),c_Finite__Set_OMax(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(60,a,22,a)].
% 1.93/2.18 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) = A. [resolve(60,a,23,a)].
% 1.93/2.18 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_nat),tc_nat) = A. [resolve(60,a,24,a)].
% 1.93/2.18 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat). [resolve(60,a,25,b)].
% 1.93/2.18 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat). [resolve(60,a,26,b)].
% 1.93/2.18 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(60,a,27,a)].
% 1.93/2.18 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(60,a,28,a)].
% 1.93/2.18 Derived: -c_less(A,B,tc_nat) | -c_less(C,B,tc_nat) | c_less(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(60,a,29,a)].
% 1.93/2.18 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(60,a,30,a)].
% 1.93/2.18 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(60,a,31,a)].
% 1.93/2.18 Derived: -c_less(A,B,tc_nat) | -c_less(A,C,tc_nat) | c_less(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(60,a,32,a)].
% 1.93/2.18 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(60,a,33,a)].
% 1.93/2.18 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(60,a,34,a)].
% 1.93/2.18 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | c_lessequals(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(60,a,35,a)].
% 1.93/2.18 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(60,a,36,a)].
% 1.93/2.18 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(60,a,37,a)].
% 1.93/2.18 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(60,a,38,a)].
% 1.93/2.18 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(60,a,39,a)].
% 1.93/2.18 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | c_lessequals(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(60,a,40,a)].
% 1.93/2.18 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(60,a,41,a)].
% 1.93/2.18 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(60,a,42,a)].
% 1.93/2.18 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(60,a,43,a)].
% 1.93/2.18 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(60,a,44,a)].
% 1.93/2.18 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(60,a,45,a)].
% 1.93/2.18 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(60,a,46,a)].
% 1.93/2.18 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(60,a,47,a)].
% 1.93/2.18 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(60,a,48,a)].
% 1.93/2.18 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(60,a,49,a)].
% 1.93/2.18 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(60,a,50,a)].
% 1.93/2.20 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(60,a,51,a)].
% 1.93/2.20 Derived: -c_lessequals(A,B,tc_nat) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_nat),c_SetInterval_OatLeastLessThan(A,B,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeastLessThan(B,C,tc_nat). [resolve(60,a,52,a)].
% 1.93/2.20 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(60,a,53,a)].
% 1.93/2.20 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(B,D,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(60,a,54,a)].
% 1.93/2.20 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)). [resolve(60,a,55,a)].
% 1.93/2.20 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)). [resolve(60,a,56,a)].
% 1.93/2.20 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(60,a,57,a)].
% 1.93/2.20 Derived: -c_lessequals(c_SetInterval_OlessThan(A,tc_nat),c_SetInterval_OlessThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(A,B,tc_nat). [resolve(60,a,58,a)].
% 1.93/2.20 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(60,a,59,a)].
% 1.93/2.20 61 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Olinorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) # label(axiom). [assumption].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(61,b,2,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(61,b,3,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(61,b,4,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(61,b,5,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(61,b,6,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(61,b,7,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(61,b,8,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(61,b,9,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(61,b,10,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(61,b,11,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(61,b,12,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(61,b,13,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(61,b,14,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(61,b,15,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(61,b,16,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(61,b,17,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(61,b,18,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(61,b,19,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(61,b,20,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(61,b,21,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(61,b,22,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(61,b,23,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(61,b,24,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(61,b,25,b)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(61,b,26,b)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(61,b,27,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(61,b,28,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(61,b,29,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(61,b,30,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(61,b,31,a)].
% 1.93/2.20 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(61,b,32,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(61,b,33,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(61,b,34,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(61,b,35,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B. [resolve(61,b,36,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(61,b,37,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(61,b,38,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(61,b,39,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(61,b,40,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B. [resolve(61,b,41,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(61,b,42,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(61,b,43,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(61,b,44,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(61,b,45,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(61,b,46,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(61,b,47,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(61,b,48,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(61,b,49,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(61,b,50,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(61,b,51,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(61,b,52,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(61,b,53,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(61,b,54,a)].
% 1.93/2.21 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(61,b,55,a)].
% 2.01/2.24 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(61,b,56,a)].
% 2.01/2.24 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(61,b,57,a)].
% 2.01/2.24 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(61,b,58,a)].
% 2.01/2.24 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(61,b,59,a)].
% 2.01/2.24 62 -class_Orderings_Olinorder(A) | class_LOrder_Olorder(A) # label(clsrel_Orderings_Olinorder_0) # label(axiom). [assumption].
% 2.01/2.24 Derived: class_LOrder_Olorder(tc_IntDef_Oint). [resolve(62,a,1,a)].
% 2.01/2.24 Derived: class_LOrder_Olorder(tc_nat). [resolve(62,a,60,a)].
% 2.01/2.24 Derived: class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(62,a,61,b)].
% 2.01/2.24 63 -class_Orderings_Olinorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Orderings_Olinorder_1) # label(axiom). [assumption].
% 2.01/2.24 Derived: class_LOrder_Ojoin__semilorder(tc_IntDef_Oint). [resolve(63,a,1,a)].
% 2.01/2.24 Derived: class_LOrder_Ojoin__semilorder(tc_nat). [resolve(63,a,60,a)].
% 2.01/2.24 Derived: class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(63,a,61,b)].
% 2.01/2.24 64 -class_Orderings_Olinorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Orderings_Olinorder_2) # label(axiom). [assumption].
% 2.01/2.24 Derived: class_LOrder_Omeet__semilorder(tc_IntDef_Oint). [resolve(64,a,1,a)].
% 2.01/2.24 Derived: class_LOrder_Omeet__semilorder(tc_nat). [resolve(64,a,60,a)].
% 2.01/2.24 Derived: class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(64,a,61,b)].
% 2.01/2.24 65 -class_Orderings_Olinorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Olinorder_3) # label(axiom). [assumption].
% 2.01/2.24 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(65,a,1,a)].
% 2.01/2.24 Derived: class_Orderings_Oord(tc_nat). [resolve(65,a,60,a)].
% 2.01/2.24 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(65,a,61,b)].
% 2.01/2.24 66 -class_Orderings_Olinorder(A) | class_Orderings_Oorder(A) # label(clsrel_Orderings_Olinorder_4) # label(axiom). [assumption].
% 2.01/2.24 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(66,a,1,a)].
% 2.01/2.24 Derived: class_Orderings_Oorder(tc_nat). [resolve(66,a,60,a)].
% 2.01/2.24 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(66,a,61,b)].
% 2.01/2.24 67 -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].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(67,b,2,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(67,b,3,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(67,b,4,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(67,b,5,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(67,b,6,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(67,b,7,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(67,b,8,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(67,b,9,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(67,b,10,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(67,b,11,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(67,b,12,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(67,b,13,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(67,b,14,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(67,b,15,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(67,b,16,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(67,b,17,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(67,b,18,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(67,b,19,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(67,b,20,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(67,b,21,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(67,b,22,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(67,b,23,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(67,b,24,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(67,b,25,b)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(67,b,26,b)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(67,b,27,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(67,b,28,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(67,b,29,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(67,b,30,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(67,b,31,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(67,b,32,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(67,b,33,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(67,b,34,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(67,b,35,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(67,b,36,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(67,b,37,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(67,b,38,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(67,b,39,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(67,b,40,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(67,b,41,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(67,b,42,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(67,b,43,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(67,b,44,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(67,b,45,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(67,b,46,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(67,b,47,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(67,b,48,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(67,b,49,a)].
% 2.01/2.24 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(67,b,50,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(67,b,51,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(67,b,52,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(67,b,53,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(67,b,54,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(67,b,55,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(67,b,56,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(67,b,57,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(67,b,58,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(67,b,59,a)].
% 2.01/2.25 68 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__field_41) # label(axiom). [assumption].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(68,b,2,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(68,b,3,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(68,b,4,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(68,b,5,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(68,b,6,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(68,b,7,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(68,b,8,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(68,b,9,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(68,b,10,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(68,b,11,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(68,b,12,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(68,b,13,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(68,b,14,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(68,b,15,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(68,b,16,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(68,b,17,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(68,b,18,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(68,b,19,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(68,b,20,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(68,b,21,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(68,b,22,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(68,b,23,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(68,b,24,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(68,b,25,b)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(68,b,26,b)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(68,b,27,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(68,b,28,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(68,b,29,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(68,b,30,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(68,b,31,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(68,b,32,a)].
% 2.01/2.25 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(68,b,33,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(68,b,34,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(68,b,35,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omin(B,B,A) = B. [resolve(68,b,36,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(68,b,37,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(68,b,38,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(68,b,39,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(68,b,40,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omax(B,B,A) = B. [resolve(68,b,41,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(68,b,42,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(68,b,43,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(68,b,44,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(68,b,45,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(68,b,46,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(68,b,47,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(68,b,48,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(68,b,49,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(68,b,50,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(68,b,51,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(68,b,52,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(68,b,53,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(68,b,54,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(68,b,55,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(68,b,56,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(68,b,57,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(68,b,58,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(68,b,59,a)].
% 2.01/2.26 69 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_33) # label(axiom). [assumption].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(69,b,2,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(69,b,3,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(69,b,4,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(69,b,5,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(69,b,6,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(69,b,7,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(69,b,8,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(69,b,9,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(69,b,10,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(69,b,11,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(69,b,12,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(69,b,13,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(69,b,14,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(69,b,15,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(69,b,16,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(69,b,17,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(69,b,18,a)].
% 2.01/2.26 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(69,b,19,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(69,b,20,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(69,b,21,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(69,b,22,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(69,b,23,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(69,b,24,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(69,b,25,b)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(69,b,26,b)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(69,b,27,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(69,b,28,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(69,b,29,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(69,b,30,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(69,b,31,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(69,b,32,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(69,b,33,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(69,b,34,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(69,b,35,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(69,b,36,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(69,b,37,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(69,b,38,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(69,b,39,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(69,b,40,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(69,b,41,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(69,b,42,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(69,b,43,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(69,b,44,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(69,b,45,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(69,b,46,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(69,b,47,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(69,b,48,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(69,b,49,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(69,b,50,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(69,b,51,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(69,b,52,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(69,b,53,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(69,b,54,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(69,b,55,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(69,b,56,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(69,b,57,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(69,b,58,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(69,b,59,a)].
% 2.01/2.27 70 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_17) # label(axiom). [assumption].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(70,b,2,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(70,b,3,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(70,b,4,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(70,b,5,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(70,b,6,a)].
% 2.01/2.27 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(70,b,7,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(70,b,8,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(70,b,9,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(70,b,10,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(70,b,11,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(70,b,12,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(70,b,13,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(70,b,14,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(70,b,15,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(70,b,16,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(70,b,17,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(70,b,18,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(70,b,19,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(70,b,20,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(70,b,21,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(70,b,22,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(70,b,23,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(70,b,24,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(70,b,25,b)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(70,b,26,b)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(70,b,27,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(70,b,28,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(70,b,29,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(70,b,30,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(70,b,31,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(70,b,32,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(70,b,33,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(70,b,34,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(70,b,35,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(70,b,36,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(70,b,37,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(70,b,38,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(70,b,39,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(70,b,40,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(70,b,41,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(70,b,42,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(70,b,43,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(70,b,44,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(70,b,45,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(70,b,46,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(70,b,47,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(70,b,48,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(70,b,49,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(70,b,50,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(70,b,51,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(70,b,52,a)].
% 2.01/2.28 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(70,b,53,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(70,b,54,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(70,b,55,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(70,b,56,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(70,b,57,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(70,b,58,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(70,b,59,a)].
% 2.01/2.29 71 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_27) # label(axiom). [assumption].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(71,b,2,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(71,b,3,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(71,b,4,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(71,b,5,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(71,b,6,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(71,b,7,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(71,b,8,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(71,b,9,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(71,b,10,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(71,b,11,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(71,b,12,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(71,b,13,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(71,b,14,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(71,b,15,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(71,b,16,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(71,b,17,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(71,b,18,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(71,b,19,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(71,b,20,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(71,b,21,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(71,b,22,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(71,b,23,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(71,b,24,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(71,b,25,b)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(71,b,26,b)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(71,b,27,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(71,b,28,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(71,b,29,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(71,b,30,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(71,b,31,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(71,b,32,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(71,b,33,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(71,b,34,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(71,b,35,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(71,b,36,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(71,b,37,a)].
% 2.01/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(71,b,38,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(71,b,39,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(71,b,40,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(71,b,41,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(71,b,42,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(71,b,43,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(71,b,44,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(71,b,45,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(71,b,46,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(71,b,47,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(71,b,48,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(71,b,49,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(71,b,50,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(71,b,51,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(71,b,52,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(71,b,53,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(71,b,54,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(71,b,55,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(71,b,56,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(71,b,57,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(71,b,58,a)].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(71,b,59,a)].
% 2.08/2.29 72 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Olinorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_10) # label(axiom). [assumption].
% 2.08/2.29 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(72,b,2,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(72,b,3,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(72,b,4,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(72,b,5,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(72,b,6,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(72,b,7,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(72,b,8,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(72,b,9,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(72,b,10,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(72,b,11,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(72,b,12,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(72,b,13,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(72,b,14,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(72,b,15,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(72,b,16,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(72,b,17,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(72,b,18,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(72,b,19,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(72,b,20,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(72,b,21,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(72,b,22,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(72,b,23,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(72,b,24,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(72,b,25,b)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(72,b,26,b)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(72,b,27,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(72,b,28,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(72,b,29,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(72,b,30,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(72,b,31,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(72,b,32,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(72,b,33,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(72,b,34,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(72,b,35,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(72,b,36,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(72,b,37,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(72,b,38,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(72,b,39,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(72,b,40,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(72,b,41,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(72,b,42,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(72,b,43,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(72,b,44,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(72,b,45,a)].
% 2.08/2.30 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(72,b,46,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(72,b,47,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(72,b,48,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(72,b,49,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(72,b,50,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(72,b,51,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(72,b,52,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(72,b,53,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(72,b,54,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(72,b,55,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(72,b,56,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(72,b,57,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(72,b,58,a)].
% 2.08/2.33 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(72,b,59,a)].
% 2.08/2.33 73 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Olinorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_5) # label(axiom). [assumption].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(73,b,2,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(73,b,3,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(73,b,4,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(73,b,5,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(73,b,6,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(73,b,7,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(73,b,8,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(73,b,9,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(73,b,10,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(73,b,11,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(73,b,12,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(73,b,13,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(73,b,14,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(73,b,15,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(73,b,16,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(73,b,17,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(73,b,18,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(73,b,19,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(73,b,20,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(73,b,21,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(73,b,22,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(73,b,23,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(73,b,24,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(73,b,25,b)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(73,b,26,b)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(73,b,27,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(73,b,28,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(73,b,29,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(73,b,30,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(73,b,31,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(73,b,32,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(73,b,33,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(73,b,34,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(73,b,35,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B. [resolve(73,b,36,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(73,b,37,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(73,b,38,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(73,b,39,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(73,b,40,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B. [resolve(73,b,41,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(73,b,42,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(73,b,43,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(73,b,44,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(73,b,45,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(73,b,46,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(73,b,47,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(73,b,48,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(73,b,49,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(73,b,50,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(73,b,51,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(73,b,52,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(73,b,53,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(73,b,54,a)].
% 2.08/2.33 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(73,b,55,a)].
% 2.21/2.52 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(73,b,56,a)].
% 2.21/2.52 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(73,b,57,a)].
% 2.21/2.52 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(73,b,58,a)].
% 2.21/2.52 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(73,b,59,a)].
% 2.21/2.52 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A). [resolve(73,b,62,a)].
% 2.21/2.52 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A). [resolve(73,b,63,a)].
% 2.21/2.52 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A). [resolve(73,b,64,a)].
% 2.21/2.52 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(73,b,65,a)].
% 2.21/2.52 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A). [resolve(73,b,66,a)].
% 2.21/2.52 74 class_Numeral_Onumber__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_60) # label(axiom). [assumption].
% 2.21/2.52 75 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) = c_1 # label(cls_IntArith_Oabs__minus__one_0) # label(axiom). [assumption].
% 2.21/2.52 76 -class_Numeral_Onumber__ring(A) | -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A),A) = c_1 # label(cls_IntArith_Oabs__power__minus__one_0) # label(axiom). [assumption].
% 2.21/2.52 77 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__10_0) # label(axiom). [assumption].
% 2.21/2.52 78 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__10_1) # label(axiom). [assumption].
% 2.21/2.52 79 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_1,c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__11_0) # label(axiom). [assumption].
% 2.21/2.52 80 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | c_less(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__11_1) # label(axiom). [assumption].
% 2.21/2.52 81 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) # label(cls_IntArith_Oarith__special__12_0) # label(axiom). [assumption].
% 2.21/2.52 82 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_IntArith_Oarith__special__12_1) # label(axiom). [assumption].
% 2.21/2.52 83 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_1,A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) # label(cls_IntArith_Oarith__special__13_0) # label(axiom). [assumption].
% 2.21/2.52 84 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | c_less(c_Numeral_Onumber__of(B,A),c_1,A) # label(cls_IntArith_Oarith__special__13_1) # label(axiom). [assumption].
% 2.21/2.52 85 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__14_0) # label(axiom). [assumption].
% 2.21/2.52 86 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__14_1) # label(axiom). [assumption].
% 2.21/2.52 87 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | -c_lessequals(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__15_0) # label(axiom). [assumption].
% 2.21/2.52 88 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | c_lessequals(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_IntArith_Oarith__special__15_1) # label(axiom). [assumption].
% 2.21/2.52 89 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_IntArith_Oarith__special__16_0) # label(axiom). [assumption].
% 2.21/2.52 90 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_IntArith_Oarith__special__16_1) # label(axiom). [assumption].
% 2.21/2.52 91 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_1,A) # label(cls_IntArith_Oarith__special__17_0) # label(axiom). [assumption].
% 2.21/2.52 92 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_1,A) # label(cls_IntArith_Oarith__special__17_1) # label(axiom). [assumption].
% 2.21/2.52 93 -class_Numeral_Onumber__ring(A) | c_plus(c_1,c_1,A) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),A) # label(cls_IntArith_Oarith__special__1_0) # label(axiom). [assumption].
% 2.21/2.52 94 -class_Numeral_Onumber__ring(A) | c_plus(c_1,c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),B),A) # label(cls_IntArith_Oarith__special__2_0) # label(axiom). [assumption].
% 2.21/2.52 95 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_1,A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),A) # label(cls_IntArith_Oarith__special__3_0) # label(axiom). [assumption].
% 2.21/2.52 96 -class_Numeral_Onumber__ring(A) | c_minus(c_1,c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A) # label(cls_IntArith_Oarith__special__4_0) # label(axiom). [assumption].
% 2.21/2.52 97 -class_Numeral_Onumber__ring(A) | c_minus(c_Numeral_Onumber__of(B,A),c_1,A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A) # label(cls_IntArith_Oarith__special__5_0) # label(axiom). [assumption].
% 2.21/2.52 98 -class_Numeral_Onumber__ring(A) | c_0 != c_Numeral_Onumber__of(B,A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__6_0) # label(axiom). [assumption].
% 2.21/2.52 99 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(B)),A),A) | c_0 = c_Numeral_Onumber__of(B,A) # label(cls_IntArith_Oarith__special__6_1) # label(axiom). [assumption].
% 2.21/2.52 100 -class_Numeral_Onumber__ring(A) | c_1 != c_Numeral_Onumber__of(B,A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) # label(cls_IntArith_Oarith__special__7_0) # label(axiom). [assumption].
% 2.21/2.52 101 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(B)),A),A) | c_1 = c_Numeral_Onumber__of(B,A) # label(cls_IntArith_Oarith__special__7_1) # label(axiom). [assumption].
% 2.21/2.52 102 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(B,A) != c_0 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) # label(cls_IntArith_Oarith__special__8_0) # label(axiom). [assumption].
% 2.21/2.52 103 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OPls)),A),A) | c_Numeral_Onumber__of(B,A) = c_0 # label(cls_IntArith_Oarith__special__8_1) # label(axiom). [assumption].
% 2.21/2.52 104 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(B,A) != c_1 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) # label(cls_IntArith_Oarith__special__9_0) # label(axiom). [assumption].
% 2.21/2.52 105 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),A),A) | c_Numeral_Onumber__of(B,A) = c_1 # label(cls_IntArith_Oarith__special__9_1) # label(axiom). [assumption].
% 2.21/2.52 106 -class_Numeral_Onumber__ring(A) | c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A) = c_Numeral_Onumber__of(c_Numeral_OMin,A) # label(cls_IntArith_Oof__int__m1_0) # label(axiom). [assumption].
% 2.21/2.52 107 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(B,tc_nat),A) = c_0 # label(cls_NatBin_Oof__nat__number__of__eq_0) # label(axiom). [assumption].
% 2.21/2.52 108 -class_Numeral_Onumber__ring(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(B,tc_nat),A) = c_Numeral_Onumber__of(B,A) # label(cls_NatBin_Oof__nat__number__of__eq_1) # label(axiom). [assumption].
% 2.21/2.52 109 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_divide(B,c_Numeral_Onumber__of(c_Numeral_OMin,A),A) = c_uminus(B,A) # label(cls_NatSimprocs_Odivide__minus1_0) # label(axiom). [assumption].
% 2.21/2.52 110 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,A) | c_less(c_0,c_divide(B,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),A),A),A) # label(cls_NatSimprocs_Ohalf__gt__zero_0) # label(axiom). [assumption].
% 2.21/2.52 111 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_uminus(c_divide(c_1,B,A),A) # label(cls_NatSimprocs_Ominus1__divide_0) # label(axiom). [assumption].
% 2.21/2.52 112 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_minus(C,c_Numeral_Onumber__of(D,A),A),A) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(D)),A),C,A) # label(cls_Numeral_Oadd__number__of__diff2_0) # label(axiom). [assumption].
% 2.21/2.52 113 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_plus(c_Numeral_Onumber__of(C,A),D,A),A) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,C),A),D,A) # label(cls_Numeral_Oadd__number__of__left_0) # label(axiom). [assumption].
% 2.21/2.52 114 -class_Numeral_Onumber__ring(A) | c_plus(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,C),A) # label(cls_Numeral_Obin__arith__extra__simps__1_0) # label(axiom). [assumption].
% 2.21/2.52 115 -class_Numeral_Onumber__ring(A) | c_uminus(c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(B),A) # label(cls_Numeral_Obin__arith__extra__simps__2_0) # label(axiom). [assumption].
% 2.21/2.52 116 -class_Numeral_Onumber__ring(A) | c_uminus(c_1,A) = c_Numeral_Onumber__of(c_Numeral_OMin,A) # label(cls_Numeral_Obin__arith__extra__simps__3_0) # label(axiom). [assumption].
% 2.21/2.52 117 -class_Numeral_Onumber__ring(A) | c_times(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(B,C),A) # label(cls_Numeral_Obin__arith__extra__simps__4_0) # label(axiom). [assumption].
% 2.21/2.52 118 -class_Numeral_Onumber__ring(A) | c_minus(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) = c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A) # label(cls_Numeral_Obin__arith__extra__simps__5_0) # label(axiom). [assumption].
% 2.21/2.52 119 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_HOL_Oabs(c_Numeral_Onumber__of(B,A),A) = c_uminus(c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__arith__extra__simps__6_0) # label(axiom). [assumption].
% 2.21/2.52 120 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_HOL_Oabs(c_Numeral_Onumber__of(B,A),A) = c_Numeral_Onumber__of(B,A) # label(cls_Numeral_Obin__arith__extra__simps__6_1) # label(axiom). [assumption].
% 2.21/2.52 121 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) # label(cls_Numeral_Obin__rel__simps__11_0) # label(axiom). [assumption].
% 2.21/2.52 122 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(B,C),A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__12_0) # label(axiom). [assumption].
% 2.21/2.52 123 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(B,C),A),A) # label(cls_Numeral_Obin__rel__simps__12_1) # label(axiom). [assumption].
% 2.21/2.52 124 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__13_0) # label(axiom). [assumption].
% 2.21/2.52 125 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__13_1) # label(axiom). [assumption].
% 2.21/2.52 126 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(B,A) != c_Numeral_Onumber__of(C,A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) # label(cls_Numeral_Obin__rel__simps__1_0) # label(axiom). [assumption].
% 2.21/2.52 127 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | c_Numeral_Onumber__of(B,A) = c_Numeral_Onumber__of(C,A) # label(cls_Numeral_Obin__rel__simps__1_1) # label(axiom). [assumption].
% 2.21/2.52 128 -class_Numeral_Onumber__ring(A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,A),A) # label(cls_Numeral_Obin__rel__simps__2_0) # label(axiom). [assumption].
% 2.21/2.52 129 -class_Numeral_Onumber__ring(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) # label(cls_Numeral_Obin__rel__simps__3_0) # label(axiom). [assumption].
% 2.21/2.52 130 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(B,c_Numeral_Obit_OB0),A),A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(B,A),A) # label(cls_Numeral_Obin__rel__simps__4_0) # label(axiom). [assumption].
% 2.21/2.52 131 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(B,A),A) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(B,c_Numeral_Obit_OB0),A),A) # label(cls_Numeral_Obin__rel__simps__4_1) # label(axiom). [assumption].
% 2.21/2.52 132 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(B,c_Numeral_Obit_OB1),A),A) # label(cls_Numeral_Obin__rel__simps__5_0) # label(axiom). [assumption].
% 2.21/2.52 133 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) # label(cls_Numeral_Obin__rel__simps__6_0) # label(axiom). [assumption].
% 2.21/2.52 134 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(B,c_Numeral_Obin__minus(C)),A),A) | c_less(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(C,A),A) # label(cls_Numeral_Obin__rel__simps__6_1) # label(axiom). [assumption].
% 2.21/2.52 135 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,A),A) # label(cls_Numeral_Obin__rel__simps__7_0) # label(axiom). [assumption].
% 2.21/2.52 136 -class_Numeral_Onumber__ring(A) | c_times(c_uminus(c_Numeral_Onumber__of(B,A),A),C,A) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(B),A),C,A) # label(cls_Numeral_Ominus__number__of__mult_0) # label(axiom). [assumption].
% 2.21/2.52 137 -class_Numeral_Onumber__ring(A) | c_times(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_uminus(B,A) # label(cls_Numeral_Omult__minus1_0) # label(axiom). [assumption].
% 2.21/2.52 138 -class_Numeral_Onumber__ring(A) | c_times(B,c_Numeral_Onumber__of(c_Numeral_OMin,A),A) = c_uminus(B,A) # label(cls_Numeral_Omult__minus1__right_0) # label(axiom). [assumption].
% 2.21/2.52 139 -class_Numeral_Onumber__ring(A) | c_times(c_Numeral_Onumber__of(B,A),c_times(c_Numeral_Onumber__of(C,A),D,A),A) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(B,C),A),D,A) # label(cls_Numeral_Omult__number__of__left_0) # label(axiom). [assumption].
% 2.21/2.52 140 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(c_Numeral_OPls,A) = c_0 # label(cls_Numeral_Onumeral__0__eq__0_0) # label(axiom). [assumption].
% 2.21/2.52 141 -class_Numeral_Onumber__ring(A) | c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),A) = c_1 # label(cls_Numeral_Onumeral__1__eq__1_0) # label(axiom). [assumption].
% 2.21/2.52 142 -class_Numeral_Onumber__ring(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_1 # label(cls_Parity_Oneg__one__even__power_0) # label(axiom). [assumption].
% 2.21/2.52 143 -class_Numeral_Onumber__ring(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,A),B,A) = c_Numeral_Onumber__of(c_Numeral_OMin,A) # label(cls_Parity_Oneg__one__odd__power_0) # label(axiom). [assumption].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_1. [resolve(74,a,75,a)].
% 2.21/2.52 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint) = c_1. [resolve(74,a,76,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,77,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,78,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,79,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,80,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,81,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(74,a,82,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,83,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(74,a,84,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,85,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,86,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,87,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,88,a)].
% 2.21/2.52 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(74,a,89,a)].
% 2.21/2.53 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(74,a,90,a)].
% 2.21/2.53 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(74,a,91,a)].
% 2.21/2.53 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(74,a,92,a)].
% 2.21/2.53 Derived: c_plus(c_1,c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint). [resolve(74,a,93,a)].
% 2.21/2.53 Derived: c_plus(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),A),tc_IntDef_Oint). [resolve(74,a,94,a)].
% 2.21/2.53 Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint). [resolve(74,a,95,a)].
% 2.21/2.53 Derived: c_minus(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint). [resolve(74,a,96,a)].
% 2.21/2.53 Derived: c_minus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint). [resolve(74,a,97,a)].
% 2.21/2.53 Derived: c_0 != c_Numeral_Onumber__of(A,tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,98,a)].
% 2.21/2.53 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_0 = c_Numeral_Onumber__of(A,tc_IntDef_Oint). [resolve(74,a,99,a)].
% 2.21/2.53 Derived: c_1 != c_Numeral_Onumber__of(A,tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,100,a)].
% 2.21/2.53 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(A)),tc_IntDef_Oint),tc_IntDef_Oint) | c_1 = c_Numeral_Onumber__of(A,tc_IntDef_Oint). [resolve(74,a,101,a)].
% 2.21/2.53 Derived: c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_0 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,102,a)].
% 2.21/2.53 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_0. [resolve(74,a,103,a)].
% 2.21/2.53 Derived: c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_1 | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,104,a)].
% 2.21/2.53 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_1. [resolve(74,a,105,a)].
% 2.21/2.53 Derived: c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint). [resolve(74,a,106,a)].
% 2.21/2.53 Derived: -c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint) = c_0. [resolve(74,a,107,a)].
% 2.31/2.53 Derived: c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_NatArith_Oof__nat(c_Numeral_Onumber__of(A,tc_nat),tc_IntDef_Oint) = c_Numeral_Onumber__of(A,tc_IntDef_Oint). [resolve(74,a,108,a)].
% 2.31/2.53 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_divide(A,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(74,a,109,a)].
% 2.31/2.53 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,A,tc_IntDef_Oint) | c_less(c_0,c_divide(A,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,110,a)].
% 2.31/2.53 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_divide(c_1,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,111,a)].
% 2.31/2.53 Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(C)),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(74,a,112,a)].
% 2.31/2.53 Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(B,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,B),tc_IntDef_Oint),C,tc_IntDef_Oint). [resolve(74,a,113,a)].
% 2.31/2.53 Derived: c_plus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,B),tc_IntDef_Oint). [resolve(74,a,114,a)].
% 2.31/2.53 Derived: c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(A),tc_IntDef_Oint). [resolve(74,a,115,a)].
% 2.31/2.53 Derived: c_uminus(c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint). [resolve(74,a,116,a)].
% 2.31/2.53 Derived: c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(A,B),tc_IntDef_Oint). [resolve(74,a,117,a)].
% 2.31/2.53 Derived: c_minus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint). [resolve(74,a,118,a)].
% 2.31/2.53 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_HOL_Oabs(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,119,a)].
% 2.31/2.53 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_HOL_Oabs(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(A,tc_IntDef_Oint). [resolve(74,a,120,a)].
% 2.31/2.53 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,121,a)].
% 2.31/2.53 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(A,B),tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,122,a)].
% 2.31/2.53 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(A,B),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,123,a)].
% 2.31/2.53 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,124,a)].
% 2.31/2.54 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,125,a)].
% 2.31/2.54 Derived: c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_Numeral_Onumber__of(B,tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,126,a)].
% 2.31/2.54 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_Numeral_Onumber__of(B,tc_IntDef_Oint). [resolve(74,a,127,a)].
% 2.31/2.54 Derived: c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,128,a)].
% 2.31/2.54 Derived: -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,129,a)].
% 2.31/2.54 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(A,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,130,a)].
% 2.31/2.54 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(A,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,131,a)].
% 2.31/2.54 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(A,c_Numeral_Obit_OB1),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,132,a)].
% 2.31/2.54 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,133,a)].
% 2.31/2.54 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(A,c_Numeral_Obin__minus(B)),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,134,a)].
% 2.31/2.54 Derived: -class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) | -c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(74,a,135,a)].
% 2.31/2.54 Derived: c_times(c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(A),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(74,a,136,a)].
% 2.31/2.54 Derived: c_times(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(74,a,137,a)].
% 2.31/2.54 Derived: c_times(A,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(74,a,138,a)].
% 2.31/2.54 Derived: c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(B,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(A,B),tc_IntDef_Oint),C,tc_IntDef_Oint). [resolve(74,a,139,a)].
% 2.31/2.54 Derived: c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) = c_0. [resolve(74,a,140,a)].
% 2.31/2.54 Derived: c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_IntDef_Oint) = c_1. [resolve(74,a,141,a)].
% 2.31/2.54 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_1. [resolve(74,a,142,a)].
% 2.31/2.54 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint). [resolve(74,a,143,a)].
% 2.31/2.54 144 -class_Numeral_Onumber__ring(A) | class_HOL_Oplus(A) # label(clsrel_Numeral_Onumber__ring_0) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(144,a,74,a)].
% 2.31/2.54 145 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Numeral_Onumber__ring_1) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(145,a,74,a)].
% 2.31/2.54 146 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Numeral_Onumber__ring_10) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint). [resolve(146,a,74,a)].
% 2.31/2.54 147 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Numeral_Onumber__ring_11) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint). [resolve(147,a,74,a)].
% 2.31/2.54 148 -class_Numeral_Onumber__ring(A) | class_HOL_Ominus(A) # label(clsrel_Numeral_Onumber__ring_12) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(148,a,74,a)].
% 2.31/2.54 149 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_13) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint). [resolve(149,a,74,a)].
% 2.31/2.54 150 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_14) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(150,a,74,a)].
% 2.31/2.54 151 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Numeral_Onumber__ring_15) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(151,a,74,a)].
% 2.31/2.54 152 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_16) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint). [resolve(152,a,74,a)].
% 2.31/2.54 153 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Numeral_Onumber__ring_17) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_Ring__and__Field_Oring(tc_IntDef_Oint). [resolve(153,a,74,a)].
% 2.31/2.54 154 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Numeral_Onumber__ring_18) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint). [resolve(154,a,74,a)].
% 2.31/2.54 155 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Numeral_Onumber__ring_19) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint). [resolve(155,a,74,a)].
% 2.31/2.54 156 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Numeral_Onumber__ring_2) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(156,a,74,a)].
% 2.31/2.54 157 -class_Numeral_Onumber__ring(A) | class_HOL_Oone(A) # label(clsrel_Numeral_Onumber__ring_20) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(157,a,74,a)].
% 2.31/2.54 158 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Numeral_Onumber__ring_21) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint). [resolve(158,a,74,a)].
% 2.31/2.54 159 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Numeral_Onumber__ring_22) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint). [resolve(159,a,74,a)].
% 2.31/2.54 160 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Numeral_Onumber__ring_23) # label(axiom). [assumption].
% 2.31/2.54 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(160,a,74,a)].
% 2.31/2.54 161 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Numeral_Onumber__ring_24) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint). [resolve(161,a,74,a)].
% 2.54/2.79 162 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Numeral_Onumber__ring_25) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint). [resolve(162,a,74,a)].
% 2.54/2.79 163 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_26) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint). [resolve(163,a,74,a)].
% 2.54/2.79 164 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Numeral_Onumber__ring_27) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_Ring__and__Field_Oring__1(tc_IntDef_Oint). [resolve(164,a,74,a)].
% 2.54/2.79 165 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Numeral_Onumber__ring_28) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint). [resolve(165,a,74,a)].
% 2.54/2.79 166 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Numeral_Onumber__ring_29) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint). [resolve(166,a,74,a)].
% 2.54/2.79 167 -class_Numeral_Onumber__ring(A) | class_HOL_Otimes(A) # label(clsrel_Numeral_Onumber__ring_3) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(167,a,74,a)].
% 2.54/2.79 168 -class_Numeral_Onumber__ring(A) | class_Numeral_Onumber(A) # label(clsrel_Numeral_Onumber__ring_30) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_Numeral_Onumber(tc_IntDef_Oint). [resolve(168,a,74,a)].
% 2.54/2.79 169 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_4) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(169,a,74,a)].
% 2.54/2.79 170 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Numeral_Onumber__ring_5) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(170,a,74,a)].
% 2.54/2.79 171 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Numeral_Onumber__ring_6) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_Ring__and__Field_Osemiring(tc_IntDef_Oint). [resolve(171,a,74,a)].
% 2.54/2.79 172 -class_Numeral_Onumber__ring(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Numeral_Onumber__ring_7) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint). [resolve(172,a,74,a)].
% 2.54/2.79 173 -class_Numeral_Onumber__ring(A) | class_HOL_Ozero(A) # label(clsrel_Numeral_Onumber__ring_8) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(173,a,74,a)].
% 2.54/2.79 174 -class_Numeral_Onumber__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Numeral_Onumber__ring_9) # label(axiom). [assumption].
% 2.54/2.79 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(174,a,74,a)].
% 2.54/2.79 175 class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_30) # label(axiom). [assumption].
% 2.54/2.79 176 -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_0,c_IntDef_OInts,A) # label(cls_IntDef_OInts__0_0) # label(axiom). [assumption].
% 2.54/2.79 177 -class_Ring__and__Field_Ocomm__ring__1(A) | c_in(c_1,c_IntDef_OInts,A) # label(cls_IntDef_OInts__1_0) # label(axiom). [assumption].
% 2.54/2.79 178 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_plus(C,B,A),c_IntDef_OInts,A) # label(cls_IntDef_OInts__add_0) # label(axiom). [assumption].
% 2.54/2.79 179 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_minus(C,B,A),c_IntDef_OInts,A) # label(cls_IntDef_OInts__diff_0) # label(axiom). [assumption].
% 2.54/2.79 180 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_OInts,A) | c_in(c_uminus(B,A),c_IntDef_OInts,A) # label(cls_IntDef_OInts__minus_0) # label(axiom). [assumption].
% 2.54/2.79 181 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_times(C,B,A),c_IntDef_OInts,A) # label(cls_IntDef_OInts__mult_0) # label(axiom). [assumption].
% 2.54/2.79 182 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_1,A) = c_1 # label(cls_IntDef_Oof__int__1_0) # label(axiom). [assumption].
% 2.54/2.79 183 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_plus(B,C,tc_IntDef_Oint),A) = c_plus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A) # label(cls_IntDef_Oof__int__add_0) # label(axiom). [assumption].
% 2.54/2.79 184 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_minus(B,C,tc_IntDef_Oint),A) = c_minus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A) # label(cls_IntDef_Oof__int__diff_0) # label(axiom). [assumption].
% 2.54/2.79 185 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_IntDef_Oint(B),A) = c_NatArith_Oof__nat(B,A) # label(cls_IntDef_Oof__int__int__eq_0) # label(axiom). [assumption].
% 2.54/2.79 186 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_uminus(B,tc_IntDef_Oint),A) = c_uminus(c_IntDef_Oof__int(B,A),A) # label(cls_IntDef_Oof__int__minus_0) # label(axiom). [assumption].
% 2.54/2.79 187 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_times(B,C,tc_IntDef_Oint),A) = c_times(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A) # label(cls_IntDef_Oof__int__mult_0) # label(axiom). [assumption].
% 2.54/2.79 188 -class_Ring__and__Field_Ocomm__ring__1(A) | c_IntDef_Oof__int(c_NatArith_Oof__nat(B,tc_IntDef_Oint),A) = c_NatArith_Oof__nat(B,A) # label(cls_IntDef_Oof__int__of__nat__eq_0) # label(axiom). [assumption].
% 2.54/2.79 189 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_lessequals(B,C,tc_nat) | c_NatArith_Oof__nat(c_minus(C,B,tc_nat),A) = c_minus(c_NatArith_Oof__nat(C,A),c_NatArith_Oof__nat(B,A),A) # label(cls_NatArith_Oof__nat__diff_0) # label(axiom). [assumption].
% 2.54/2.79 190 -class_Power_Orecpower(A) | -class_Ring__and__Field_Ocomm__ring__1(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) # label(cls_NatBin_Opower__minus__even_0) # label(axiom). [assumption].
% 2.54/2.79 191 -class_Power_Orecpower(A) | -class_Ring__and__Field_Ocomm__ring__1(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 # label(cls_Parity_Ominus__one__even__power_0) # label(axiom). [assumption].
% 2.54/2.79 192 -class_Power_Orecpower(A) | -class_Ring__and__Field_Ocomm__ring__1(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) # label(cls_Parity_Ominus__one__odd__power_0) # label(axiom). [assumption].
% 2.54/2.79 193 -class_Power_Orecpower(A) | -class_Ring__and__Field_Ocomm__ring__1(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) # label(cls_Parity_Opower__minus__even_0) # label(axiom). [assumption].
% 2.54/2.79 194 -class_Power_Orecpower(A) | -class_Ring__and__Field_Ocomm__ring__1(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) # label(cls_Parity_Opower__minus__odd_0) # label(axiom). [assumption].
% 2.54/2.79 Derived: c_in(c_0,c_IntDef_OInts,tc_IntDef_Oint). [resolve(175,a,176,a)].
% 2.54/2.79 Derived: c_in(c_1,c_IntDef_OInts,tc_IntDef_Oint). [resolve(175,a,177,a)].
% 2.54/2.79 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_plus(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(175,a,178,a)].
% 2.54/2.79 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_minus(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(175,a,179,a)].
% 2.54/2.79 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_uminus(A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(175,a,180,a)].
% 2.54/2.79 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_times(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(175,a,181,a)].
% 2.54/2.82 Derived: c_IntDef_Oof__int(c_1,tc_IntDef_Oint) = c_1. [resolve(175,a,182,a)].
% 2.54/2.82 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(175,a,183,a)].
% 2.54/2.82 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(175,a,184,a)].
% 2.54/2.82 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),tc_IntDef_Oint) = c_NatArith_Oof__nat(A,tc_IntDef_Oint). [resolve(175,a,185,a)].
% 2.54/2.82 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_IntDef_Oof__int(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(175,a,186,a)].
% 2.54/2.82 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(175,a,187,a)].
% 2.54/2.82 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_NatArith_Oof__nat(A,tc_IntDef_Oint). [resolve(175,a,188,a)].
% 2.54/2.82 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),tc_IntDef_Oint) = c_minus(c_NatArith_Oof__nat(B,tc_IntDef_Oint),c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(175,a,189,a)].
% 2.54/2.82 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Nat_Opower(c_uminus(A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),B,tc_nat),tc_IntDef_Oint) = c_Nat_Opower(A,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),B,tc_nat),tc_IntDef_Oint). [resolve(175,a,190,b)].
% 2.54/2.82 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_1. [resolve(175,a,191,b)].
% 2.54/2.82 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint). [resolve(175,a,192,b)].
% 2.54/2.82 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(B,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_Nat_Opower(B,A,tc_IntDef_Oint). [resolve(175,a,193,b)].
% 2.54/2.82 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(B,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_Nat_Opower(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(175,a,194,b)].
% 2.54/2.82 195 -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].
% 2.54/2.82 196 -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].
% 2.54/2.82 197 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_10) # label(axiom). [assumption].
% 2.54/2.82 198 -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].
% 2.54/2.82 199 -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_12) # label(axiom). [assumption].
% 2.54/2.82 200 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_13) # label(axiom). [assumption].
% 2.54/2.82 201 -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_14) # label(axiom). [assumption].
% 2.54/2.82 202 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_15) # label(axiom). [assumption].
% 2.54/2.82 203 -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].
% 2.54/2.83 204 -class_Ring__and__Field_Ocomm__ring__1(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_17) # label(axiom). [assumption].
% 2.54/2.83 205 -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].
% 2.54/2.83 206 -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_19) # label(axiom). [assumption].
% 2.54/2.83 207 -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].
% 2.54/2.83 208 -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].
% 2.54/2.83 209 -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].
% 2.54/2.83 210 -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].
% 2.54/2.83 211 -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].
% 2.54/2.83 212 -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].
% 2.54/2.83 213 -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_25) # label(axiom). [assumption].
% 2.54/2.83 214 -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].
% 2.54/2.83 215 -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].
% 2.54/2.83 216 -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].
% 2.54/2.83 217 -class_Ring__and__Field_Ocomm__ring__1(A) | class_HOL_Ominus(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_3) # label(axiom). [assumption].
% 2.54/2.83 218 -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].
% 2.54/2.83 219 -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].
% 2.54/2.83 220 -class_Ring__and__Field_Ocomm__ring__1(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring__1_6) # label(axiom). [assumption].
% 2.54/2.83 221 -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].
% 2.54/2.83 222 -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].
% 2.54/2.83 223 -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].
% 2.54/2.83 224 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Ofield_0) # label(axiom). [assumption].
% 2.54/2.83 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_0,c_IntDef_OInts,A). [resolve(224,b,176,a)].
% 2.54/2.83 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_1,c_IntDef_OInts,A). [resolve(224,b,177,a)].
% 2.54/2.83 Derived: -class_Ring__and__Field_Ofield(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_plus(C,B,A),c_IntDef_OInts,A). [resolve(224,b,178,a)].
% 2.54/2.83 Derived: -class_Ring__and__Field_Ofield(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_minus(C,B,A),c_IntDef_OInts,A). [resolve(224,b,179,a)].
% 2.54/2.83 Derived: -class_Ring__and__Field_Ofield(A) | -c_in(B,c_IntDef_OInts,A) | c_in(c_uminus(B,A),c_IntDef_OInts,A). [resolve(224,b,180,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_times(C,B,A),c_IntDef_OInts,A). [resolve(224,b,181,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | c_IntDef_Oof__int(c_1,A) = c_1. [resolve(224,b,182,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | c_IntDef_Oof__int(c_plus(B,C,tc_IntDef_Oint),A) = c_plus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(224,b,183,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | c_IntDef_Oof__int(c_minus(B,C,tc_IntDef_Oint),A) = c_minus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(224,b,184,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | c_IntDef_Oof__int(c_IntDef_Oint(B),A) = c_NatArith_Oof__nat(B,A). [resolve(224,b,185,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | c_IntDef_Oof__int(c_uminus(B,tc_IntDef_Oint),A) = c_uminus(c_IntDef_Oof__int(B,A),A). [resolve(224,b,186,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | c_IntDef_Oof__int(c_times(B,C,tc_IntDef_Oint),A) = c_times(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(224,b,187,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | c_IntDef_Oof__int(c_NatArith_Oof__nat(B,tc_IntDef_Oint),A) = c_NatArith_Oof__nat(B,A). [resolve(224,b,188,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | -c_lessequals(B,C,tc_nat) | c_NatArith_Oof__nat(c_minus(C,B,tc_nat),A) = c_minus(c_NatArith_Oof__nat(C,A),c_NatArith_Oof__nat(B,A),A). [resolve(224,b,189,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A). [resolve(224,b,190,b)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1. [resolve(224,b,191,b)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A). [resolve(224,b,192,b)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A). [resolve(224,b,193,b)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Ofield(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A). [resolve(224,b,194,b)].
% 2.54/2.84 225 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring__1(A) # label(clsrel_Ring__and__Field_Oidom_0) # label(axiom). [assumption].
% 2.54/2.84 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_OInts,A). [resolve(225,b,176,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_OInts,A). [resolve(225,b,177,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_plus(C,B,A),c_IntDef_OInts,A). [resolve(225,b,178,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_minus(C,B,A),c_IntDef_OInts,A). [resolve(225,b,179,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_OInts,A) | c_in(c_uminus(B,A),c_IntDef_OInts,A). [resolve(225,b,180,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_times(C,B,A),c_IntDef_OInts,A). [resolve(225,b,181,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_1,A) = c_1. [resolve(225,b,182,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_plus(B,C,tc_IntDef_Oint),A) = c_plus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(225,b,183,a)].
% 2.54/2.84 Derived: -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_minus(B,C,tc_IntDef_Oint),A) = c_minus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(225,b,184,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_IntDef_Oint(B),A) = c_NatArith_Oof__nat(B,A). [resolve(225,b,185,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_uminus(B,tc_IntDef_Oint),A) = c_uminus(c_IntDef_Oof__int(B,A),A). [resolve(225,b,186,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_times(B,C,tc_IntDef_Oint),A) = c_times(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(225,b,187,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_NatArith_Oof__nat(B,tc_IntDef_Oint),A) = c_NatArith_Oof__nat(B,A). [resolve(225,b,188,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oidom(A) | -c_lessequals(B,C,tc_nat) | c_NatArith_Oof__nat(c_minus(C,B,tc_nat),A) = c_minus(c_NatArith_Oof__nat(C,A),c_NatArith_Oof__nat(B,A),A). [resolve(225,b,189,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oidom(A) | -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A). [resolve(225,b,190,b)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oidom(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1. [resolve(225,b,191,b)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oidom(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A). [resolve(225,b,192,b)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oidom(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A). [resolve(225,b,193,b)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oidom(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A). [resolve(225,b,194,b)].
% 2.64/2.85 226 -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].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_0,c_IntDef_OInts,A). [resolve(226,b,176,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_1,c_IntDef_OInts,A). [resolve(226,b,177,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_plus(C,B,A),c_IntDef_OInts,A). [resolve(226,b,178,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_minus(C,B,A),c_IntDef_OInts,A). [resolve(226,b,179,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_IntDef_OInts,A) | c_in(c_uminus(B,A),c_IntDef_OInts,A). [resolve(226,b,180,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_times(C,B,A),c_IntDef_OInts,A). [resolve(226,b,181,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_IntDef_Oof__int(c_1,A) = c_1. [resolve(226,b,182,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_IntDef_Oof__int(c_plus(B,C,tc_IntDef_Oint),A) = c_plus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(226,b,183,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_IntDef_Oof__int(c_minus(B,C,tc_IntDef_Oint),A) = c_minus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(226,b,184,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_IntDef_Oof__int(c_IntDef_Oint(B),A) = c_NatArith_Oof__nat(B,A). [resolve(226,b,185,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_IntDef_Oof__int(c_uminus(B,tc_IntDef_Oint),A) = c_uminus(c_IntDef_Oof__int(B,A),A). [resolve(226,b,186,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_IntDef_Oof__int(c_times(B,C,tc_IntDef_Oint),A) = c_times(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(226,b,187,a)].
% 2.64/2.85 Derived: -class_Ring__and__Field_Oordered__field(A) | c_IntDef_Oof__int(c_NatArith_Oof__nat(B,tc_IntDef_Oint),A) = c_NatArith_Oof__nat(B,A). [resolve(226,b,188,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,tc_nat) | c_NatArith_Oof__nat(c_minus(C,B,tc_nat),A) = c_minus(c_NatArith_Oof__nat(C,A),c_NatArith_Oof__nat(B,A),A). [resolve(226,b,189,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A). [resolve(226,b,190,b)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1. [resolve(226,b,191,b)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A). [resolve(226,b,192,b)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A). [resolve(226,b,193,b)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A). [resolve(226,b,194,b)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring(A). [resolve(226,b,197,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(226,b,198,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(226,b,200,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(226,b,202,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(226,b,203,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(226,b,204,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(226,b,205,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(226,b,208,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(226,b,209,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__1(A). [resolve(226,b,210,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(226,b,211,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A). [resolve(226,b,212,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oone(A). [resolve(226,b,213,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(226,b,215,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(226,b,218,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(226,b,219,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring(A). [resolve(226,b,220,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(226,b,221,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(226,b,222,a)].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__0(A). [resolve(226,b,223,a)].
% 2.64/2.86 227 -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].
% 2.64/2.86 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_0,c_IntDef_OInts,A). [resolve(227,b,176,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_1,c_IntDef_OInts,A). [resolve(227,b,177,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_plus(C,B,A),c_IntDef_OInts,A). [resolve(227,b,178,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_minus(C,B,A),c_IntDef_OInts,A). [resolve(227,b,179,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_IntDef_OInts,A) | c_in(c_uminus(B,A),c_IntDef_OInts,A). [resolve(227,b,180,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_times(C,B,A),c_IntDef_OInts,A). [resolve(227,b,181,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oof__int(c_1,A) = c_1. [resolve(227,b,182,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oof__int(c_plus(B,C,tc_IntDef_Oint),A) = c_plus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(227,b,183,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oof__int(c_minus(B,C,tc_IntDef_Oint),A) = c_minus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(227,b,184,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oof__int(c_IntDef_Oint(B),A) = c_NatArith_Oof__nat(B,A). [resolve(227,b,185,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oof__int(c_uminus(B,tc_IntDef_Oint),A) = c_uminus(c_IntDef_Oof__int(B,A),A). [resolve(227,b,186,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oof__int(c_times(B,C,tc_IntDef_Oint),A) = c_times(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(227,b,187,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oof__int(c_NatArith_Oof__nat(B,tc_IntDef_Oint),A) = c_NatArith_Oof__nat(B,A). [resolve(227,b,188,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,tc_nat) | c_NatArith_Oof__nat(c_minus(C,B,tc_nat),A) = c_minus(c_NatArith_Oof__nat(C,A),c_NatArith_Oof__nat(B,A),A). [resolve(227,b,189,a)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A). [resolve(227,b,190,b)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1. [resolve(227,b,191,b)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A). [resolve(227,b,192,b)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A). [resolve(227,b,193,b)].
% 2.79/3.00 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A). [resolve(227,b,194,b)].
% 2.79/3.00 228 class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint). [resolve(166,a,74,a)].
% 2.79/3.00 Derived: class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint). [resolve(228,a,195,a)].
% 2.79/3.00 Derived: class_Ring__and__Field_Oring(tc_IntDef_Oint). [resolve(228,a,196,a)].
% 2.79/3.00 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(228,a,202,a)].
% 2.79/3.00 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(228,a,203,a)].
% 2.79/3.00 Derived: class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint). [resolve(228,a,204,a)].
% 2.79/3.00 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(228,a,205,a)].
% 2.79/3.00 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(228,a,206,a)].
% 2.79/3.00 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(228,a,207,a)].
% 2.84/3.11 Derived: class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint). [resolve(228,a,208,a)].
% 2.84/3.11 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(228,a,209,a)].
% 2.84/3.11 Derived: class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint). [resolve(228,a,210,a)].
% 2.84/3.11 Derived: class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint). [resolve(228,a,211,a)].
% 2.84/3.11 Derived: class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint). [resolve(228,a,212,a)].
% 2.84/3.11 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(228,a,213,a)].
% 2.84/3.11 Derived: class_Ring__and__Field_Oring__1(tc_IntDef_Oint). [resolve(228,a,214,a)].
% 2.84/3.11 Derived: class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint). [resolve(228,a,215,a)].
% 2.84/3.11 Derived: class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint). [resolve(228,a,216,a)].
% 2.84/3.11 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(228,a,217,a)].
% 2.84/3.11 Derived: class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint). [resolve(228,a,218,a)].
% 2.84/3.11 Derived: class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint). [resolve(228,a,219,a)].
% 2.84/3.11 Derived: class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint). [resolve(228,a,222,a)].
% 2.84/3.11 Derived: class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint). [resolve(228,a,223,a)].
% 2.84/3.11 229 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_29) # label(axiom). [assumption].
% 2.84/3.11 230 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_in(c_0,c_IntDef_ONats,A) # label(cls_IntDef_ONats__0_0) # label(axiom). [assumption].
% 2.84/3.11 231 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_in(c_1,c_IntDef_ONats,A) # label(cls_IntDef_ONats__1_0) # label(axiom). [assumption].
% 2.84/3.11 232 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A) # label(cls_IntDef_ONats__add_0) # label(axiom). [assumption].
% 2.84/3.11 233 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A) # label(cls_IntDef_ONats__mult_0) # label(axiom). [assumption].
% 2.84/3.11 234 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A) # label(cls_IntDef_Oof__nat__in__Nats_0) # label(axiom). [assumption].
% 2.84/3.11 235 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A) # label(cls_NatArith_Oof__nat_Oof__nat__Suc_0) # label(axiom). [assumption].
% 2.84/3.11 236 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_1,A) = c_1 # label(cls_NatArith_Oof__nat__1_0) # label(axiom). [assumption].
% 2.84/3.11 237 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__add_0) # label(axiom). [assumption].
% 2.84/3.11 238 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__mult_0) # label(axiom). [assumption].
% 2.84/3.11 239 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -c_IntDef_Oiszero(c_1,A) # label(cls_Numeral_Obin__rel__simps__10_0) # label(axiom). [assumption].
% 2.84/3.11 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(229,a,230,a)].
% 2.84/3.11 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(229,a,231,a)].
% 2.84/3.11 Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_plus(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(229,a,232,a)].
% 2.84/3.11 Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_times(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(229,a,233,a)].
% 2.84/3.11 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(229,a,234,a)].
% 2.84/3.11 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(229,a,235,a)].
% 2.84/3.13 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(229,a,236,a)].
% 2.84/3.13 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(229,a,237,a)].
% 2.84/3.13 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_IntDef_Oint) = c_times(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(229,a,238,a)].
% 2.84/3.13 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(229,a,239,a)].
% 2.84/3.13 240 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) # label(clsarity_nat_32) # label(axiom). [assumption].
% 2.84/3.13 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(240,a,230,a)].
% 2.84/3.13 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(240,a,231,a)].
% 2.84/3.13 Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_plus(B,A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(240,a,232,a)].
% 2.84/3.13 Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_times(B,A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(240,a,233,a)].
% 2.84/3.13 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(240,a,234,a)].
% 2.84/3.13 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat). [resolve(240,a,235,a)].
% 2.84/3.13 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(240,a,236,a)].
% 2.84/3.13 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(240,a,237,a)].
% 2.84/3.13 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_nat) = c_times(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(240,a,238,a)].
% 2.84/3.13 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(240,a,239,a)].
% 2.84/3.13 241 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1__cancel(A) # label(clsrel_Power_Orecpower_24) # label(axiom). [assumption].
% 2.84/3.13 Derived: -class_Power_Orecpower(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(241,b,230,a)].
% 2.84/3.13 Derived: -class_Power_Orecpower(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(241,b,231,a)].
% 2.84/3.13 Derived: -class_Power_Orecpower(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(241,b,232,a)].
% 2.84/3.13 Derived: -class_Power_Orecpower(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(241,b,233,a)].
% 2.84/3.13 Derived: -class_Power_Orecpower(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(241,b,234,a)].
% 2.84/3.13 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(241,b,235,a)].
% 2.84/3.13 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(241,b,236,a)].
% 2.84/3.13 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(241,b,237,a)].
% 2.84/3.13 Derived: -class_Power_Orecpower(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(241,b,238,a)].
% 2.84/3.13 Derived: -class_Power_Orecpower(A) | -c_IntDef_Oiszero(c_1,A). [resolve(241,b,239,a)].
% 2.84/3.13 242 -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].
% 2.84/3.13 Derived: class_Ring__and__Field_Ocomm__semiring__1(tc_nat). [resolve(242,a,240,a)].
% 2.84/3.13 Derived: class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Power_Orecpower(A). [resolve(242,a,241,b)].
% 2.84/3.13 243 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) # label(axiom). [assumption].
% 2.84/3.13 Derived: class_Ring__and__Field_Ocomm__semiring__0(tc_nat). [resolve(243,a,240,a)].
% 2.84/3.13 Derived: class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Orecpower(A). [resolve(243,a,241,b)].
% 2.84/3.13 244 -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].
% 2.84/3.14 Derived: class_HOL_Ozero(tc_nat). [resolve(244,a,240,a)].
% 2.84/3.14 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(244,a,241,b)].
% 2.84/3.14 245 -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].
% 2.84/3.14 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(245,a,240,a)].
% 2.84/3.14 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(245,a,241,b)].
% 2.84/3.14 246 -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].
% 2.84/3.14 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(246,a,240,a)].
% 2.84/3.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(246,a,241,b)].
% 2.84/3.14 247 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) # label(axiom). [assumption].
% 2.84/3.14 Derived: class_HOL_Oplus(tc_nat). [resolve(247,a,240,a)].
% 2.84/3.14 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(247,a,241,b)].
% 2.84/3.14 248 -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].
% 2.84/3.14 Derived: class_OrderedGroup_Omonoid__mult(tc_nat). [resolve(248,a,240,a)].
% 2.84/3.14 Derived: class_OrderedGroup_Omonoid__mult(A) | -class_Power_Orecpower(A). [resolve(248,a,241,b)].
% 2.84/3.14 249 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) # label(axiom). [assumption].
% 2.84/3.14 Derived: class_HOL_Oone(tc_nat). [resolve(249,a,240,a)].
% 2.84/3.14 Derived: class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(249,a,241,b)].
% 2.84/3.14 250 -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].
% 2.84/3.14 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(250,a,240,a)].
% 2.84/3.14 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(250,a,241,b)].
% 2.84/3.14 251 -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].
% 2.84/3.14 Derived: class_HOL_Otimes(tc_nat). [resolve(251,a,240,a)].
% 2.84/3.14 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(251,a,241,b)].
% 2.84/3.14 252 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) # label(axiom). [assumption].
% 2.84/3.14 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat). [resolve(252,a,240,a)].
% 2.84/3.14 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(252,a,241,b)].
% 2.84/3.14 253 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) # label(axiom). [assumption].
% 2.84/3.14 Derived: class_OrderedGroup_Ocancel__semigroup__add(tc_nat). [resolve(253,a,240,a)].
% 2.84/3.14 Derived: class_OrderedGroup_Ocancel__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(253,a,241,b)].
% 2.84/3.14 254 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) # label(axiom). [assumption].
% 2.84/3.14 Derived: class_Ring__and__Field_Ocomm__semiring(tc_nat). [resolve(254,a,240,a)].
% 2.84/3.14 Derived: class_Ring__and__Field_Ocomm__semiring(A) | -class_Power_Orecpower(A). [resolve(254,a,241,b)].
% 2.84/3.14 255 -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].
% 2.84/3.14 Derived: class_Ring__and__Field_Osemiring__1__cancel(tc_nat). [resolve(255,a,240,a)].
% 2.94/3.15 Derived: class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Power_Orecpower(A). [resolve(255,a,241,b)].
% 2.94/3.15 256 -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].
% 2.94/3.15 Derived: class_Ring__and__Field_Osemiring__0__cancel(tc_nat). [resolve(256,a,240,a)].
% 2.94/3.15 Derived: class_Ring__and__Field_Osemiring__0__cancel(A) | -class_Power_Orecpower(A). [resolve(256,a,241,b)].
% 2.94/3.15 257 -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].
% 2.94/3.15 Derived: class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat). [resolve(257,a,240,a)].
% 2.94/3.15 Derived: class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Power_Orecpower(A). [resolve(257,a,241,b)].
% 2.94/3.15 258 -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].
% 2.94/3.15 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_nat). [resolve(258,a,240,a)].
% 2.94/3.15 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Power_Orecpower(A). [resolve(258,a,241,b)].
% 2.94/3.15 259 -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].
% 2.94/3.15 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(259,a,240,a)].
% 2.94/3.15 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Power_Orecpower(A). [resolve(259,a,241,b)].
% 2.94/3.15 260 -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].
% 2.94/3.15 Derived: class_Ring__and__Field_Osemiring__1(tc_nat). [resolve(260,a,240,a)].
% 2.94/3.15 Derived: class_Ring__and__Field_Osemiring__1(A) | -class_Power_Orecpower(A). [resolve(260,a,241,b)].
% 2.94/3.15 261 -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].
% 2.94/3.15 Derived: class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat). [resolve(261,a,240,a)].
% 2.94/3.15 Derived: class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_Power_Orecpower(A). [resolve(261,a,241,b)].
% 2.94/3.15 262 -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].
% 2.94/3.15 Derived: class_Ring__and__Field_Osemiring__0(tc_nat). [resolve(262,a,240,a)].
% 2.94/3.15 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Power_Orecpower(A). [resolve(262,a,241,b)].
% 2.94/3.15 263 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) # label(axiom). [assumption].
% 2.94/3.15 Derived: class_Ring__and__Field_Osemiring(tc_nat). [resolve(263,a,240,a)].
% 2.94/3.15 Derived: class_Ring__and__Field_Osemiring(A) | -class_Power_Orecpower(A). [resolve(263,a,241,b)].
% 2.94/3.15 264 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) # label(axiom). [assumption].
% 2.94/3.15 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(264,a,240,a)].
% 2.94/3.15 Derived: class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A). [resolve(264,a,241,b)].
% 2.94/3.15 265 -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].
% 2.94/3.15 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(265,b,230,a)].
% 2.94/3.15 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(265,b,231,a)].
% 2.94/3.15 Derived: -class_Ring__and__Field_Ofield(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(265,b,232,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(265,b,233,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(265,b,234,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(265,b,235,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(265,b,236,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(265,b,237,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(265,b,238,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | -c_IntDef_Oiszero(c_1,A). [resolve(265,b,239,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(265,b,243,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_HOL_Ozero(A). [resolve(265,b,244,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(265,b,245,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(265,b,246,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_HOL_Oplus(A). [resolve(265,b,247,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A). [resolve(265,b,248,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_HOL_Oone(A). [resolve(265,b,249,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(265,b,250,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_HOL_Otimes(A). [resolve(265,b,251,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(265,b,252,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(265,b,253,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A). [resolve(265,b,254,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(265,b,256,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(265,b,257,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(265,b,259,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A). [resolve(265,b,260,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(265,b,261,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A). [resolve(265,b,262,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring(A). [resolve(265,b,263,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(265,b,264,a)].
% 2.94/3.16 266 -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].
% 2.94/3.16 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(266,b,230,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(266,b,231,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(266,b,232,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(266,b,233,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(266,b,234,a)].
% 2.94/3.16 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(266,b,235,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(266,b,236,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(266,b,237,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(266,b,238,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(266,b,239,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(266,b,243,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_HOL_Ozero(A). [resolve(266,b,244,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(266,b,245,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(266,b,246,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_HOL_Oplus(A). [resolve(266,b,247,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A). [resolve(266,b,248,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A). [resolve(266,b,249,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(266,b,250,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_HOL_Otimes(A). [resolve(266,b,251,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(266,b,252,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(266,b,253,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A). [resolve(266,b,254,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(266,b,256,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(266,b,257,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(266,b,259,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A). [resolve(266,b,260,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(266,b,261,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A). [resolve(266,b,262,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A). [resolve(266,b,263,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(266,b,264,a)].
% 2.94/3.17 267 -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].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(267,b,230,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(267,b,231,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(267,b,232,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(267,b,233,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oordered__field(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(267,b,234,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(267,b,235,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(267,b,236,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(267,b,237,a)].
% 2.94/3.17 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(267,b,238,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_IntDef_Oiszero(c_1,A). [resolve(267,b,239,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Ozero(A). [resolve(267,b,244,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(267,b,247,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Otimes(A). [resolve(267,b,251,a)].
% 2.94/3.18 268 -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].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(268,b,230,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(268,b,231,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(268,b,232,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(268,b,233,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(268,b,234,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(268,b,235,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(268,b,236,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(268,b,237,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(268,b,238,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(268,b,239,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(268,b,243,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ozero(A). [resolve(268,b,244,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(268,b,245,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(268,b,246,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(268,b,247,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A). [resolve(268,b,248,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oone(A). [resolve(268,b,249,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(268,b,250,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Otimes(A). [resolve(268,b,251,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(268,b,252,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(268,b,253,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring(A). [resolve(268,b,254,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(268,b,256,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(268,b,257,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(268,b,259,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__1(A). [resolve(268,b,260,a)].
% 2.94/3.18 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(268,b,261,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__0(A). [resolve(268,b,262,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring(A). [resolve(268,b,263,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(268,b,264,a)].
% 3.15/3.42 269 -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].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(269,b,230,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(269,b,231,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(269,b,232,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(269,b,233,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(269,b,234,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(269,b,235,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(269,b,236,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(269,b,237,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(269,b,238,a)].
% 3.15/3.42 Derived: -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(269,b,239,a)].
% 3.15/3.42 270 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint). [resolve(165,a,74,a)].
% 3.15/3.42 271 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint). [resolve(228,a,216,a)].
% 3.15/3.42 Derived: class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint). [resolve(271,a,242,a)].
% 3.15/3.42 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(271,a,244,a)].
% 3.15/3.42 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(271,a,245,a)].
% 3.15/3.42 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(271,a,246,a)].
% 3.15/3.42 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(271,a,247,a)].
% 3.15/3.42 Derived: class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint). [resolve(271,a,248,a)].
% 3.15/3.42 Derived: class_HOL_Oone(tc_IntDef_Oint). [resolve(271,a,249,a)].
% 3.15/3.42 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(271,a,250,a)].
% 3.15/3.42 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(271,a,251,a)].
% 3.15/3.42 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(271,a,252,a)].
% 3.15/3.42 Derived: class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint). [resolve(271,a,253,a)].
% 3.15/3.42 Derived: class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint). [resolve(271,a,254,a)].
% 3.15/3.42 Derived: class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint). [resolve(271,a,255,a)].
% 3.15/3.42 Derived: class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(271,a,258,a)].
% 3.15/3.42 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(271,a,259,a)].
% 3.15/3.42 Derived: class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint). [resolve(271,a,260,a)].
% 3.15/3.42 Derived: class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint). [resolve(271,a,261,a)].
% 3.15/3.42 Derived: class_Ring__and__Field_Osemiring(tc_IntDef_Oint). [resolve(271,a,263,a)].
% 3.15/3.42 Derived: class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(271,a,264,a)].
% 3.15/3.42 272 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_33) # label(axiom). [assumption].
% 3.15/3.42 273 -class_LOrder_Ojoin__semilorder(A) | c_LOrder_Ojoin(B,B,A) = B # label(cls_LOrder_Ojoin__idempotent_0) # label(axiom). [assumption].
% 3.15/3.42 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(272,a,273,a)].
% 3.23/3.48 274 class_LOrder_Ojoin__semilorder(tc_nat) # label(clsarity_nat_5) # label(axiom). [assumption].
% 3.23/3.48 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(274,a,273,a)].
% 3.23/3.48 275 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Ojoin__semilorder_0) # label(axiom). [assumption].
% 3.23/3.48 276 -class_LOrder_Ojoin__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Ojoin__semilorder_1) # label(axiom). [assumption].
% 3.23/3.48 277 -class_LOrder_Olorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_LOrder_Olorder_3) # label(axiom). [assumption].
% 3.23/3.48 Derived: -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(277,b,273,a)].
% 3.23/3.48 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(277,b,275,a)].
% 3.23/3.48 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oorder(A). [resolve(277,b,276,a)].
% 3.23/3.48 278 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_16) # label(axiom). [assumption].
% 3.23/3.48 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(278,b,273,a)].
% 3.23/3.48 279 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_15) # label(axiom). [assumption].
% 3.23/3.48 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(279,b,273,a)].
% 3.23/3.48 280 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_15) # label(axiom). [assumption].
% 3.23/3.48 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(280,b,273,a)].
% 3.23/3.48 281 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_18) # label(axiom). [assumption].
% 3.23/3.48 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(281,b,273,a)].
% 3.23/3.48 282 -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].
% 3.23/3.48 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(282,b,273,a)].
% 3.23/3.48 283 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_27) # label(axiom). [assumption].
% 3.23/3.48 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(283,b,273,a)].
% 3.23/3.48 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(283,b,275,a)].
% 3.23/3.48 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A). [resolve(283,b,276,a)].
% 3.23/3.48 284 -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].
% 3.23/3.48 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(284,b,273,a)].
% 3.23/3.48 285 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_52) # label(axiom). [assumption].
% 3.23/3.48 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(285,b,273,a)].
% 3.23/3.48 286 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_35) # label(axiom). [assumption].
% 3.23/3.48 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(286,b,273,a)].
% 3.23/3.48 287 -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].
% 3.23/3.48 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(287,b,273,a)].
% 3.23/3.48 288 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_29) # label(axiom). [assumption].
% 3.53/3.75 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(288,b,273,a)].
% 3.53/3.75 289 -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].
% 3.53/3.75 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(289,b,273,a)].
% 3.53/3.75 290 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_3) # label(axiom). [assumption].
% 3.53/3.75 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(290,b,273,a)].
% 3.53/3.75 291 class_LOrder_Ojoin__semilorder(tc_IntDef_Oint). [resolve(63,a,1,a)].
% 3.53/3.75 292 class_LOrder_Ojoin__semilorder(tc_nat). [resolve(63,a,60,a)].
% 3.53/3.75 293 class_LOrder_Ojoin__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(63,a,61,b)].
% 3.53/3.75 294 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Ojoin__semilorder(A). [resolve(73,b,63,a)].
% 3.53/3.75 295 class_LOrder_Omeet__semilorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_32) # label(axiom). [assumption].
% 3.53/3.75 296 -class_LOrder_Omeet__semilorder(A) | c_LOrder_Omeet(B,B,A) = B # label(cls_LOrder_Omeet__idempotent_0) # label(axiom). [assumption].
% 3.53/3.75 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(295,a,296,a)].
% 3.53/3.75 297 class_LOrder_Omeet__semilorder(tc_nat) # label(clsarity_nat_4) # label(axiom). [assumption].
% 3.53/3.75 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(297,a,296,a)].
% 3.53/3.75 298 -class_LOrder_Olorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_LOrder_Olorder_0) # label(axiom). [assumption].
% 3.53/3.75 Derived: -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(298,b,296,a)].
% 3.53/3.75 299 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Omeet__semilorder_0) # label(axiom). [assumption].
% 3.53/3.75 300 -class_LOrder_Omeet__semilorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Omeet__semilorder_1) # label(axiom). [assumption].
% 3.53/3.75 301 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_17) # label(axiom). [assumption].
% 3.53/3.75 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(301,b,296,a)].
% 3.53/3.75 302 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_16) # label(axiom). [assumption].
% 3.53/3.75 Derived: -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(302,b,296,a)].
% 3.53/3.75 303 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_18) # label(axiom). [assumption].
% 3.53/3.75 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(303,b,296,a)].
% 3.53/3.75 304 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_15) # label(axiom). [assumption].
% 3.53/3.75 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(304,b,296,a)].
% 3.53/3.75 305 -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].
% 3.53/3.75 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(305,b,296,a)].
% 3.53/3.75 306 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_28) # label(axiom). [assumption].
% 3.53/3.75 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(306,b,296,a)].
% 3.53/3.75 307 -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].
% 3.53/3.75 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(307,b,296,a)].
% 3.75/3.98 308 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__field_53) # label(axiom). [assumption].
% 3.75/3.98 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(308,b,296,a)].
% 3.75/3.98 309 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_36) # label(axiom). [assumption].
% 3.75/3.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(309,b,296,a)].
% 3.75/3.98 310 -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].
% 3.75/3.98 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(310,b,296,a)].
% 3.75/3.98 311 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_30) # label(axiom). [assumption].
% 3.75/3.98 Derived: -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(311,b,296,a)].
% 3.75/3.98 312 -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].
% 3.75/3.98 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(312,b,296,a)].
% 3.75/3.98 313 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_2) # label(axiom). [assumption].
% 3.75/3.98 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(313,b,296,a)].
% 3.75/3.98 314 class_LOrder_Omeet__semilorder(tc_IntDef_Oint). [resolve(64,a,1,a)].
% 3.75/3.98 315 class_LOrder_Omeet__semilorder(tc_nat). [resolve(64,a,60,a)].
% 3.75/3.98 316 class_LOrder_Omeet__semilorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(64,a,61,b)].
% 3.75/3.98 317 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Omeet__semilorder(A). [resolve(73,b,64,a)].
% 3.75/3.98 318 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_56) # label(axiom). [assumption].
% 3.75/3.98 319 -class_Ring__and__Field_Oordered__semidom(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B # label(cls_NatArith_Oof__nat__0__eq__iff_0) # label(axiom). [assumption].
% 3.75/3.98 320 -class_Ring__and__Field_Oordered__semidom(A) | c_0 = c_NatArith_Oof__nat(c_0,A) # label(cls_NatArith_Oof__nat__0__eq__iff_1) # label(axiom). [assumption].
% 3.75/3.98 321 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A) # label(cls_NatArith_Oof__nat__0__le__iff_0) # label(axiom). [assumption].
% 3.75/3.98 322 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_0,c_NatArith_Oof__nat(B,A),A) | c_less(c_0,B,tc_nat) # label(cls_NatArith_Oof__nat__0__less__iff_0) # label(axiom). [assumption].
% 3.75/3.98 323 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_0,B,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(B,A),A) # label(cls_NatArith_Oof__nat__0__less__iff_1) # label(axiom). [assumption].
% 3.75/3.98 324 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0 # label(cls_NatArith_Oof__nat__eq__0__iff_0) # label(axiom). [assumption].
% 3.75/3.98 325 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_0,A) = c_0 # label(cls_NatArith_Oof__nat__eq__0__iff_1) # label(axiom). [assumption].
% 3.75/3.98 326 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C # label(cls_NatArith_Oof__nat__eq__iff_0) # label(axiom). [assumption].
% 3.75/3.98 327 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0 # label(cls_NatArith_Oof__nat__le__0__iff_0) # label(axiom). [assumption].
% 3.75/3.98 328 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A) # label(cls_NatArith_Oof__nat__le__0__iff_1) # label(axiom). [assumption].
% 3.75/3.98 329 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_lessequals(B,C,tc_nat) # label(cls_NatArith_Oof__nat__le__iff_0) # label(axiom). [assumption].
% 3.75/3.99 330 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__le__iff_1) # label(axiom). [assumption].
% 3.75/3.99 331 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A) # label(cls_NatArith_Oof__nat__less__0__iff_0) # label(axiom). [assumption].
% 3.75/3.99 332 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_less(B,C,tc_nat) # label(cls_NatArith_Oof__nat__less__iff_0) # label(axiom). [assumption].
% 3.75/3.99 333 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,tc_nat) | c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) # label(cls_NatArith_Oof__nat__less__iff_1) # label(axiom). [assumption].
% 3.75/3.99 334 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | -c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_lessequals(C,D,tc_nat) # label(cls_Power_Opower__increasing__iff_0) # label(axiom). [assumption].
% 3.75/3.99 335 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) # label(cls_Power_Opower__increasing__iff_1) # label(axiom). [assumption].
% 3.75/3.99 336 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D # label(cls_Power_Opower__inject__exp_0) # label(axiom). [assumption].
% 3.75/3.99 337 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,B,A) | -c_less(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_less(C,D,tc_nat) # label(cls_Power_Opower__strict__increasing__iff_0) # label(axiom). [assumption].
% 3.75/3.99 338 -class_Power_Orecpower(A) | -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,tc_nat) | -c_less(c_1,D,A) | c_less(c_Nat_Opower(D,B,A),c_Nat_Opower(D,C,A),A) # label(cls_Power_Opower__strict__increasing__iff_1) # label(axiom). [assumption].
% 3.75/3.99 339 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_1,c_0,A) # label(cls_Ring__and__Field_Onot__one__le__zero_0) # label(axiom). [assumption].
% 3.75/3.99 340 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_1,c_0,A) # label(cls_Ring__and__Field_Onot__one__less__zero_0) # label(axiom). [assumption].
% 3.75/3.99 341 -class_Ring__and__Field_Oordered__semidom(A) | c_less(c_0,c_1,A) # label(cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) # label(axiom). [assumption].
% 3.75/3.99 342 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_0,c_1,A) # label(cls_Ring__and__Field_Ozero__le__one_0) # label(axiom). [assumption].
% 3.75/3.99 Derived: c_0 != c_NatArith_Oof__nat(A,tc_IntDef_Oint) | c_0 = A. [resolve(318,a,319,a)].
% 3.75/3.99 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint). [resolve(318,a,320,a)].
% 3.75/3.99 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(318,a,321,a)].
% 3.75/3.99 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,A,tc_nat). [resolve(318,a,322,a)].
% 3.75/3.99 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(318,a,323,a)].
% 3.75/3.99 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(318,a,324,a)].
% 3.75/3.99 Derived: c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) = c_0. [resolve(318,a,325,a)].
% 3.75/3.99 Derived: c_NatArith_Oof__nat(A,tc_IntDef_Oint) != c_NatArith_Oof__nat(B,tc_IntDef_Oint) | A = B. [resolve(318,a,326,a)].
% 3.75/3.99 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(318,a,327,a)].
% 3.75/3.99 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(318,a,328,a)].
% 3.75/3.99 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_nat). [resolve(318,a,329,a)].
% 3.75/3.99 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(318,a,330,a)].
% 3.75/4.00 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(318,a,331,a)].
% 3.75/4.00 Derived: -c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_nat). [resolve(318,a,332,a)].
% 3.75/4.00 Derived: -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(318,a,333,a)].
% 3.75/4.00 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | -c_lessequals(c_Nat_Opower(A,B,tc_IntDef_Oint),c_Nat_Opower(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_nat). [resolve(318,a,334,b)].
% 3.75/4.00 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_Nat_Opower(A,B,tc_IntDef_Oint),c_Nat_Opower(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(318,a,335,b)].
% 3.75/4.00 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | c_Nat_Opower(A,B,tc_IntDef_Oint) != c_Nat_Opower(A,C,tc_IntDef_Oint) | B = C. [resolve(318,a,336,b)].
% 3.75/4.00 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(c_1,A,tc_IntDef_Oint) | -c_less(c_Nat_Opower(A,B,tc_IntDef_Oint),c_Nat_Opower(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_nat). [resolve(318,a,337,b)].
% 3.75/4.00 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_less(A,B,tc_nat) | -c_less(c_1,C,tc_IntDef_Oint) | c_less(c_Nat_Opower(C,A,tc_IntDef_Oint),c_Nat_Opower(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(318,a,338,b)].
% 3.75/4.00 Derived: -c_lessequals(c_1,c_0,tc_IntDef_Oint). [resolve(318,a,339,a)].
% 3.75/4.00 Derived: -c_less(c_1,c_0,tc_IntDef_Oint). [resolve(318,a,340,a)].
% 3.75/4.00 Derived: c_less(c_0,c_1,tc_IntDef_Oint). [resolve(318,a,341,a)].
% 3.75/4.00 Derived: c_lessequals(c_0,c_1,tc_IntDef_Oint). [resolve(318,a,342,a)].
% 3.75/4.00 343 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat_43) # label(axiom). [assumption].
% 3.75/4.00 Derived: c_0 != c_NatArith_Oof__nat(A,tc_nat) | c_0 = A. [resolve(343,a,319,a)].
% 3.75/4.00 Derived: c_0 = c_NatArith_Oof__nat(c_0,tc_nat). [resolve(343,a,320,a)].
% 3.75/4.00 Derived: c_lessequals(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(343,a,321,a)].
% 3.75/4.00 Derived: -c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat) | c_less(c_0,A,tc_nat). [resolve(343,a,322,a)].
% 3.75/4.00 Derived: -c_less(c_0,A,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(A,tc_nat),tc_nat). [resolve(343,a,323,a)].
% 3.75/4.00 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_0 | A = c_0. [resolve(343,a,324,a)].
% 3.75/4.00 Derived: c_NatArith_Oof__nat(c_0,tc_nat) = c_0. [resolve(343,a,325,a)].
% 3.75/4.00 Derived: c_NatArith_Oof__nat(A,tc_nat) != c_NatArith_Oof__nat(B,tc_nat) | A = B. [resolve(343,a,326,a)].
% 3.75/4.00 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat) | A = c_0. [resolve(343,a,327,a)].
% 3.75/4.00 Derived: c_lessequals(c_NatArith_Oof__nat(c_0,tc_nat),c_0,tc_nat). [resolve(343,a,328,a)].
% 3.75/4.00 Derived: -c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(343,a,329,a)].
% 3.75/4.00 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(343,a,330,a)].
% 3.75/4.00 Derived: -c_less(c_NatArith_Oof__nat(A,tc_nat),c_0,tc_nat). [resolve(343,a,331,a)].
% 3.75/4.00 Derived: -c_less(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(343,a,332,a)].
% 3.75/4.00 Derived: -c_less(A,B,tc_nat) | c_less(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(343,a,333,a)].
% 3.75/4.00 Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | -c_lessequals(c_Nat_Opower(A,B,tc_nat),c_Nat_Opower(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(343,a,334,b)].
% 3.75/4.00 Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_Nat_Opower(A,B,tc_nat),c_Nat_Opower(A,C,tc_nat),tc_nat). [resolve(343,a,335,b)].
% 3.75/4.00 Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | c_Nat_Opower(A,B,tc_nat) != c_Nat_Opower(A,C,tc_nat) | B = C. [resolve(343,a,336,b)].
% 3.82/4.03 Derived: -class_Power_Orecpower(tc_nat) | -c_less(c_1,A,tc_nat) | -c_less(c_Nat_Opower(A,B,tc_nat),c_Nat_Opower(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(343,a,337,b)].
% 3.82/4.03 Derived: -class_Power_Orecpower(tc_nat) | -c_less(A,B,tc_nat) | -c_less(c_1,C,tc_nat) | c_less(c_Nat_Opower(C,A,tc_nat),c_Nat_Opower(C,B,tc_nat),tc_nat). [resolve(343,a,338,b)].
% 3.82/4.03 Derived: -c_lessequals(c_1,c_0,tc_nat). [resolve(343,a,339,a)].
% 3.82/4.03 Derived: -c_less(c_1,c_0,tc_nat). [resolve(343,a,340,a)].
% 3.82/4.03 Derived: c_less(c_0,c_1,tc_nat). [resolve(343,a,341,a)].
% 3.82/4.03 Derived: c_lessequals(c_0,c_1,tc_nat). [resolve(343,a,342,a)].
% 3.82/4.03 344 -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].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B. [resolve(344,b,319,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_NatArith_Oof__nat(c_0,A). [resolve(344,b,320,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(344,b,321,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_NatArith_Oof__nat(B,A),A) | c_less(c_0,B,tc_nat). [resolve(344,b,322,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(344,b,323,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0. [resolve(344,b,324,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(c_0,A) = c_0. [resolve(344,b,325,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C. [resolve(344,b,326,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0. [resolve(344,b,327,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A). [resolve(344,b,328,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_lessequals(B,C,tc_nat). [resolve(344,b,329,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(344,b,330,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A). [resolve(344,b,331,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_less(B,C,tc_nat). [resolve(344,b,332,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,tc_nat) | c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(344,b,333,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_lessequals(C,D,tc_nat). [resolve(344,b,334,b)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A). [resolve(344,b,335,b)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D. [resolve(344,b,336,b)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_less(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_less(C,D,tc_nat). [resolve(344,b,337,b)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_Power_Orecpower(A) | -c_less(B,C,tc_nat) | -c_less(c_1,D,A) | c_less(c_Nat_Opower(D,B,A),c_Nat_Opower(D,C,A),A). [resolve(344,b,338,b)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_1,c_0,A). [resolve(344,b,339,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_1,c_0,A). [resolve(344,b,340,a)].
% 3.82/4.03 Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_1,A). [resolve(344,b,341,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_1,A). [resolve(344,b,342,a)].
% 3.82/4.04 345 -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].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_NatArith_Oof__nat(B,A) | c_0 = B. [resolve(345,b,319,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_NatArith_Oof__nat(c_0,A). [resolve(345,b,320,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(345,b,321,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_NatArith_Oof__nat(B,A),A) | c_less(c_0,B,tc_nat). [resolve(345,b,322,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,B,tc_nat) | c_less(c_0,c_NatArith_Oof__nat(B,A),A). [resolve(345,b,323,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_0 | B = c_0. [resolve(345,b,324,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(c_0,A) = c_0. [resolve(345,b,325,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_NatArith_Oof__nat(B,A) != c_NatArith_Oof__nat(C,A) | B = C. [resolve(345,b,326,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_0,A) | B = c_0. [resolve(345,b,327,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_NatArith_Oof__nat(c_0,A),c_0,A). [resolve(345,b,328,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_lessequals(B,C,tc_nat). [resolve(345,b,329,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,tc_nat) | c_lessequals(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(345,b,330,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_0,A). [resolve(345,b,331,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) | c_less(B,C,tc_nat). [resolve(345,b,332,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,tc_nat) | c_less(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(345,b,333,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_lessequals(C,D,tc_nat). [resolve(345,b,334,b)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A). [resolve(345,b,335,b)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | c_Nat_Opower(B,C,A) != c_Nat_Opower(B,D,A) | C = D. [resolve(345,b,336,b)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(c_1,B,A) | -c_less(c_Nat_Opower(B,C,A),c_Nat_Opower(B,D,A),A) | c_less(C,D,tc_nat). [resolve(345,b,337,b)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Power_Orecpower(A) | -c_less(B,C,tc_nat) | -c_less(c_1,D,A) | c_less(c_Nat_Opower(D,B,A),c_Nat_Opower(D,C,A),A). [resolve(345,b,338,b)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_1,c_0,A). [resolve(345,b,339,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_1,c_0,A). [resolve(345,b,340,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_1,A). [resolve(345,b,341,a)].
% 3.82/4.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_1,A). [resolve(345,b,342,a)].
% 3.82/4.04 346 -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].
% 3.82/4.04 Derived: class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(346,a,345,b)].
% 3.82/4.05 347 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_10) # label(axiom). [assumption].
% 3.82/4.05 348 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_11) # label(axiom). [assumption].
% 3.82/4.05 349 -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].
% 3.82/4.05 350 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semidom_13) # label(axiom). [assumption].
% 3.82/4.05 351 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oordered__semidom_14) # label(axiom). [assumption].
% 3.82/4.05 352 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_15) # label(axiom). [assumption].
% 3.82/4.05 353 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oordered__semidom_16) # label(axiom). [assumption].
% 3.82/4.05 354 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_17) # label(axiom). [assumption].
% 3.82/4.05 355 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oordered__semidom_18) # label(axiom). [assumption].
% 3.82/4.05 356 -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].
% 3.82/4.05 357 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_2) # label(axiom). [assumption].
% 3.82/4.05 Derived: class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(357,a,345,b)].
% 3.82/4.05 358 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_20) # label(axiom). [assumption].
% 3.82/4.05 359 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_21) # label(axiom). [assumption].
% 3.82/4.05 360 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__semidom_22) # label(axiom). [assumption].
% 3.82/4.05 361 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Oordered__semidom_23) # label(axiom). [assumption].
% 3.82/4.05 362 -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].
% 3.82/4.05 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint). [resolve(362,a,318,a)].
% 3.82/4.05 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). [resolve(362,a,343,a)].
% 3.82/4.05 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(362,a,344,b)].
% 3.82/4.05 Derived: class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(362,a,345,b)].
% 3.82/4.05 363 -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].
% 3.82/4.05 Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint). [resolve(363,a,318,a)].
% 3.82/4.05 Derived: class_Ring__and__Field_Oordered__semiring__strict(tc_nat). [resolve(363,a,343,a)].
% 3.82/4.05 Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(363,a,344,b)].
% 3.82/4.05 Derived: class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(363,a,345,b)].
% 3.82/4.05 364 -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].
% 3.82/4.06 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(364,a,318,a)].
% 3.82/4.06 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat). [resolve(364,a,343,a)].
% 3.82/4.06 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(364,a,344,b)].
% 3.82/4.06 Derived: class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(364,a,345,b)].
% 3.82/4.06 365 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_28) # label(axiom). [assumption].
% 3.82/4.06 Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(365,a,344,b)].
% 3.82/4.06 Derived: class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(365,a,345,b)].
% 3.82/4.06 366 -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].
% 3.82/4.06 Derived: class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(366,a,345,b)].
% 3.82/4.06 367 -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].
% 3.82/4.06 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(367,a,318,a)].
% 3.82/4.06 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). [resolve(367,a,343,a)].
% 3.82/4.06 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(367,a,344,b)].
% 3.82/4.06 Derived: class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(367,a,345,b)].
% 3.82/4.06 368 -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].
% 3.82/4.06 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(368,a,318,a)].
% 3.82/4.06 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). [resolve(368,a,343,a)].
% 3.82/4.06 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(368,a,344,b)].
% 3.82/4.06 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(368,a,345,b)].
% 3.82/4.06 369 -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].
% 3.82/4.06 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint). [resolve(369,a,318,a)].
% 3.82/4.06 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat). [resolve(369,a,343,a)].
% 3.82/4.06 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(369,a,344,b)].
% 3.82/4.06 Derived: class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(369,a,345,b)].
% 3.82/4.06 370 -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].
% 3.82/4.06 Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint). [resolve(370,a,318,a)].
% 3.82/4.06 Derived: class_Ring__and__Field_Opordered__cancel__semiring(tc_nat). [resolve(370,a,343,a)].
% 3.82/4.06 Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(370,a,344,b)].
% 3.82/4.06 Derived: class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(370,a,345,b)].
% 3.82/4.06 371 -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].
% 3.92/4.13 Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint). [resolve(371,a,318,a)].
% 3.92/4.13 Derived: class_Ring__and__Field_Opordered__comm__semiring(tc_nat). [resolve(371,a,343,a)].
% 3.92/4.13 Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(371,a,344,b)].
% 3.92/4.13 Derived: class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(371,a,345,b)].
% 3.92/4.13 372 -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].
% 3.92/4.13 Derived: class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint). [resolve(372,a,318,a)].
% 3.92/4.13 Derived: class_Ring__and__Field_Opordered__semiring(tc_nat). [resolve(372,a,343,a)].
% 3.92/4.13 Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(372,a,344,b)].
% 3.92/4.13 Derived: class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(372,a,345,b)].
% 3.92/4.13 373 -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].
% 3.92/4.13 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(373,a,318,a)].
% 3.92/4.13 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat). [resolve(373,a,343,a)].
% 3.92/4.13 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(373,a,344,b)].
% 3.92/4.13 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(373,a,345,b)].
% 3.92/4.13 374 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semidom_38) # label(axiom). [assumption].
% 3.92/4.13 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(374,a,344,b)].
% 3.92/4.13 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(374,a,345,b)].
% 3.92/4.13 375 -class_Ring__and__Field_Oordered__semidom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semidom_39) # label(axiom). [assumption].
% 3.92/4.13 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(375,a,344,b)].
% 3.92/4.13 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(375,a,345,b)].
% 3.92/4.13 376 -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].
% 3.92/4.13 377 -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].
% 3.92/4.13 378 -class_Ring__and__Field_Oordered__semidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__semidom_6) # label(axiom). [assumption].
% 3.92/4.13 379 -class_Ring__and__Field_Oordered__semidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__semidom_7) # label(axiom). [assumption].
% 3.92/4.13 380 -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].
% 3.92/4.13 381 -class_Ring__and__Field_Oordered__semidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oordered__semidom_9) # label(axiom). [assumption].
% 3.92/4.13 382 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(71,b,2,a)].
% 3.92/4.13 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) | B = c_emptyset. [resolve(382,a,318,a)].
% 3.92/4.13 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset. [resolve(382,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(382,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(382,a,345,b)].
% 3.92/4.14 383 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(71,b,3,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMax(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(383,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(383,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(383,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(383,a,345,b)].
% 3.92/4.14 384 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(71,b,4,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(384,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat). [resolve(384,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(384,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(384,a,345,b)].
% 3.92/4.14 385 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(71,b,5,a)].
% 3.92/4.14 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(385,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset. [resolve(385,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(385,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(385,a,345,b)].
% 3.92/4.14 386 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(71,b,6,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(386,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(386,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(386,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(386,a,345,b)].
% 3.92/4.14 387 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(71,b,7,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(387,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(387,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(387,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(387,a,345,b)].
% 3.92/4.14 388 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(71,b,8,a)].
% 3.92/4.14 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(388,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat) | B = c_emptyset. [resolve(388,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(388,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(388,a,345,b)].
% 3.92/4.14 389 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(71,b,9,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(389,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_nat),A,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(389,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(389,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(389,a,345,b)].
% 3.92/4.14 390 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(71,b,10,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(390,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_nat),B,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(390,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(390,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(390,a,345,b)].
% 3.92/4.14 391 -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(71,b,11,a)].
% 3.92/4.14 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(391,a,318,a)].
% 3.92/4.14 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(391,a,343,a)].
% 3.92/4.14 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(391,a,344,b)].
% 3.92/4.14 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(391,a,345,b)].
% 3.92/4.14 392 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(71,b,12,a)].
% 3.92/4.14 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(392,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset. [resolve(392,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(392,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(392,a,345,b)].
% 3.92/4.14 393 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(71,b,13,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(393,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(393,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(393,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(393,a,345,b)].
% 3.92/4.14 394 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(71,b,14,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(394,a,318,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(394,a,343,a)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(394,a,344,b)].
% 3.92/4.14 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(394,a,345,b)].
% 3.92/4.14 395 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(71,b,15,a)].
% 3.92/4.14 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(395,a,318,a)].
% 3.92/4.15 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(395,a,343,a)].
% 3.92/4.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(395,a,344,b)].
% 3.92/4.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(395,a,345,b)].
% 3.92/4.15 396 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(71,b,16,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(396,a,318,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(396,a,343,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(396,a,344,b)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(396,a,345,b)].
% 3.92/4.15 397 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(71,b,17,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(397,a,318,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(397,a,343,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(397,a,344,b)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(397,a,345,b)].
% 3.92/4.15 398 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(71,b,18,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(398,a,318,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(398,a,343,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(398,a,344,b)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(398,a,345,b)].
% 3.92/4.15 399 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(71,b,19,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(399,a,318,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_nat),tc_nat). [resolve(399,a,343,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(399,a,344,b)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(399,a,345,b)].
% 3.92/4.15 400 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(71,b,20,a)].
% 3.92/4.15 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(400,a,318,a)].
% 3.92/4.15 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset. [resolve(400,a,343,a)].
% 3.92/4.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(400,a,344,b)].
% 3.92/4.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(400,a,345,b)].
% 3.92/4.15 401 -class_Ring__and__Field_Oordered__semidom(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(71,b,21,a)].
% 3.92/4.15 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(401,a,318,a)].
% 3.92/4.15 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(401,a,343,a)].
% 3.92/4.15 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(401,a,344,b)].
% 3.92/4.15 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(401,a,345,b)].
% 3.92/4.15 402 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(71,b,22,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(402,a,318,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(A,tc_nat),c_Finite__Set_OMax(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(402,a,343,a)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(402,a,344,b)].
% 3.92/4.15 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(402,a,345,b)].
% 3.92/4.15 403 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(71,b,23,a)].
% 3.92/4.15 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(403,a,318,a)].
% 3.92/4.15 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) = A. [resolve(403,a,343,a)].
% 3.92/4.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C). [resolve(403,a,344,b)].
% 3.92/4.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C). [resolve(403,a,345,b)].
% 3.92/4.15 404 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(71,b,24,a)].
% 3.92/4.15 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(404,a,318,a)].
% 3.92/4.15 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_nat),tc_nat) = A. [resolve(404,a,343,a)].
% 3.92/4.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C). [resolve(404,a,344,b)].
% 3.92/4.15 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C). [resolve(404,a,345,b)].
% 3.92/4.15 405 -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(71,b,25,b)].
% 3.92/4.15 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint). [resolve(405,a,318,a)].
% 3.92/4.15 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat). [resolve(405,a,343,a)].
% 3.92/4.15 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(405,a,344,b)].
% 3.92/4.15 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(405,a,345,b)].
% 3.92/4.15 406 -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(71,b,26,b)].
% 3.92/4.15 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(406,a,318,a)].
% 3.92/4.15 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat). [resolve(406,a,343,a)].
% 3.92/4.15 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(406,a,344,b)].
% 3.92/4.15 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(406,a,345,b)].
% 3.92/4.16 407 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(71,b,27,a)].
% 3.92/4.16 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(407,a,318,a)].
% 3.92/4.16 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(407,a,343,a)].
% 3.92/4.16 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(407,a,344,b)].
% 3.92/4.16 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(407,a,345,b)].
% 3.92/4.16 408 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(71,b,28,a)].
% 3.92/4.16 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(408,a,318,a)].
% 3.92/4.16 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(408,a,343,a)].
% 3.92/4.16 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(408,a,344,b)].
% 3.92/4.16 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(408,a,345,b)].
% 3.92/4.16 409 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(71,b,29,a)].
% 3.92/4.16 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(409,a,318,a)].
% 3.92/4.16 Derived: -c_less(A,B,tc_nat) | -c_less(C,B,tc_nat) | c_less(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(409,a,343,a)].
% 3.92/4.16 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(409,a,344,b)].
% 3.92/4.16 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(409,a,345,b)].
% 3.92/4.16 410 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(71,b,30,a)].
% 3.92/4.16 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(410,a,318,a)].
% 3.92/4.16 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(410,a,343,a)].
% 3.92/4.16 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(410,a,344,b)].
% 3.92/4.16 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(410,a,345,b)].
% 3.92/4.16 411 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(71,b,31,a)].
% 3.92/4.16 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(411,a,318,a)].
% 3.92/4.16 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(411,a,343,a)].
% 3.92/4.16 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(411,a,344,b)].
% 3.92/4.16 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(411,a,345,b)].
% 3.92/4.16 412 -class_Ring__and__Field_Oordered__semidom(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(71,b,32,a)].
% 3.92/4.16 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(412,a,318,a)].
% 3.92/4.16 Derived: -c_less(A,B,tc_nat) | -c_less(A,C,tc_nat) | c_less(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(412,a,343,a)].
% 3.92/4.16 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(412,a,344,b)].
% 3.92/4.16 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(412,a,345,b)].
% 3.92/4.16 413 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(71,b,33,a)].
% 3.92/4.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(413,a,318,a)].
% 3.92/4.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(413,a,343,a)].
% 3.92/4.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(413,a,344,b)].
% 3.92/4.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(413,a,345,b)].
% 3.92/4.16 414 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(71,b,34,a)].
% 3.92/4.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(414,a,318,a)].
% 3.92/4.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(414,a,343,a)].
% 3.92/4.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(414,a,344,b)].
% 3.92/4.16 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(414,a,345,b)].
% 3.92/4.16 415 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(71,b,35,a)].
% 3.92/4.16 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(415,a,318,a)].
% 3.92/4.16 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | c_lessequals(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(415,a,343,a)].
% 3.92/4.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(415,a,344,b)].
% 3.92/4.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(415,a,345,b)].
% 3.92/4.16 416 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,B,A) = B. [resolve(71,b,36,a)].
% 3.92/4.16 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(416,a,318,a)].
% 3.92/4.16 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(416,a,343,a)].
% 3.92/4.16 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(416,a,344,b)].
% 3.92/4.16 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(416,a,345,b)].
% 3.92/4.16 417 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(71,b,37,a)].
% 3.92/4.16 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(A,B,tc_IntDef_Oint). [resolve(417,a,318,a)].
% 3.92/4.16 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(417,a,343,a)].
% 3.92/4.16 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(417,a,344,b)].
% 3.92/4.16 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(417,a,345,b)].
% 3.92/4.16 418 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(71,b,38,a)].
% 3.92/4.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(418,a,318,a)].
% 3.92/4.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(418,a,343,a)].
% 3.92/4.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(418,a,344,b)].
% 3.92/4.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(418,a,345,b)].
% 3.92/4.16 419 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(71,b,39,a)].
% 3.92/4.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(419,a,318,a)].
% 3.95/4.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(419,a,343,a)].
% 3.95/4.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(419,a,344,b)].
% 3.95/4.16 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(419,a,345,b)].
% 3.95/4.16 420 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(71,b,40,a)].
% 3.95/4.16 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(420,a,318,a)].
% 3.95/4.16 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | c_lessequals(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(420,a,343,a)].
% 3.95/4.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(420,a,344,b)].
% 3.95/4.16 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(420,a,345,b)].
% 3.95/4.16 421 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,B,A) = B. [resolve(71,b,41,a)].
% 3.95/4.16 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(421,a,318,a)].
% 3.95/4.16 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(421,a,343,a)].
% 3.95/4.16 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(421,a,344,b)].
% 3.95/4.16 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(421,a,345,b)].
% 3.95/4.16 422 -class_Ring__and__Field_Oordered__semidom(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(71,b,42,a)].
% 3.95/4.16 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint). [resolve(422,a,318,a)].
% 3.95/4.16 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(422,a,343,a)].
% 3.95/4.16 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(422,a,344,b)].
% 3.95/4.16 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(422,a,345,b)].
% 3.95/4.16 423 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(71,b,43,a)].
% 3.95/4.16 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(423,a,318,a)].
% 3.95/4.16 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(423,a,343,a)].
% 3.95/4.16 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(423,a,344,b)].
% 3.95/4.16 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(423,a,345,b)].
% 3.95/4.16 424 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(71,b,44,a)].
% 3.95/4.16 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(424,a,318,a)].
% 3.95/4.16 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(424,a,343,a)].
% 3.95/4.16 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(424,a,344,b)].
% 3.95/4.16 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(424,a,345,b)].
% 3.95/4.16 425 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(71,b,45,a)].
% 3.95/4.17 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(425,a,318,a)].
% 3.95/4.17 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(425,a,343,a)].
% 3.95/4.17 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(425,a,344,b)].
% 3.95/4.17 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(425,a,345,b)].
% 3.95/4.17 426 -class_Ring__and__Field_Oordered__semidom(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(71,b,46,a)].
% 3.95/4.17 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(426,a,318,a)].
% 3.95/4.17 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(426,a,343,a)].
% 3.95/4.17 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(426,a,344,b)].
% 3.95/4.17 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(426,a,345,b)].
% 3.95/4.17 427 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(71,b,47,a)].
% 3.95/4.17 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(427,a,318,a)].
% 3.95/4.17 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(427,a,343,a)].
% 3.95/4.17 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(427,a,344,b)].
% 3.95/4.17 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(427,a,345,b)].
% 3.95/4.17 428 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(71,b,48,a)].
% 3.95/4.17 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(428,a,318,a)].
% 3.95/4.17 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(428,a,343,a)].
% 3.95/4.17 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(428,a,344,b)].
% 3.95/4.17 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(428,a,345,b)].
% 3.95/4.17 429 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(71,b,49,a)].
% 3.95/4.17 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(429,a,318,a)].
% 3.95/4.17 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(429,a,343,a)].
% 3.95/4.17 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(429,a,344,b)].
% 3.95/4.17 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(429,a,345,b)].
% 3.95/4.17 430 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(71,b,50,a)].
% 3.95/4.17 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(430,a,318,a)].
% 3.95/4.17 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(430,a,343,a)].
% 3.95/4.17 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(430,a,344,b)].
% 3.95/4.17 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(430,a,345,b)].
% 3.95/4.17 431 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(71,b,51,a)].
% 3.95/4.17 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(431,a,318,a)].
% 3.95/4.17 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(431,a,343,a)].
% 3.95/4.17 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(431,a,344,b)].
% 3.95/4.17 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(431,a,345,b)].
% 3.95/4.17 432 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(71,b,52,a)].
% 3.95/4.17 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint). [resolve(432,a,318,a)].
% 3.95/4.17 Derived: -c_lessequals(A,B,tc_nat) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_nat),c_SetInterval_OatLeastLessThan(A,B,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeastLessThan(B,C,tc_nat). [resolve(432,a,343,a)].
% 3.95/4.17 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(432,a,344,b)].
% 3.95/4.17 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(432,a,345,b)].
% 3.95/4.17 433 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(71,b,53,a)].
% 3.95/4.17 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(433,a,318,a)].
% 3.95/4.17 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(433,a,343,a)].
% 3.95/4.17 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(433,a,344,b)].
% 3.95/4.17 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(433,a,345,b)].
% 3.95/4.17 434 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(71,b,54,a)].
% 3.95/4.17 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,D,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(434,a,318,a)].
% 3.95/4.17 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(B,D,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(434,a,343,a)].
% 3.95/4.18 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(434,a,344,b)].
% 3.95/4.18 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(434,a,345,b)].
% 3.95/4.18 435 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(71,b,55,a)].
% 3.95/4.18 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(435,a,318,a)].
% 3.95/4.18 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)). [resolve(435,a,343,a)].
% 3.95/4.18 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(435,a,344,b)].
% 3.95/4.18 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(435,a,345,b)].
% 3.95/4.18 436 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(71,b,56,a)].
% 3.95/4.18 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(436,a,318,a)].
% 3.95/4.18 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)). [resolve(436,a,343,a)].
% 3.95/4.18 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(436,a,344,b)].
% 3.95/4.18 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(436,a,345,b)].
% 3.95/4.18 437 -class_Ring__and__Field_Oordered__semidom(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(71,b,57,a)].
% 3.95/4.18 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(437,a,318,a)].
% 3.95/4.18 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(437,a,343,a)].
% 3.95/4.18 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(437,a,344,b)].
% 3.95/4.18 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(437,a,345,b)].
% 3.95/4.18 438 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(71,b,58,a)].
% 3.95/4.18 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(438,a,318,a)].
% 3.95/4.18 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(438,a,343,a)].
% 3.95/4.18 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(438,a,344,b)].
% 4.02/4.25 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(438,a,345,b)].
% 4.02/4.25 439 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(71,b,59,a)].
% 4.02/4.25 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(439,a,318,a)].
% 4.02/4.25 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(439,a,343,a)].
% 4.02/4.25 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(439,a,344,b)].
% 4.02/4.25 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(439,a,345,b)].
% 4.02/4.25 440 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(269,b,230,a)].
% 4.02/4.25 Derived: c_in(c_0,c_IntDef_ONats,tc_IntDef_Oint). [resolve(440,a,318,a)].
% 4.02/4.25 Derived: c_in(c_0,c_IntDef_ONats,tc_nat). [resolve(440,a,343,a)].
% 4.02/4.25 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(440,a,344,b)].
% 4.02/4.25 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(440,a,345,b)].
% 4.02/4.25 441 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(269,b,231,a)].
% 4.02/4.25 Derived: c_in(c_1,c_IntDef_ONats,tc_IntDef_Oint). [resolve(441,a,318,a)].
% 4.02/4.25 Derived: c_in(c_1,c_IntDef_ONats,tc_nat). [resolve(441,a,343,a)].
% 4.02/4.25 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(441,a,344,b)].
% 4.02/4.25 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(441,a,345,b)].
% 4.02/4.25 442 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(269,b,232,a)].
% 4.02/4.25 Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_plus(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(442,a,318,a)].
% 4.02/4.25 Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_plus(B,A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(442,a,343,a)].
% 4.02/4.25 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(442,a,344,b)].
% 4.02/4.25 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(442,a,345,b)].
% 4.02/4.25 443 -class_Ring__and__Field_Oordered__semidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(269,b,233,a)].
% 4.02/4.25 Derived: -c_in(A,c_IntDef_ONats,tc_IntDef_Oint) | -c_in(B,c_IntDef_ONats,tc_IntDef_Oint) | c_in(c_times(B,A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(443,a,318,a)].
% 4.02/4.25 Derived: -c_in(A,c_IntDef_ONats,tc_nat) | -c_in(B,c_IntDef_ONats,tc_nat) | c_in(c_times(B,A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(443,a,343,a)].
% 4.02/4.25 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_times(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(443,a,344,b)].
% 4.02/4.25 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_times(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(443,a,345,b)].
% 4.02/4.25 444 -class_Ring__and__Field_Oordered__semidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(269,b,234,a)].
% 4.02/4.25 Derived: c_in(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_IntDef_ONats,tc_IntDef_Oint). [resolve(444,a,318,a)].
% 4.02/4.25 Derived: c_in(c_NatArith_Oof__nat(A,tc_nat),c_IntDef_ONats,tc_nat). [resolve(444,a,343,a)].
% 4.02/4.25 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(444,a,344,b)].
% 4.02/4.26 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(444,a,345,b)].
% 4.02/4.26 445 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(269,b,235,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(445,a,318,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_Suc(A),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_1,tc_nat). [resolve(445,a,343,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(445,a,344,b)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(445,a,345,b)].
% 4.02/4.26 446 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(269,b,236,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) = c_1. [resolve(446,a,318,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_1,tc_nat) = c_1. [resolve(446,a,343,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(446,a,344,b)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(446,a,345,b)].
% 4.02/4.26 447 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(269,b,237,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_IntDef_Oint) = c_plus(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(447,a,318,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),tc_nat) = c_plus(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(447,a,343,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),C) = c_plus(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(447,a,344,b)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),C) = c_plus(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(447,a,345,b)].
% 4.02/4.26 448 -class_Ring__and__Field_Oordered__semidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(269,b,238,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_IntDef_Oint) = c_times(c_NatArith_Oof__nat(A,tc_IntDef_Oint),c_NatArith_Oof__nat(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(448,a,318,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),tc_nat) = c_times(c_NatArith_Oof__nat(A,tc_nat),c_NatArith_Oof__nat(B,tc_nat),tc_nat). [resolve(448,a,343,a)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),C) = c_times(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(448,a,344,b)].
% 4.02/4.26 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),C) = c_times(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(448,a,345,b)].
% 4.02/4.26 449 -class_Ring__and__Field_Oordered__semidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(269,b,239,a)].
% 4.02/4.26 Derived: -c_IntDef_Oiszero(c_1,tc_IntDef_Oint). [resolve(449,a,318,a)].
% 4.02/4.26 Derived: -c_IntDef_Oiszero(c_1,tc_nat). [resolve(449,a,343,a)].
% 4.02/4.26 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(449,a,344,b)].
% 4.02/4.26 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(449,a,345,b)].
% 4.02/4.26 450 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(288,b,273,a)].
% 4.02/4.26 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(450,a,318,a)].
% 4.02/4.26 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(450,a,343,a)].
% 4.02/4.26 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(450,a,344,b)].
% 4.02/4.26 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(450,a,345,b)].
% 4.17/4.42 451 -class_Ring__and__Field_Oordered__semidom(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(311,b,296,a)].
% 4.17/4.42 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(451,a,318,a)].
% 4.17/4.42 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(451,a,343,a)].
% 4.17/4.42 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(451,a,344,b)].
% 4.17/4.42 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(451,a,345,b)].
% 4.17/4.42 452 class_Numeral_Onumber(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_59) # label(axiom). [assumption].
% 4.17/4.42 453 -class_Numeral_Onumber(A) | -class_Power_Orecpower(A) | c_Nat_Opower(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),A) = c_times(c_Numeral_Onumber__of(B,A),c_Numeral_Onumber__of(B,A),A) # label(cls_NatBin_Opower2__eq__square__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 454 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | B = c_times(c_divide(B,c_Numeral_Onumber__of(C,A),A),c_Numeral_Onumber__of(C,A),A) | c_Numeral_Onumber__of(C,A) = c_0 # label(cls_NatSimprocs_Odivide__eq__eq__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 455 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_Numeral_Onumber__of(B,A) != c_0 | c_divide(C,c_Numeral_Onumber__of(B,A),A) = c_0 # label(cls_NatSimprocs_Odivide__eq__eq__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 456 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_Numeral_Onumber__of(B,A) = c_0 | c_divide(c_times(C,c_Numeral_Onumber__of(B,A),A),c_Numeral_Onumber__of(B,A),A) = C # label(cls_NatSimprocs_Odivide__eq__eq__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 457 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_divide(c_times(c_0,c_Numeral_Onumber__of(B,A),A),c_Numeral_Onumber__of(B,A),A) = c_0 # label(cls_NatSimprocs_Odivide__eq__eq__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 458 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_divide(c_Numeral_Onumber__of(B,A),C,A),c_0,A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Odivide__le__0__iff__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 459 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_divide(c_Numeral_Onumber__of(B,A),C,A),c_0,A) | c_lessequals(c_0,C,A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Odivide__le__0__iff__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 460 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_divide(c_Numeral_Onumber__of(B,A),C,A),c_0,A) | c_lessequals(C,c_0,A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Odivide__le__0__iff__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 461 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_divide(c_Numeral_Onumber__of(B,A),C,A),c_0,A) | c_lessequals(C,c_0,A) | c_lessequals(c_0,C,A) # label(cls_NatSimprocs_Odivide__le__0__iff__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 462 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | -c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_divide(c_Numeral_Onumber__of(C,A),B,A),c_0,A) # label(cls_NatSimprocs_Odivide__le__0__iff__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 463 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) | c_lessequals(c_divide(c_Numeral_Onumber__of(C,A),B,A),c_0,A) # label(cls_NatSimprocs_Odivide__le__0__iff__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 464 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_divide(C,c_Numeral_Onumber__of(B,A),A),D,A) | c_lessequals(C,c_times(D,c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Odivide__le__eq__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 465 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_divide(C,c_Numeral_Onumber__of(B,A),A),D,A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_times(D,c_Numeral_Onumber__of(B,A),A),C,A) # label(cls_NatSimprocs_Odivide__le__eq__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 466 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_divide(B,c_Numeral_Onumber__of(C,A),A),D,A) | c_less(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(c_Numeral_Onumber__of(C,A),c_0,A) | c_lessequals(c_0,D,A) # label(cls_NatSimprocs_Odivide__le__eq__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 467 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_less(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(c_Numeral_Onumber__of(C,A),c_0,A) | c_lessequals(c_divide(D,c_Numeral_Onumber__of(C,A),A),B,A) # label(cls_NatSimprocs_Odivide__le__eq__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 468 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),D,A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_divide(D,c_Numeral_Onumber__of(B,A),A),C,A) # label(cls_NatSimprocs_Odivide__le__eq__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 469 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(C,A),A),D,A) | c_less(c_0,c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_divide(D,c_Numeral_Onumber__of(C,A),A),B,A) # label(cls_NatSimprocs_Odivide__le__eq__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 470 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(C,c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(c_divide(C,c_Numeral_Onumber__of(B,A),A),D,A) # label(cls_NatSimprocs_Odivide__le__eq__number__of_6) # label(axiom). [assumption].
% 4.17/4.42 471 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -c_lessequals(c_0,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_divide(B,c_Numeral_Onumber__of(D,A),A),C,A) # label(cls_NatSimprocs_Odivide__le__eq__number__of_7) # label(axiom). [assumption].
% 4.17/4.42 472 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(C,c_times(D,c_Numeral_Onumber__of(B,A),A),A) | -c_lessequals(c_times(D,c_Numeral_Onumber__of(B,A),A),C,A) | c_lessequals(c_divide(C,c_Numeral_Onumber__of(B,A),A),D,A) # label(cls_NatSimprocs_Odivide__le__eq__number__of_8) # label(axiom). [assumption].
% 4.17/4.42 473 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -c_lessequals(c_0,C,A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),B,A) | c_lessequals(c_divide(B,c_Numeral_Onumber__of(D,A),A),C,A) # label(cls_NatSimprocs_Odivide__le__eq__number__of_9) # label(axiom). [assumption].
% 4.17/4.42 474 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_divide(c_Numeral_Onumber__of(B,A),C,A),c_0,A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Odivide__less__0__iff__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 475 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_divide(c_Numeral_Onumber__of(B,A),C,A),c_0,A) | c_less(c_0,C,A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Odivide__less__0__iff__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 476 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_divide(c_Numeral_Onumber__of(B,A),C,A),c_0,A) | c_less(C,c_0,A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Odivide__less__0__iff__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 477 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_divide(c_Numeral_Onumber__of(B,A),C,A),c_0,A) | c_less(C,c_0,A) | c_less(c_0,C,A) # label(cls_NatSimprocs_Odivide__less__0__iff__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 478 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_0,A) | -c_less(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(c_divide(c_Numeral_Onumber__of(C,A),B,A),c_0,A) # label(cls_NatSimprocs_Odivide__less__0__iff__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 479 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,A) | -c_less(c_Numeral_Onumber__of(C,A),c_0,A) | c_less(c_divide(c_Numeral_Onumber__of(C,A),B,A),c_0,A) # label(cls_NatSimprocs_Odivide__less__0__iff__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 480 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_less(c_divide(C,c_Numeral_Onumber__of(B,A),A),D,A) | c_less(C,c_times(D,c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Odivide__less__eq__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 481 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_less(c_divide(C,c_Numeral_Onumber__of(B,A),A),D,A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_times(D,c_Numeral_Onumber__of(B,A),A),C,A) # label(cls_NatSimprocs_Odivide__less__eq__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 482 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_divide(B,c_Numeral_Onumber__of(C,A),A),D,A) | c_less(c_0,D,A) | c_less(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(c_Numeral_Onumber__of(C,A),c_0,A) # label(cls_NatSimprocs_Odivide__less__eq__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 483 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,A) | c_less(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(c_Numeral_Onumber__of(C,A),c_0,A) | c_less(c_divide(D,c_Numeral_Onumber__of(C,A),A),B,A) # label(cls_NatSimprocs_Odivide__less__eq__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 484 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_less(c_times(C,c_Numeral_Onumber__of(B,A),A),D,A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_divide(D,c_Numeral_Onumber__of(B,A),A),C,A) # label(cls_NatSimprocs_Odivide__less__eq__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 485 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),D,A) | c_less(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(c_divide(D,c_Numeral_Onumber__of(C,A),A),B,A) # label(cls_NatSimprocs_Odivide__less__eq__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 486 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_less(c_divide(B,c_Numeral_Onumber__of(D,A),A),C,A) # label(cls_NatSimprocs_Odivide__less__eq__number__of_6) # label(axiom). [assumption].
% 4.17/4.42 487 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -c_less(c_0,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_less(c_divide(B,c_Numeral_Onumber__of(D,A),A),C,A) # label(cls_NatSimprocs_Odivide__less__eq__number__of_7) # label(axiom). [assumption].
% 4.17/4.42 488 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -c_less(c_Numeral_Onumber__of(D,A),c_0,A) | -c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),B,A) | c_less(c_divide(B,c_Numeral_Onumber__of(D,A),A),C,A) # label(cls_NatSimprocs_Odivide__less__eq__number__of_8) # label(axiom). [assumption].
% 4.17/4.42 489 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -c_less(c_0,C,A) | -c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),B,A) | c_less(c_divide(B,c_Numeral_Onumber__of(D,A),A),C,A) # label(cls_NatSimprocs_Odivide__less__eq__number__of_9) # label(axiom). [assumption].
% 4.17/4.42 490 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_Numeral_Onumber__of(B,A) = c_0 | c_times(c_divide(C,c_Numeral_Onumber__of(B,A),A),c_Numeral_Onumber__of(B,A),A) = C # label(cls_NatSimprocs_Oeq__divide__eq__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 491 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_Numeral_Onumber__of(B,A) != c_0 | c_0 = c_divide(C,c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Oeq__divide__eq__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 492 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | B = c_divide(c_times(B,c_Numeral_Onumber__of(C,A),A),c_Numeral_Onumber__of(C,A),A) | c_Numeral_Onumber__of(C,A) = c_0 # label(cls_NatSimprocs_Oeq__divide__eq__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 493 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Ofield(A) | c_0 = c_divide(c_times(c_0,c_Numeral_Onumber__of(B,A),A),c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Oeq__divide__eq__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 494 -class_Numeral_Onumber(A) | -class_OrderedGroup_Oab__group__add(A) | c_Numeral_Onumber__of(B,A) != c_uminus(C,A) | C = c_uminus(c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Oequation__minus__iff__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 495 -class_Numeral_Onumber(A) | -class_OrderedGroup_Oab__group__add(A) | c_Numeral_Onumber__of(B,A) = c_uminus(c_uminus(c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Oequation__minus__iff__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 496 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse(c_Numeral_Onumber__of(B,A),A) = c_divide(c_1,c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Oinverse__eq__divide__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 497 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(C,c_divide(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),D,A) # label(cls_NatSimprocs_Ole__divide__eq__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 498 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(C,c_divide(D,c_Numeral_Onumber__of(B,A),A),A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(D,c_times(C,c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Ole__divide__eq__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 499 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_divide(C,c_Numeral_Onumber__of(D,A),A),A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(B,c_0,A) # label(cls_NatSimprocs_Ole__divide__eq__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 500 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_less(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(c_Numeral_Onumber__of(C,A),c_0,A) | c_lessequals(B,c_divide(D,c_Numeral_Onumber__of(C,A),A),A) # label(cls_NatSimprocs_Ole__divide__eq__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 501 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(C,c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(D,c_divide(C,c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Ole__divide__eq__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 502 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | -c_lessequals(C,c_times(B,c_Numeral_Onumber__of(D,A),A),A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(B,c_divide(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Ole__divide__eq__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 503 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),D,A) | c_lessequals(C,c_divide(D,c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Ole__divide__eq__number__of_6) # label(axiom). [assumption].
% 4.17/4.42 504 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(C,A),A),D,A) | c_less(c_Numeral_Onumber__of(C,A),c_0,A) | c_lessequals(B,c_divide(D,c_Numeral_Onumber__of(C,A),A),A) # label(cls_NatSimprocs_Ole__divide__eq__number__of_7) # label(axiom). [assumption].
% 4.17/4.42 505 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(C,c_times(D,c_Numeral_Onumber__of(B,A),A),A) | -c_lessequals(c_times(D,c_Numeral_Onumber__of(B,A),A),C,A) | c_lessequals(D,c_divide(C,c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Ole__divide__eq__number__of_8) # label(axiom). [assumption].
% 4.17/4.42 506 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | -c_lessequals(C,c_times(B,c_Numeral_Onumber__of(D,A),A),A) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(D,A),A),C,A) | c_lessequals(B,c_divide(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Ole__divide__eq__number__of_9) # label(axiom). [assumption].
% 4.17/4.42 507 -class_Numeral_Onumber(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_uminus(C,A),A) | c_lessequals(C,c_uminus(c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Ole__minus__iff__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 508 -class_Numeral_Onumber(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_Numeral_Onumber__of(C,A),A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_uminus(B,A),A) # label(cls_NatSimprocs_Ole__minus__iff__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 509 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oring(A) | c_times(c_minus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_minus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Oleft__diff__distrib__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 510 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Osemiring(A) | c_times(c_plus(B,C,A),c_Numeral_Onumber__of(D,A),A) = c_plus(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Oleft__distrib__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 511 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_divide(C,c_Numeral_Onumber__of(D,A),A),A) | -c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_less(c_times(B,c_Numeral_Onumber__of(D,A),A),C,A) # label(cls_NatSimprocs_Oless__divide__eq__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 512 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_divide(C,c_Numeral_Onumber__of(D,A),A),A) | -c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_less(C,c_times(B,c_Numeral_Onumber__of(D,A),A),A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) # label(cls_NatSimprocs_Oless__divide__eq__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 513 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_divide(C,c_Numeral_Onumber__of(D,A),A),A) | c_less(B,c_0,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) # label(cls_NatSimprocs_Oless__divide__eq__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 514 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_0,A) | c_less(B,c_divide(C,c_Numeral_Onumber__of(D,A),A),A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) # label(cls_NatSimprocs_Oless__divide__eq__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 515 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_less(C,c_divide(B,c_Numeral_Onumber__of(D,A),A),A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) # label(cls_NatSimprocs_Oless__divide__eq__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 516 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_0,A) | -c_less(C,c_times(B,c_Numeral_Onumber__of(D,A),A),A) | c_less(B,c_divide(C,c_Numeral_Onumber__of(D,A),A),A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) # label(cls_NatSimprocs_Oless__divide__eq__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 517 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_less(c_times(C,c_Numeral_Onumber__of(B,A),A),D,A) | c_less(C,c_divide(D,c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Oless__divide__eq__number__of_6) # label(axiom). [assumption].
% 4.17/4.42 518 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_0,A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),D,A) | c_less(B,c_divide(D,c_Numeral_Onumber__of(C,A),A),A) | c_less(c_Numeral_Onumber__of(C,A),c_0,A) # label(cls_NatSimprocs_Oless__divide__eq__number__of_7) # label(axiom). [assumption].
% 4.17/4.42 519 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -c_less(c_Numeral_Onumber__of(D,A),c_0,A) | -c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),B,A) | c_less(C,c_divide(B,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Oless__divide__eq__number__of_8) # label(axiom). [assumption].
% 4.17/4.42 520 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_0,A) | -c_less(C,c_times(B,c_Numeral_Onumber__of(D,A),A),A) | -c_less(c_times(B,c_Numeral_Onumber__of(D,A),A),C,A) | c_less(B,c_divide(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Oless__divide__eq__number__of_9) # label(axiom). [assumption].
% 4.17/4.42 521 -class_Numeral_Onumber(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_Numeral_Onumber__of(B,A),c_uminus(C,A),A) | c_less(C,c_uminus(c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Oless__minus__iff__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 522 -class_Numeral_Onumber(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_Numeral_Onumber__of(C,A),A),A) | c_less(c_Numeral_Onumber__of(C,A),c_uminus(B,A),A) # label(cls_NatSimprocs_Oless__minus__iff__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 523 -class_Numeral_Onumber(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_Numeral_Onumber__of(C,A) | c_uminus(c_Numeral_Onumber__of(C,A),A) = B # label(cls_NatSimprocs_Ominus__equation__iff__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 524 -class_Numeral_Onumber(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_Numeral_Onumber__of(B,A),A),A) = c_Numeral_Onumber__of(B,A) # label(cls_NatSimprocs_Ominus__equation__iff__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 525 -class_Numeral_Onumber(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_uminus(c_Numeral_Onumber__of(C,A),A),B,A) # label(cls_NatSimprocs_Ominus__le__iff__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 526 -class_Numeral_Onumber(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_Numeral_Onumber__of(B,A),A),C,A) | c_lessequals(c_uminus(C,A),c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Ominus__le__iff__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 527 -class_Numeral_Onumber(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_Numeral_Onumber__of(C,A),A) | c_less(c_uminus(c_Numeral_Onumber__of(C,A),A),B,A) # label(cls_NatSimprocs_Ominus__less__iff__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 528 -class_Numeral_Onumber(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_Numeral_Onumber__of(B,A),A),C,A) | c_less(c_uminus(C,A),c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Ominus__less__iff__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 529 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(C,D,A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 530 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(D,C,A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 531 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 532 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 533 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 534 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) # label(cls_NatSimprocs_Omult__le__cancel__left__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 535 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_0,c_Numeral_Onumber__of(B,A),A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(C,D,A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 536 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_Numeral_Onumber__of(B,A),c_0,A) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) | c_lessequals(D,C,A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 537 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(B,A),A),c_times(D,c_Numeral_Onumber__of(B,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 538 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 539 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_lessequals(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 540 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) | c_lessequals(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__le__cancel__right__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 541 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(C,D,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 542 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | -c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) | c_less(D,C,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 543 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 544 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 545 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),B,A),c_times(c_Numeral_Onumber__of(D,A),C,A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 546 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(c_Numeral_Onumber__of(D,A),C,A),c_times(c_Numeral_Onumber__of(D,A),B,A),A) # label(cls_NatSimprocs_Omult__less__cancel__left__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 547 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(B,D,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 548 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) | c_less(D,B,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 549 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_times(B,c_Numeral_Onumber__of(C,A),A),c_times(D,c_Numeral_Onumber__of(C,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 550 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(D,A),A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 551 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_times(B,c_Numeral_Onumber__of(D,A),A),c_times(C,c_Numeral_Onumber__of(D,A),A),A) | c_lessequals(c_Numeral_Onumber__of(D,A),c_0,A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 552 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(C,B,A) | c_less(c_times(C,c_Numeral_Onumber__of(D,A),A),c_times(B,c_Numeral_Onumber__of(D,A),A),A) # label(cls_NatSimprocs_Omult__less__cancel__right__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 553 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Oring(A) | c_times(c_Numeral_Onumber__of(B,A),c_minus(C,D,A),A) = c_minus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) # label(cls_NatSimprocs_Oright__diff__distrib__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 554 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Osemiring(A) | c_times(c_Numeral_Onumber__of(B,A),c_plus(C,D,A),A) = c_plus(c_times(c_Numeral_Onumber__of(B,A),C,A),c_times(c_Numeral_Onumber__of(B,A),D,A),A) # label(cls_NatSimprocs_Oright__distrib__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 555 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(B,A),C,A),A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Ozero__le__divide__iff__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 556 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(B,A),C,A),A) | c_lessequals(C,c_0,A) | c_lessequals(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Ozero__le__divide__iff__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 557 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(B,A),C,A),A) | c_lessequals(c_0,C,A) | c_lessequals(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Ozero__le__divide__iff__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 558 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(B,A),C,A),A) | c_lessequals(C,c_0,A) | c_lessequals(c_0,C,A) # label(cls_NatSimprocs_Ozero__le__divide__iff__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 559 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | -c_lessequals(c_0,c_Numeral_Onumber__of(C,A),A) | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(C,A),B,A),A) # label(cls_NatSimprocs_Ozero__le__divide__iff__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 560 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | -c_lessequals(c_Numeral_Onumber__of(C,A),c_0,A) | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(C,A),B,A),A) # label(cls_NatSimprocs_Ozero__le__divide__iff__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 561 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(B,A),C,A),A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Ozero__less__divide__iff__number__of_0) # label(axiom). [assumption].
% 4.17/4.42 562 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(B,A),C,A),A) | c_less(C,c_0,A) | c_less(c_0,c_Numeral_Onumber__of(B,A),A) # label(cls_NatSimprocs_Ozero__less__divide__iff__number__of_1) # label(axiom). [assumption].
% 4.17/4.42 563 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(B,A),C,A),A) | c_less(c_0,C,A) | c_less(c_Numeral_Onumber__of(B,A),c_0,A) # label(cls_NatSimprocs_Ozero__less__divide__iff__number__of_2) # label(axiom). [assumption].
% 4.17/4.42 564 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(B,A),C,A),A) | c_less(C,c_0,A) | c_less(c_0,C,A) # label(cls_NatSimprocs_Ozero__less__divide__iff__number__of_3) # label(axiom). [assumption].
% 4.17/4.42 565 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,B,A) | -c_less(c_0,c_Numeral_Onumber__of(C,A),A) | c_less(c_0,c_divide(c_Numeral_Onumber__of(C,A),B,A),A) # label(cls_NatSimprocs_Ozero__less__divide__iff__number__of_4) # label(axiom). [assumption].
% 4.17/4.42 566 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_0,A) | -c_less(c_Numeral_Onumber__of(C,A),c_0,A) | c_less(c_0,c_divide(c_Numeral_Onumber__of(C,A),B,A),A) # label(cls_NatSimprocs_Ozero__less__divide__iff__number__of_5) # label(axiom). [assumption].
% 4.17/4.42 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Nat_Opower(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_IntDef_Oint) = c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,453,a)].
% 4.17/4.42 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | A = c_times(c_divide(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(B,tc_IntDef_Oint) = c_0. [resolve(452,a,454,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_0 | c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(452,a,455,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_0 | c_divide(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = B. [resolve(452,a,456,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_divide(c_times(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(452,a,457,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,458,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,459,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(B,c_0,tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,460,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(B,c_0,tc_IntDef_Oint) | c_lessequals(c_0,B,tc_IntDef_Oint). [resolve(452,a,461,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(A,c_0,tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_divide(c_Numeral_Onumber__of(B,tc_IntDef_Oint),A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,462,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_divide(c_Numeral_Onumber__of(B,tc_IntDef_Oint),A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,463,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,464,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,465,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_divide(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_0,C,tc_IntDef_Oint). [resolve(452,a,466,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_divide(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(452,a,467,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_divide(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,468,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_divide(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(452,a,469,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(B,c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint). [resolve(452,a,470,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(A,c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_divide(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,471,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(B,c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint). [resolve(452,a,472,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(A,c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,B,tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_divide(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,473,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,474,a)].
% 4.17/4.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(c_0,B,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,475,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(B,c_0,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,476,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(B,c_0,tc_IntDef_Oint) | c_less(c_0,B,tc_IntDef_Oint). [resolve(452,a,477,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_divide(c_Numeral_Onumber__of(B,tc_IntDef_Oint),A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,478,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,A,tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(c_divide(c_Numeral_Onumber__of(B,tc_IntDef_Oint),A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,479,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,480,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_less(c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,481,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_divide(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(c_0,C,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,482,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,A,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(c_divide(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(452,a,483,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_less(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_divide(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,484,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,A,tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_divide(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(452,a,485,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_divide(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,486,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_0,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(c_divide(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,487,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_divide(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,488,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_0,B,tc_IntDef_Oint) | -c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_divide(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,489,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_0 | c_times(c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = B. [resolve(452,a,490,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_0 | c_0 = c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,491,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | A = c_divide(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_Numeral_Onumber__of(B,tc_IntDef_Oint) = c_0. [resolve(452,a,492,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_0 = c_divide(c_times(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,493,a)].
% 4.17/4.44 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) != c_uminus(B,tc_IntDef_Oint) | B = c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,494,a)].
% 4.17/4.44 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_Numeral_Onumber__of(A,tc_IntDef_Oint) = c_uminus(c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,495,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Ofield(tc_IntDef_Oint) | c_HOL_Oinverse(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_divide(c_1,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,496,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(B,c_divide(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint). [resolve(452,a,497,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(B,c_divide(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,498,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(A,c_divide(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(452,a,499,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(A,c_0,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_divide(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,500,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(B,c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,501,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(A,c_0,tc_IntDef_Oint) | -c_lessequals(B,c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_divide(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,502,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,c_divide(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,503,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(A,c_0,tc_IntDef_Oint) | -c_lessequals(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_divide(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,504,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(B,c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(C,c_divide(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,505,a)].
% 4.17/4.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(A,c_0,tc_IntDef_Oint) | -c_lessequals(B,c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(A,c_divide(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,506,a)].
% 4.25/4.45 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,507,a)].
% 4.25/4.45 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,508,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Oring(tc_IntDef_Oint) | c_times(c_minus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,509,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Osemiring(tc_IntDef_Oint) | c_times(c_plus(A,B,tc_IntDef_Oint),c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,510,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(452,a,511,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(B,c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,512,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,513,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,514,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(B,c_divide(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,515,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | -c_less(B,c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,516,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,c_divide(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,517,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,c_divide(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,518,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_divide(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,519,a)].
% 4.25/4.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | -c_less(B,c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,520,a)].
% 4.25/4.45 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,521,a)].
% 4.25/4.45 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,522,a)].
% 4.25/4.45 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_Numeral_Onumber__of(B,tc_IntDef_Oint) | c_uminus(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(452,a,523,a)].
% 4.25/4.45 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(A,tc_IntDef_Oint). [resolve(452,a,524,a)].
% 4.25/4.45 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_uminus(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(452,a,525,a)].
% 4.25/4.45 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_uminus(B,tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,526,a)].
% 4.25/4.45 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_uminus(c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(452,a,527,a)].
% 4.25/4.45 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_uminus(B,tc_IntDef_Oint),c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,528,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(452,a,529,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(452,a,530,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,531,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,532,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,533,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(B,A,tc_IntDef_Oint) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,534,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(452,a,535,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,B,tc_IntDef_Oint). [resolve(452,a,536,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,537,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,538,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,539,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(B,A,tc_IntDef_Oint) | c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,540,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(452,a,541,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(C,B,tc_IntDef_Oint). [resolve(452,a,542,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,543,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,544,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,545,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | -c_less(B,A,tc_IntDef_Oint) | c_less(c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(C,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,546,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(452,a,547,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint). [resolve(452,a,548,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | c_less(c_times(A,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),c_times(C,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,549,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,550,a)].
% 4.25/4.46 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | c_less(c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(C,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,551,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) | -c_less(A,B,tc_IntDef_Oint) | -c_less(B,A,tc_IntDef_Oint) | c_less(c_times(B,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),c_times(A,c_Numeral_Onumber__of(C,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,552,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Oring(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_minus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,553,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Osemiring(tc_IntDef_Oint) | c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(A,tc_IntDef_Oint),C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,554,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,555,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_0,tc_IntDef_Oint) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,556,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,B,tc_IntDef_Oint) | c_lessequals(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,557,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_0,tc_IntDef_Oint) | c_lessequals(c_0,B,tc_IntDef_Oint). [resolve(452,a,558,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(c_0,A,tc_IntDef_Oint) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(B,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,559,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_lessequals(A,c_0,tc_IntDef_Oint) | -c_lessequals(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(B,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,560,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,561,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_0,tc_IntDef_Oint) | c_less(c_0,c_Numeral_Onumber__of(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,562,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,B,tc_IntDef_Oint) | c_less(c_Numeral_Onumber__of(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(452,a,563,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(A,tc_IntDef_Oint),B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_0,tc_IntDef_Oint) | c_less(c_0,B,tc_IntDef_Oint). [resolve(452,a,564,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(c_0,A,tc_IntDef_Oint) | -c_less(c_0,c_Numeral_Onumber__of(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_0,c_divide(c_Numeral_Onumber__of(B,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,565,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_IntDef_Oint) | -class_Ring__and__Field_Oordered__field(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | -c_less(c_Numeral_Onumber__of(B,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(c_0,c_divide(c_Numeral_Onumber__of(B,tc_IntDef_Oint),A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(452,a,566,a)].
% 4.25/4.47 567 class_Numeral_Onumber(tc_nat) # label(clsarity_nat_46) # label(axiom). [assumption].
% 4.25/4.47 Derived: -class_Power_Orecpower(tc_nat) | c_Nat_Opower(c_Numeral_Onumber__of(A,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_times(c_Numeral_Onumber__of(A,tc_nat),c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,453,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Ofield(tc_nat) | A = c_times(c_divide(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_Numeral_Onumber__of(B,tc_nat) = c_0. [resolve(567,a,454,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Ofield(tc_nat) | c_Numeral_Onumber__of(A,tc_nat) != c_0 | c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat) = c_0. [resolve(567,a,455,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Ofield(tc_nat) | c_Numeral_Onumber__of(A,tc_nat) = c_0 | c_divide(c_times(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),c_Numeral_Onumber__of(A,tc_nat),tc_nat) = B. [resolve(567,a,456,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Ofield(tc_nat) | c_divide(c_times(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat),c_Numeral_Onumber__of(A,tc_nat),tc_nat) = c_0. [resolve(567,a,457,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_0,tc_nat) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat). [resolve(567,a,458,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_0,tc_nat) | c_lessequals(c_0,B,tc_nat) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,459,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_0,tc_nat) | c_lessequals(B,c_0,tc_nat) | c_lessequals(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat). [resolve(567,a,460,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_0,tc_nat) | c_lessequals(B,c_0,tc_nat) | c_lessequals(c_0,B,tc_nat). [resolve(567,a,461,a)].
% 4.25/4.47 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(A,c_0,tc_nat) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_divide(c_Numeral_Onumber__of(B,tc_nat),A,tc_nat),c_0,tc_nat). [resolve(567,a,462,a)].
% 4.25/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_0,A,tc_nat) | -c_lessequals(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat) | c_lessequals(c_divide(c_Numeral_Onumber__of(B,tc_nat),A,tc_nat),c_0,tc_nat). [resolve(567,a,463,a)].
% 4.25/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_lessequals(c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat) | c_lessequals(B,c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,464,a)].
% 4.25/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | -c_lessequals(c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,465,a)].
% 4.25/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_divide(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),C,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat) | c_lessequals(c_0,C,tc_nat). [resolve(567,a,466,a)].
% 4.25/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_0,A,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat) | c_lessequals(c_divide(C,c_Numeral_Onumber__of(B,tc_nat),tc_nat),A,tc_nat). [resolve(567,a,467,a)].
% 4.25/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(c_divide(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,468,a)].
% 4.25/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_0,A,tc_nat) | -c_lessequals(c_times(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),C,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_divide(C,c_Numeral_Onumber__of(B,tc_nat),tc_nat),A,tc_nat). [resolve(567,a,469,a)].
% 4.25/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_lessequals(B,c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat) | c_lessequals(c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat). [resolve(567,a,470,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(A,c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_lessequals(c_0,B,tc_nat) | c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat) | c_lessequals(c_divide(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,471,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | -c_lessequals(B,c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),B,tc_nat) | c_lessequals(c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat). [resolve(567,a,472,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(A,c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_lessequals(c_0,B,tc_nat) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),A,tc_nat) | c_lessequals(c_divide(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,473,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_0,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat). [resolve(567,a,474,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_0,tc_nat) | c_less(c_0,B,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,475,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_0,tc_nat) | c_less(B,c_0,tc_nat) | c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat). [resolve(567,a,476,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_0,tc_nat) | c_less(B,c_0,tc_nat) | c_less(c_0,B,tc_nat). [resolve(567,a,477,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_0,tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_divide(c_Numeral_Onumber__of(B,tc_nat),A,tc_nat),c_0,tc_nat). [resolve(567,a,478,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,A,tc_nat) | -c_less(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat) | c_less(c_divide(c_Numeral_Onumber__of(B,tc_nat),A,tc_nat),c_0,tc_nat). [resolve(567,a,479,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_less(c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat) | c_less(B,c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,480,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | -c_less(c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_less(c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,481,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_divide(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),C,tc_nat) | c_less(c_0,C,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat). [resolve(567,a,482,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,A,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat) | c_less(c_divide(C,c_Numeral_Onumber__of(B,tc_nat),tc_nat),A,tc_nat). [resolve(567,a,483,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | -c_less(c_times(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_less(c_divide(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,484,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,A,tc_nat) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),C,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_divide(C,c_Numeral_Onumber__of(B,tc_nat),tc_nat),A,tc_nat). [resolve(567,a,485,a)].
% 4.28/4.48 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_divide(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,486,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_less(c_0,B,tc_nat) | c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat) | c_less(c_divide(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,487,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat) | -c_less(c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),A,tc_nat) | c_less(c_divide(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,488,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_less(c_0,B,tc_nat) | -c_less(c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),A,tc_nat) | c_less(c_divide(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,489,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Ofield(tc_nat) | c_Numeral_Onumber__of(A,tc_nat) = c_0 | c_times(c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),c_Numeral_Onumber__of(A,tc_nat),tc_nat) = B. [resolve(567,a,490,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Ofield(tc_nat) | c_Numeral_Onumber__of(A,tc_nat) != c_0 | c_0 = c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,491,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Ofield(tc_nat) | A = c_divide(c_times(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_Numeral_Onumber__of(B,tc_nat) = c_0. [resolve(567,a,492,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Ofield(tc_nat) | c_0 = c_divide(c_times(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat),c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,493,a)].
% 4.28/4.49 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_Numeral_Onumber__of(A,tc_nat) != c_uminus(B,tc_nat) | B = c_uminus(c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,494,a)].
% 4.28/4.49 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_Numeral_Onumber__of(A,tc_nat) = c_uminus(c_uminus(c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,495,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Ofield(tc_nat) | c_HOL_Oinverse(c_Numeral_Onumber__of(A,tc_nat),tc_nat) = c_divide(c_1,c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,496,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_lessequals(B,c_divide(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat) | c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat). [resolve(567,a,497,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | -c_lessequals(B,c_divide(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(C,c_times(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,498,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(A,c_divide(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat) | c_lessequals(A,c_0,tc_nat). [resolve(567,a,499,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(A,c_0,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat) | c_lessequals(A,c_divide(C,c_Numeral_Onumber__of(B,tc_nat),tc_nat),tc_nat). [resolve(567,a,500,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | -c_lessequals(B,c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(C,c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,501,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(A,c_0,tc_nat) | -c_lessequals(B,c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(A,c_divide(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(567,a,502,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat) | c_lessequals(B,c_divide(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,503,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(A,c_0,tc_nat) | -c_lessequals(c_times(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),C,tc_nat) | c_less(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat) | c_lessequals(A,c_divide(C,c_Numeral_Onumber__of(B,tc_nat),tc_nat),tc_nat). [resolve(567,a,504,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | -c_lessequals(B,c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat) | -c_lessequals(c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),B,tc_nat) | c_lessequals(C,c_divide(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,505,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(A,c_0,tc_nat) | -c_lessequals(B,c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_lessequals(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),B,tc_nat) | c_lessequals(A,c_divide(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(567,a,506,a)].
% 4.28/4.49 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_Numeral_Onumber__of(A,tc_nat),c_uminus(B,tc_nat),tc_nat) | c_lessequals(B,c_uminus(c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,507,a)].
% 4.28/4.49 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(A,c_uminus(c_Numeral_Onumber__of(B,tc_nat),tc_nat),tc_nat) | c_lessequals(c_Numeral_Onumber__of(B,tc_nat),c_uminus(A,tc_nat),tc_nat). [resolve(567,a,508,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Oring(tc_nat) | c_times(c_minus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_minus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(567,a,509,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Osemiring(tc_nat) | c_times(c_plus(A,B,tc_nat),c_Numeral_Onumber__of(C,tc_nat),tc_nat) = c_plus(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(567,a,510,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),B,tc_nat). [resolve(567,a,511,a)].
% 4.28/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat) | c_less(B,c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat). [resolve(567,a,512,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | c_less(A,c_0,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat). [resolve(567,a,513,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat). [resolve(567,a,514,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat) | c_less(B,c_divide(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat). [resolve(567,a,515,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_0,tc_nat) | -c_less(B,c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat). [resolve(567,a,516,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_less(c_times(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),C,tc_nat) | c_less(B,c_divide(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,517,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_0,tc_nat) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),C,tc_nat) | c_less(A,c_divide(C,c_Numeral_Onumber__of(B,tc_nat),tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat). [resolve(567,a,518,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat) | -c_less(c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),A,tc_nat) | c_less(B,c_divide(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(567,a,519,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_0,tc_nat) | -c_less(B,c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | -c_less(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),B,tc_nat) | c_less(A,c_divide(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(567,a,520,a)].
% 4.28/4.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_uminus(B,tc_nat),tc_nat) | c_less(B,c_uminus(c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,521,a)].
% 4.28/4.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_uminus(c_Numeral_Onumber__of(B,tc_nat),tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(B,tc_nat),c_uminus(A,tc_nat),tc_nat). [resolve(567,a,522,a)].
% 4.28/4.50 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(A,tc_nat) != c_Numeral_Onumber__of(B,tc_nat) | c_uminus(c_Numeral_Onumber__of(B,tc_nat),tc_nat) = A. [resolve(567,a,523,a)].
% 4.28/4.50 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(c_uminus(c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat) = c_Numeral_Onumber__of(A,tc_nat). [resolve(567,a,524,a)].
% 4.28/4.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(A,tc_nat),c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_uminus(c_Numeral_Onumber__of(B,tc_nat),tc_nat),A,tc_nat). [resolve(567,a,525,a)].
% 4.28/4.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(c_Numeral_Onumber__of(A,tc_nat),tc_nat),B,tc_nat) | c_lessequals(c_uminus(B,tc_nat),c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,526,a)].
% 4.28/4.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(A,tc_nat),c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_uminus(c_Numeral_Onumber__of(B,tc_nat),tc_nat),A,tc_nat). [resolve(567,a,527,a)].
% 4.28/4.50 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(c_Numeral_Onumber__of(A,tc_nat),tc_nat),B,tc_nat) | c_less(c_uminus(B,tc_nat),c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,528,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(567,a,529,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | -c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat) | c_lessequals(C,B,tc_nat). [resolve(567,a,530,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | c_lessequals(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(567,a,531,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_lessequals(A,B,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(C,tc_nat),A,tc_nat),tc_nat). [resolve(567,a,532,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_lessequals(A,B,tc_nat) | c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_nat),A,tc_nat),c_times(c_Numeral_Onumber__of(C,tc_nat),B,tc_nat),tc_nat). [resolve(567,a,533,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(B,A,tc_nat) | c_lessequals(c_times(c_Numeral_Onumber__of(C,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(C,tc_nat),A,tc_nat),tc_nat). [resolve(567,a,534,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(567,a,535,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | -c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat) | c_lessequals(C,B,tc_nat). [resolve(567,a,536,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | c_lessequals(c_times(B,c_Numeral_Onumber__of(A,tc_nat),tc_nat),c_times(C,c_Numeral_Onumber__of(A,tc_nat),tc_nat),tc_nat). [resolve(567,a,537,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_lessequals(A,B,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat) | c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(567,a,538,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_lessequals(A,B,tc_nat) | c_less(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat) | c_lessequals(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(567,a,539,a)].
% 4.28/4.50 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(B,A,tc_nat) | c_lessequals(c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(567,a,540,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat) | -c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(567,a,541,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat) | -c_lessequals(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat) | c_less(C,B,tc_nat). [resolve(567,a,542,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | c_less(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat). [resolve(567,a,543,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(A,B,tc_nat) | c_less(c_times(c_Numeral_Onumber__of(C,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(C,tc_nat),A,tc_nat),tc_nat) | c_lessequals(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat). [resolve(567,a,544,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(A,B,tc_nat) | c_less(c_times(c_Numeral_Onumber__of(C,tc_nat),A,tc_nat),c_times(c_Numeral_Onumber__of(C,tc_nat),B,tc_nat),tc_nat) | c_lessequals(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat). [resolve(567,a,545,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(A,B,tc_nat) | -c_less(B,A,tc_nat) | c_less(c_times(c_Numeral_Onumber__of(C,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(C,tc_nat),A,tc_nat),tc_nat). [resolve(567,a,546,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),c_times(C,c_Numeral_Onumber__of(B,tc_nat),tc_nat),tc_nat) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(567,a,547,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(c_times(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),c_times(C,c_Numeral_Onumber__of(B,tc_nat),tc_nat),tc_nat) | -c_lessequals(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat) | c_less(C,A,tc_nat). [resolve(567,a,548,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | c_less(c_times(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),c_times(C,c_Numeral_Onumber__of(B,tc_nat),tc_nat),tc_nat) | c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat). [resolve(567,a,549,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(A,B,tc_nat) | c_less(c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | c_lessequals(c_0,c_Numeral_Onumber__of(C,tc_nat),tc_nat). [resolve(567,a,550,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(A,B,tc_nat) | c_less(c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat) | c_lessequals(c_Numeral_Onumber__of(C,tc_nat),c_0,tc_nat). [resolve(567,a,551,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | -c_less(A,B,tc_nat) | -c_less(B,A,tc_nat) | c_less(c_times(B,c_Numeral_Onumber__of(C,tc_nat),tc_nat),c_times(A,c_Numeral_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(567,a,552,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Oring(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_minus(B,C,tc_nat),tc_nat) = c_minus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(567,a,553,a)].
% 4.28/4.51 Derived: -class_Ring__and__Field_Osemiring(tc_nat) | c_times(c_Numeral_Onumber__of(A,tc_nat),c_plus(B,C,tc_nat),tc_nat) = c_plus(c_times(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),c_times(c_Numeral_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(567,a,554,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),tc_nat) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat). [resolve(567,a,555,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),tc_nat) | c_lessequals(B,c_0,tc_nat) | c_lessequals(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,556,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),tc_nat) | c_lessequals(c_0,B,tc_nat) | c_lessequals(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat). [resolve(567,a,557,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),tc_nat) | c_lessequals(B,c_0,tc_nat) | c_lessequals(c_0,B,tc_nat). [resolve(567,a,558,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(c_0,A,tc_nat) | -c_lessequals(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(B,tc_nat),A,tc_nat),tc_nat). [resolve(567,a,559,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_lessequals(A,c_0,tc_nat) | -c_lessequals(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat) | c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(B,tc_nat),A,tc_nat),tc_nat). [resolve(567,a,560,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat) | c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat). [resolve(567,a,561,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),tc_nat) | c_less(B,c_0,tc_nat) | c_less(c_0,c_Numeral_Onumber__of(A,tc_nat),tc_nat). [resolve(567,a,562,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),tc_nat) | c_less(c_0,B,tc_nat) | c_less(c_Numeral_Onumber__of(A,tc_nat),c_0,tc_nat). [resolve(567,a,563,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,c_divide(c_Numeral_Onumber__of(A,tc_nat),B,tc_nat),tc_nat) | c_less(B,c_0,tc_nat) | c_less(c_0,B,tc_nat). [resolve(567,a,564,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(c_0,A,tc_nat) | -c_less(c_0,c_Numeral_Onumber__of(B,tc_nat),tc_nat) | c_less(c_0,c_divide(c_Numeral_Onumber__of(B,tc_nat),A,tc_nat),tc_nat). [resolve(567,a,565,a)].
% 4.62/4.84 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_nat) | -class_Ring__and__Field_Oordered__field(tc_nat) | -c_less(A,c_0,tc_nat) | -c_less(c_Numeral_Onumber__of(B,tc_nat),c_0,tc_nat) | c_less(c_0,c_divide(c_Numeral_Onumber__of(B,tc_nat),A,tc_nat),tc_nat). [resolve(567,a,566,a)].
% 4.62/4.84 568 class_Numeral_Onumber(tc_IntDef_Oint). [resolve(168,a,74,a)].
% 4.62/4.84 569 class_HOL_Oone(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_1) # label(axiom). [assumption].
% 4.62/4.84 570 -class_HOL_Oone(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) # label(cls_NatSimprocs_Oequation__minus__iff__1_0) # label(axiom). [assumption].
% 4.62/4.84 571 -class_HOL_Oone(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 # label(cls_NatSimprocs_Oequation__minus__iff__1_1) # label(axiom). [assumption].
% 4.64/4.85 572 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) # label(cls_NatSimprocs_Ole__minus__iff__1_0) # label(axiom). [assumption].
% 4.64/4.85 573 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) # label(cls_NatSimprocs_Ole__minus__iff__1_1) # label(axiom). [assumption].
% 4.64/4.85 574 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) # label(cls_NatSimprocs_Oless__minus__iff__1_0) # label(axiom). [assumption].
% 4.64/4.85 575 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) # label(cls_NatSimprocs_Oless__minus__iff__1_1) # label(axiom). [assumption].
% 4.64/4.85 576 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) # label(cls_NatSimprocs_Ominus__le__iff__1_0) # label(axiom). [assumption].
% 4.64/4.85 577 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) # label(cls_NatSimprocs_Ominus__le__iff__1_1) # label(axiom). [assumption].
% 4.64/4.85 578 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) # label(cls_NatSimprocs_Ominus__less__iff__1_0) # label(axiom). [assumption].
% 4.64/4.85 579 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) # label(cls_NatSimprocs_Ominus__less__iff__1_1) # label(axiom). [assumption].
% 4.64/4.85 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_1 | A = c_uminus(c_1,tc_IntDef_Oint). [resolve(569,a,570,a)].
% 4.64/4.85 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) = c_1. [resolve(569,a,571,a)].
% 4.64/4.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(569,a,572,a)].
% 4.64/4.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(569,a,573,a)].
% 4.64/4.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(569,a,574,a)].
% 4.64/4.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(569,a,575,a)].
% 4.64/4.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(569,a,576,a)].
% 4.64/4.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(569,a,577,a)].
% 4.64/4.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(569,a,578,a)].
% 4.64/4.85 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(569,a,579,a)].
% 4.64/4.85 580 class_HOL_Oone(tc_nat) # label(clsarity_nat_0) # label(axiom). [assumption].
% 4.64/4.85 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(A,tc_nat) != c_1 | A = c_uminus(c_1,tc_nat). [resolve(580,a,570,a)].
% 4.64/4.85 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(c_uminus(c_1,tc_nat),tc_nat) = c_1. [resolve(580,a,571,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat) | c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(580,a,572,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat) | c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(580,a,573,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_1,c_uminus(A,tc_nat),tc_nat) | c_less(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(580,a,574,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_uminus(c_1,tc_nat),tc_nat) | c_less(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(580,a,575,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat) | c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(580,a,576,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat) | c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(580,a,577,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(A,tc_nat),c_1,tc_nat) | c_less(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(580,a,578,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(c_1,tc_nat),A,tc_nat) | c_less(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(580,a,579,a)].
% 4.64/4.87 581 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_0) # label(axiom). [assumption].
% 4.64/4.87 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(581,b,570,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(581,b,571,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(581,b,572,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(581,b,573,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(581,b,574,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(581,b,575,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(581,b,576,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(581,b,577,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(581,b,578,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(581,b,579,a)].
% 4.64/4.87 582 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Oone(A) # label(clsrel_OrderedGroup_Omonoid__mult_0) # label(axiom). [assumption].
% 4.64/4.87 Derived: -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(582,b,570,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(582,b,571,a)].
% 4.64/4.87 Derived: -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(582,b,572,a)].
% 4.64/4.88 Derived: -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(582,b,573,a)].
% 4.64/4.88 Derived: -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(582,b,574,a)].
% 4.64/4.88 Derived: -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(582,b,575,a)].
% 4.64/4.88 Derived: -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(582,b,576,a)].
% 4.64/4.88 Derived: -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(582,b,577,a)].
% 4.64/4.88 Derived: -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(582,b,578,a)].
% 4.64/4.88 Derived: -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(582,b,579,a)].
% 4.64/4.88 583 -class_Power_Orecpower(A) | class_HOL_Oone(A) # label(clsrel_Power_Orecpower_2) # label(axiom). [assumption].
% 4.64/4.88 Derived: -class_Power_Orecpower(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(583,b,570,a)].
% 4.64/4.88 Derived: -class_Power_Orecpower(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(583,b,571,a)].
% 4.64/4.88 Derived: -class_Power_Orecpower(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(583,b,572,a)].
% 4.64/4.88 Derived: -class_Power_Orecpower(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(583,b,573,a)].
% 4.64/4.88 Derived: -class_Power_Orecpower(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(583,b,574,a)].
% 4.64/4.88 Derived: -class_Power_Orecpower(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(583,b,575,a)].
% 4.64/4.88 Derived: -class_Power_Orecpower(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(583,b,576,a)].
% 4.64/4.88 Derived: -class_Power_Orecpower(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(583,b,577,a)].
% 4.64/4.88 Derived: -class_Power_Orecpower(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(583,b,578,a)].
% 4.64/4.88 Derived: -class_Power_Orecpower(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(583,b,579,a)].
% 4.64/4.88 584 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) # label(axiom). [assumption].
% 4.64/4.88 Derived: -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(584,b,570,a)].
% 4.64/4.88 Derived: -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(584,b,571,a)].
% 4.64/4.88 Derived: -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(584,b,572,a)].
% 4.64/4.88 Derived: -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(584,b,573,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(584,b,574,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(584,b,575,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(584,b,576,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(584,b,577,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(584,b,578,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(584,b,579,a)].
% 4.64/4.89 585 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_2) # label(axiom). [assumption].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(585,b,570,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(585,b,571,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(585,b,572,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(585,b,573,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(585,b,574,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(585,b,575,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(585,b,576,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(585,b,577,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(585,b,578,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(585,b,579,a)].
% 4.64/4.89 586 -class_Ring__and__Field_Ofield(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Ofield_13) # label(axiom). [assumption].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(586,b,570,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(586,b,571,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(586,b,572,a)].
% 4.64/4.89 Derived: -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(586,b,573,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(586,b,574,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(586,b,575,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(586,b,576,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(586,b,577,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(586,b,578,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Ofield(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(586,b,579,a)].
% 4.64/4.90 587 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oidom_13) # label(axiom). [assumption].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(587,b,570,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(587,b,571,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(587,b,572,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(587,b,573,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(587,b,574,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(587,b,575,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(587,b,576,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(587,b,577,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(587,b,578,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(587,b,579,a)].
% 4.64/4.90 588 -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__field_16) # label(axiom). [assumption].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(588,b,570,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(588,b,571,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(588,b,572,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(588,b,573,a)].
% 4.64/4.90 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(588,b,574,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(588,b,575,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(588,b,576,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(588,b,577,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(588,b,578,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__field(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(588,b,579,a)].
% 4.64/4.93 589 -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oordered__idom_13) # label(axiom). [assumption].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(589,b,570,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(589,b,571,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(589,b,572,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(589,b,573,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(589,b,574,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(589,b,575,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(589,b,576,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(589,b,577,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(589,b,578,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(589,b,579,a)].
% 4.64/4.93 590 -class_Ring__and__Field_Oring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Oring__1_18) # label(axiom). [assumption].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(590,b,570,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(590,b,571,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(590,b,572,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(590,b,573,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(590,b,574,a)].
% 4.64/4.93 Derived: -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(590,b,575,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(590,b,576,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(590,b,577,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(590,b,578,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(590,b,579,a)].
% 4.72/4.94 591 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1_2) # label(axiom). [assumption].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(591,b,570,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(591,b,571,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(591,b,572,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(591,b,573,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(591,b,574,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(591,b,575,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(591,b,576,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(591,b,577,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(591,b,578,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(591,b,579,a)].
% 4.72/4.94 592 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Oone(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_10) # label(axiom). [assumption].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(592,b,570,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(592,b,571,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(592,b,572,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(592,b,573,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(592,b,574,a)].
% 4.72/4.94 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(592,b,575,a)].
% 5.02/5.25 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(592,b,576,a)].
% 5.02/5.25 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(592,b,577,a)].
% 5.02/5.25 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(592,b,578,a)].
% 5.02/5.25 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(592,b,579,a)].
% 5.02/5.25 593 class_HOL_Oone(tc_IntDef_Oint). [resolve(157,a,74,a)].
% 5.02/5.25 594 -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oone(A). [resolve(226,b,213,a)].
% 5.02/5.25 595 class_HOL_Oone(tc_IntDef_Oint). [resolve(228,a,213,a)].
% 5.02/5.25 596 class_HOL_Oone(tc_nat). [resolve(249,a,240,a)].
% 5.02/5.25 597 class_HOL_Oone(A) | -class_Power_Orecpower(A). [resolve(249,a,241,b)].
% 5.02/5.25 598 -class_Ring__and__Field_Ofield(A) | class_HOL_Oone(A). [resolve(265,b,249,a)].
% 5.02/5.25 599 -class_Ring__and__Field_Oidom(A) | class_HOL_Oone(A). [resolve(266,b,249,a)].
% 5.02/5.25 600 -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oone(A). [resolve(268,b,249,a)].
% 5.02/5.25 601 class_HOL_Oone(tc_IntDef_Oint). [resolve(271,a,249,a)].
% 5.02/5.25 602 class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_50) # label(axiom). [assumption].
% 5.02/5.25 603 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0 # label(cls_OrderedGroup_Oabs__0__eq_0) # label(axiom). [assumption].
% 5.02/5.25 604 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_0 = c_HOL_Oabs(c_0,A) # label(cls_OrderedGroup_Oabs__0__eq_1) # label(axiom). [assumption].
% 5.02/5.25 605 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A) # label(cls_OrderedGroup_Oabs__add__abs_0) # label(axiom). [assumption].
% 5.02/5.25 606 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0 # label(cls_OrderedGroup_Oabs__eq__0_0) # label(axiom). [assumption].
% 5.02/5.25 607 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_0,A) = c_0 # label(cls_OrderedGroup_Oabs__eq__0_1) # label(axiom). [assumption].
% 5.02/5.25 608 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A) # label(cls_OrderedGroup_Oabs__ge__zero_0) # label(axiom). [assumption].
% 5.02/5.25 609 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A) # label(cls_OrderedGroup_Oabs__idempotent_0) # label(axiom). [assumption].
% 5.02/5.25 610 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0 # label(cls_OrderedGroup_Oabs__le__zero__iff_0) # label(axiom). [assumption].
% 5.02/5.25 611 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A) # label(cls_OrderedGroup_Oabs__le__zero__iff_1) # label(axiom). [assumption].
% 5.02/5.25 612 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A) # label(cls_OrderedGroup_Oabs__minus__cancel_0) # label(axiom). [assumption].
% 5.02/5.25 613 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_less(c_HOL_Oabs(B,A),c_0,A) # label(cls_OrderedGroup_Oabs__not__less__zero_0) # label(axiom). [assumption].
% 5.02/5.25 614 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B # label(cls_OrderedGroup_Oabs__of__nonneg_0) # label(axiom). [assumption].
% 5.02/5.25 615 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A) # label(cls_OrderedGroup_Oabs__of__nonpos_0) # label(axiom). [assumption].
% 5.02/5.25 616 -class_OrderedGroup_Olordered__ab__group__abs(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A) # label(cls_OrderedGroup_Ozero__less__abs__iff_0) # label(axiom). [assumption].
% 5.02/5.26 617 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0 # label(cls_OrderedGroup_Ozero__less__abs__iff_1) # label(axiom). [assumption].
% 5.02/5.26 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(602,a,603,a)].
% 5.02/5.26 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(602,a,604,a)].
% 5.02/5.26 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(602,a,605,a)].
% 5.02/5.26 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(602,a,606,a)].
% 5.02/5.26 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(602,a,607,a)].
% 5.02/5.26 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(602,a,608,a)].
% 5.02/5.26 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(602,a,609,a)].
% 5.02/5.26 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(602,a,610,a)].
% 5.02/5.26 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(602,a,611,a)].
% 5.02/5.26 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(602,a,612,a)].
% 5.02/5.26 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(602,a,613,a)].
% 5.02/5.26 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(602,a,614,a)].
% 5.02/5.26 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(602,a,615,a)].
% 5.02/5.26 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(602,a,616,a)].
% 5.02/5.26 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(602,a,617,a)].
% 5.02/5.26 618 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_0) # label(axiom). [assumption].
% 5.02/5.26 Derived: class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(618,a,602,a)].
% 5.02/5.26 619 -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].
% 5.02/5.26 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(619,a,602,a)].
% 5.02/5.26 620 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_10) # label(axiom). [assumption].
% 5.02/5.26 621 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_11) # label(axiom). [assumption].
% 5.02/5.26 622 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_12) # label(axiom). [assumption].
% 5.02/5.26 623 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_13) # label(axiom). [assumption].
% 5.02/5.26 624 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_14) # label(axiom). [assumption].
% 5.02/5.26 625 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_17) # label(axiom). [assumption].
% 5.02/5.26 626 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_18) # label(axiom). [assumption].
% 5.02/5.26 627 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_2) # label(axiom). [assumption].
% 5.02/5.26 628 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_3) # label(axiom). [assumption].
% 5.02/5.26 629 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_4) # label(axiom). [assumption].
% 5.09/5.29 630 -class_OrderedGroup_Olordered__ab__group__abs(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group__abs_5) # label(axiom). [assumption].
% 5.09/5.29 631 -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].
% 5.09/5.29 632 -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].
% 5.09/5.29 633 -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].
% 5.09/5.29 634 -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].
% 5.09/5.29 635 -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].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(635,b,603,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(635,b,604,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A). [resolve(635,b,605,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(635,b,606,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(635,b,607,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(635,b,608,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(635,b,609,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(635,b,610,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(635,b,611,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(635,b,612,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(635,b,613,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(635,b,614,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(635,b,615,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(635,b,616,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(635,b,617,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(635,b,619,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(635,b,620,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(635,b,621,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(635,b,622,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(635,b,623,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(635,b,629,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ozero(A). [resolve(635,b,630,a)].
% 5.09/5.29 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(635,b,634,a)].
% 5.09/5.29 636 -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].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(636,b,603,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(636,b,604,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A). [resolve(636,b,605,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(636,b,606,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(636,b,607,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(636,b,608,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(636,b,609,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(636,b,610,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(636,b,611,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(636,b,612,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(636,b,613,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(636,b,614,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(636,b,615,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(636,b,616,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__field(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(636,b,617,a)].
% 5.09/5.31 637 -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].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(637,b,603,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(637,b,604,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A). [resolve(637,b,605,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(637,b,606,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(637,b,607,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(637,b,608,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(637,b,609,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(637,b,610,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(637,b,611,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(637,b,612,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(637,b,613,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(637,b,614,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(637,b,615,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(637,b,616,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(637,b,617,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__group__add(A). [resolve(637,b,627,a)].
% 5.09/5.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ominus(A). [resolve(637,b,628,a)].
% 5.09/5.31 638 -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].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(638,b,603,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(638,b,604,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A). [resolve(638,b,605,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(638,b,606,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(638,b,607,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(638,b,608,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(638,b,609,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(638,b,610,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(638,b,611,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(638,b,612,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(638,b,613,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(638,b,614,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(638,b,615,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(638,b,616,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(638,b,617,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(638,b,618,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(638,b,619,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(638,b,620,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(638,b,622,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(638,b,623,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Olorder(A). [resolve(638,b,624,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oorder(A). [resolve(638,b,625,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A). [resolve(638,b,626,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__group__add(A). [resolve(638,b,627,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ominus(A). [resolve(638,b,628,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(638,b,629,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ozero(A). [resolve(638,b,630,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(638,b,631,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(638,b,632,a)].
% 5.18/5.41 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(638,b,633,a)].
% 5.18/5.41 639 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(279,b,273,a)].
% 5.18/5.41 640 -class_OrderedGroup_Olordered__ab__group__abs(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(302,b,296,a)].
% 5.40/5.64 641 class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_12) # label(axiom). [assumption].
% 5.40/5.64 642 -class_OrderedGroup_Ocomm__monoid__add(A) | c_plus(B,c_0,A) = B # label(cls_OrderedGroup_Oadd__0__right_0) # label(axiom). [assumption].
% 5.40/5.64 643 -class_OrderedGroup_Ocomm__monoid__add(A) | c_plus(c_0,B,A) = B # label(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) # label(axiom). [assumption].
% 5.40/5.64 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(641,a,642,a)].
% 5.40/5.64 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(641,a,643,a)].
% 5.40/5.64 644 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat_20) # label(axiom). [assumption].
% 5.40/5.64 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(644,a,642,a)].
% 5.40/5.64 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(644,a,643,a)].
% 5.40/5.64 645 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Oab__group__add_1) # label(axiom). [assumption].
% 5.40/5.64 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,c_0,A) = B. [resolve(645,b,642,a)].
% 5.40/5.64 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(c_0,B,A) = B. [resolve(645,b,643,a)].
% 5.40/5.64 646 -class_OrderedGroup_Ocomm__monoid__add(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_0) # label(axiom). [assumption].
% 5.40/5.64 Derived: class_HOL_Ozero(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(646,a,645,b)].
% 5.40/5.64 647 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_1) # label(axiom). [assumption].
% 5.40/5.64 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(647,a,645,b)].
% 5.40/5.64 648 -class_OrderedGroup_Ocomm__monoid__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_2) # label(axiom). [assumption].
% 5.40/5.64 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(648,a,645,b)].
% 5.40/5.64 649 -class_OrderedGroup_Ocomm__monoid__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocomm__monoid__add_3) # label(axiom). [assumption].
% 5.40/5.64 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(649,a,645,b)].
% 5.40/5.64 650 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_3) # label(axiom). [assumption].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,c_0,A) = B. [resolve(650,b,642,a)].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(c_0,B,A) = B. [resolve(650,b,643,a)].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(650,b,647,a)].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(650,b,648,a)].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A). [resolve(650,b,649,a)].
% 5.40/5.64 651 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_3) # label(axiom). [assumption].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,c_0,A) = B. [resolve(651,b,642,a)].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(c_0,B,A) = B. [resolve(651,b,643,a)].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(651,b,647,a)].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(651,b,648,a)].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A). [resolve(651,b,649,a)].
% 5.40/5.64 652 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_3) # label(axiom). [assumption].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,c_0,A) = B. [resolve(652,b,642,a)].
% 5.40/5.64 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(c_0,B,A) = B. [resolve(652,b,643,a)].
% 5.40/5.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(652,b,647,a)].
% 5.40/5.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(652,b,648,a)].
% 5.40/5.66 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A). [resolve(652,b,649,a)].
% 5.40/5.66 653 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_2) # label(axiom). [assumption].
% 5.40/5.66 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_plus(B,c_0,A) = B. [resolve(653,b,642,a)].
% 5.40/5.66 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_plus(c_0,B,A) = B. [resolve(653,b,643,a)].
% 5.40/5.66 654 -class_Power_Orecpower(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Power_Orecpower_12) # label(axiom). [assumption].
% 5.40/5.66 Derived: -class_Power_Orecpower(A) | c_plus(B,c_0,A) = B. [resolve(654,b,642,a)].
% 5.40/5.66 Derived: -class_Power_Orecpower(A) | c_plus(c_0,B,A) = B. [resolve(654,b,643,a)].
% 5.40/5.66 655 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_7) # label(axiom). [assumption].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,c_0,A) = B. [resolve(655,b,642,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_plus(c_0,B,A) = B. [resolve(655,b,643,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(655,b,646,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Oplus(A). [resolve(655,b,649,a)].
% 5.40/5.66 656 -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].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_plus(B,c_0,A) = B. [resolve(656,b,642,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_plus(c_0,B,A) = B. [resolve(656,b,643,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(656,b,647,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(656,b,648,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A). [resolve(656,b,649,a)].
% 5.40/5.66 657 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) # label(axiom). [assumption].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,c_0,A) = B. [resolve(657,b,642,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(c_0,B,A) = B. [resolve(657,b,643,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(657,b,646,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Oplus(A). [resolve(657,b,649,a)].
% 5.40/5.66 658 -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].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_plus(B,c_0,A) = B. [resolve(658,b,642,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_plus(c_0,B,A) = B. [resolve(658,b,643,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A). [resolve(658,b,646,a)].
% 5.40/5.66 659 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Ofield_23) # label(axiom). [assumption].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,c_0,A) = B. [resolve(659,b,642,a)].
% 5.40/5.66 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(c_0,B,A) = B. [resolve(659,b,643,a)].
% 5.40/5.66 660 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oidom_23) # label(axiom). [assumption].
% 5.40/5.66 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,c_0,A) = B. [resolve(660,b,642,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(c_0,B,A) = B. [resolve(660,b,643,a)].
% 5.47/5.68 661 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_17) # label(axiom). [assumption].
% 5.47/5.68 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,c_0,A) = B. [resolve(661,b,642,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_plus(c_0,B,A) = B. [resolve(661,b,643,a)].
% 5.47/5.68 662 -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].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,c_0,A) = B. [resolve(662,b,642,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(c_0,B,A) = B. [resolve(662,b,643,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Ozero(A). [resolve(662,b,646,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Oplus(A). [resolve(662,b,649,a)].
% 5.47/5.68 663 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__field_25) # label(axiom). [assumption].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,c_0,A) = B. [resolve(663,b,642,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(c_0,B,A) = B. [resolve(663,b,643,a)].
% 5.47/5.68 664 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_23) # label(axiom). [assumption].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,c_0,A) = B. [resolve(664,b,642,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(c_0,B,A) = B. [resolve(664,b,643,a)].
% 5.47/5.68 665 -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].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_plus(B,c_0,A) = B. [resolve(665,b,642,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_plus(c_0,B,A) = B. [resolve(665,b,643,a)].
% 5.47/5.68 666 -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].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,c_0,A) = B. [resolve(666,b,642,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(c_0,B,A) = B. [resolve(666,b,643,a)].
% 5.47/5.68 667 -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].
% 5.47/5.68 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,c_0,A) = B. [resolve(667,b,642,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(c_0,B,A) = B. [resolve(667,b,643,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(667,b,647,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(667,b,648,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_HOL_Oplus(A). [resolve(667,b,649,a)].
% 5.47/5.68 668 -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].
% 5.47/5.68 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,c_0,A) = B. [resolve(668,b,642,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(c_0,B,A) = B. [resolve(668,b,643,a)].
% 5.47/5.68 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Oplus(A). [resolve(668,b,649,a)].
% 5.47/5.68 669 -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].
% 5.47/5.69 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_plus(B,c_0,A) = B. [resolve(669,b,642,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_plus(c_0,B,A) = B. [resolve(669,b,643,a)].
% 5.47/5.69 670 -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].
% 5.47/5.69 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_plus(B,c_0,A) = B. [resolve(670,b,642,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_plus(c_0,B,A) = B. [resolve(670,b,643,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Ozero(A). [resolve(670,b,646,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | class_HOL_Oplus(A). [resolve(670,b,649,a)].
% 5.47/5.69 671 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_10) # label(axiom). [assumption].
% 5.47/5.69 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,c_0,A) = B. [resolve(671,b,642,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_plus(c_0,B,A) = B. [resolve(671,b,643,a)].
% 5.47/5.69 672 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_4) # label(axiom). [assumption].
% 5.47/5.69 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_plus(B,c_0,A) = B. [resolve(672,b,642,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_plus(c_0,B,A) = B. [resolve(672,b,643,a)].
% 5.47/5.69 673 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring_8) # label(axiom). [assumption].
% 5.47/5.69 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,c_0,A) = B. [resolve(673,b,642,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Oring(A) | c_plus(c_0,B,A) = B. [resolve(673,b,643,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(673,b,647,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(673,b,648,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Oring(A) | class_HOL_Oplus(A). [resolve(673,b,649,a)].
% 5.47/5.69 674 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Oring__1_10) # label(axiom). [assumption].
% 5.47/5.69 Derived: -class_Ring__and__Field_Oring__1(A) | c_plus(B,c_0,A) = B. [resolve(674,b,642,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Oring__1(A) | c_plus(c_0,B,A) = B. [resolve(674,b,643,a)].
% 5.47/5.69 675 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_6) # label(axiom). [assumption].
% 5.47/5.69 Derived: -class_Ring__and__Field_Osemiring__0(A) | c_plus(B,c_0,A) = B. [resolve(675,b,642,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Osemiring__0(A) | c_plus(c_0,B,A) = B. [resolve(675,b,643,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(675,b,647,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(675,b,648,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A). [resolve(675,b,649,a)].
% 5.47/5.69 676 -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].
% 5.47/5.69 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,c_0,A) = B. [resolve(676,b,642,a)].
% 5.47/5.69 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(c_0,B,A) = B. [resolve(676,b,643,a)].
% 5.47/5.69 677 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Ocomm__monoid__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_7) # label(axiom). [assumption].
% 5.47/5.69 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_plus(B,c_0,A) = B. [resolve(677,b,642,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_plus(c_0,B,A) = B. [resolve(677,b,643,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(677,b,646,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Oplus(A). [resolve(677,b,649,a)].
% 5.71/5.91 678 -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].
% 5.71/5.91 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,c_0,A) = B. [resolve(678,b,642,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(c_0,B,A) = B. [resolve(678,b,643,a)].
% 5.71/5.91 679 class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(174,a,74,a)].
% 5.71/5.91 680 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(226,b,200,a)].
% 5.71/5.91 681 class_OrderedGroup_Ocomm__monoid__add(tc_nat). [resolve(264,a,240,a)].
% 5.71/5.91 Derived: class_HOL_Ozero(tc_nat). [resolve(681,a,646,a)].
% 5.71/5.91 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(681,a,647,a)].
% 5.71/5.91 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(681,a,648,a)].
% 5.71/5.91 Derived: class_HOL_Oplus(tc_nat). [resolve(681,a,649,a)].
% 5.71/5.91 682 class_OrderedGroup_Ocomm__monoid__add(A) | -class_Power_Orecpower(A). [resolve(264,a,241,b)].
% 5.71/5.91 Derived: -class_Power_Orecpower(A) | class_HOL_Ozero(A). [resolve(682,a,646,a)].
% 5.71/5.91 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(682,a,647,a)].
% 5.71/5.91 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(682,a,648,a)].
% 5.71/5.91 Derived: -class_Power_Orecpower(A) | class_HOL_Oplus(A). [resolve(682,a,649,a)].
% 5.71/5.91 683 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(265,b,264,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Ofield(A) | class_HOL_Ozero(A). [resolve(683,b,646,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(683,b,647,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(683,b,648,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Ofield(A) | class_HOL_Oplus(A). [resolve(683,b,649,a)].
% 5.71/5.91 684 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(266,b,264,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Oidom(A) | class_HOL_Ozero(A). [resolve(684,b,646,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(684,b,647,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(684,b,648,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Oidom(A) | class_HOL_Oplus(A). [resolve(684,b,649,a)].
% 5.71/5.91 685 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(268,b,264,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Ozero(A). [resolve(685,b,646,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(685,b,647,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(685,b,648,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(685,b,649,a)].
% 5.71/5.91 686 class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint). [resolve(271,a,264,a)].
% 5.71/5.91 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(686,a,646,a)].
% 5.71/5.91 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(686,a,647,a)].
% 5.71/5.91 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(686,a,648,a)].
% 5.71/5.91 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(686,a,649,a)].
% 5.71/5.91 687 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(635,b,629,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(687,b,647,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(687,b,648,a)].
% 5.71/5.91 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(687,b,649,a)].
% 5.83/6.04 688 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocomm__monoid__add(A). [resolve(638,b,629,a)].
% 5.83/6.04 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(688,b,647,a)].
% 5.83/6.04 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(688,b,648,a)].
% 5.83/6.04 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(688,b,649,a)].
% 5.83/6.04 689 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_38) # label(axiom). [assumption].
% 5.83/6.04 690 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A) # label(cls_OrderedGroup_Oadd__le__cancel__left_0) # label(axiom). [assumption].
% 5.83/6.04 691 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A) # label(cls_OrderedGroup_Oadd__le__cancel__left_1) # label(axiom). [assumption].
% 5.83/6.04 692 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A) # label(cls_OrderedGroup_Oadd__le__cancel__right_0) # label(axiom). [assumption].
% 5.83/6.04 693 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A) # label(cls_OrderedGroup_Oadd__le__cancel__right_1) # label(axiom). [assumption].
% 5.83/6.04 694 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A) # label(cls_OrderedGroup_Oadd__less__cancel__left_0) # label(axiom). [assumption].
% 5.83/6.04 695 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A) # label(cls_OrderedGroup_Oadd__less__cancel__left_1) # label(axiom). [assumption].
% 5.83/6.04 696 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A) # label(cls_OrderedGroup_Oadd__less__cancel__right_0) # label(axiom). [assumption].
% 5.83/6.04 697 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A) # label(cls_OrderedGroup_Oadd__less__cancel__right_1) # label(axiom). [assumption].
% 5.83/6.04 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(689,a,690,a)].
% 5.83/6.04 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(689,a,691,a)].
% 5.83/6.04 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(689,a,692,a)].
% 5.83/6.04 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(689,a,693,a)].
% 5.83/6.04 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(689,a,694,a)].
% 5.83/6.04 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(689,a,695,a)].
% 5.83/6.04 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(689,a,696,a)].
% 5.83/6.04 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(689,a,697,a)].
% 5.83/6.04 698 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat_35) # label(axiom). [assumption].
% 5.83/6.04 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(698,a,690,a)].
% 5.83/6.04 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(698,a,691,a)].
% 5.83/6.04 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(698,a,692,a)].
% 5.83/6.04 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(698,a,693,a)].
% 5.86/6.05 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(698,a,694,a)].
% 5.86/6.05 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(698,a,695,a)].
% 5.86/6.05 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(698,a,696,a)].
% 5.86/6.05 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(698,a,697,a)].
% 5.86/6.05 699 -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].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(699,b,690,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(699,b,691,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(699,b,692,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(699,b,693,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(699,b,694,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(699,b,695,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(699,b,696,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(699,b,697,a)].
% 5.86/6.05 700 -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].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(700,b,690,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(700,b,691,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(700,b,692,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(700,b,693,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(700,b,694,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(700,b,695,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(700,b,696,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(700,b,697,a)].
% 5.86/6.05 701 -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].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(701,b,690,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(701,b,691,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(701,b,692,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(701,b,693,a)].
% 5.86/6.05 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(701,b,694,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(701,b,695,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(701,b,696,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(701,b,697,a)].
% 5.86/6.06 702 -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].
% 5.86/6.06 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(702,b,690,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(702,b,691,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(702,b,692,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(702,b,693,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(702,b,694,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(702,b,695,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(702,b,696,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(702,b,697,a)].
% 5.86/6.06 703 -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].
% 5.86/6.06 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(703,b,690,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(703,b,691,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(703,b,692,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(703,b,693,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(703,b,694,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(703,b,695,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(703,b,696,a)].
% 5.86/6.06 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(703,b,697,a)].
% 5.86/6.06 704 -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].
% 5.86/6.06 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(704,a,699,b)].
% 5.86/6.06 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(704,a,700,b)].
% 5.86/6.06 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(704,a,701,b)].
% 5.86/6.06 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(704,a,702,b)].
% 5.86/6.07 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(704,a,703,b)].
% 5.86/6.07 705 -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].
% 5.86/6.07 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(705,a,699,b)].
% 5.86/6.07 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(705,a,700,b)].
% 5.86/6.07 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(705,a,701,b)].
% 5.86/6.07 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(705,a,702,b)].
% 5.86/6.07 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(705,a,703,b)].
% 5.86/6.07 706 -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].
% 5.86/6.07 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(706,a,699,b)].
% 5.86/6.07 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(706,a,700,b)].
% 5.86/6.07 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(706,a,701,b)].
% 5.86/6.07 Derived: class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(706,a,703,b)].
% 5.86/6.07 707 -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].
% 5.86/6.07 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(707,a,699,b)].
% 5.86/6.07 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(707,a,700,b)].
% 5.86/6.07 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(707,a,701,b)].
% 5.86/6.07 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(707,a,703,b)].
% 5.86/6.07 708 -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].
% 5.86/6.07 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(708,a,699,b)].
% 5.86/6.07 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(708,a,700,b)].
% 5.86/6.07 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(708,a,701,b)].
% 5.86/6.07 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(708,a,702,b)].
% 5.86/6.07 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(708,a,703,b)].
% 5.86/6.07 709 -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].
% 5.86/6.07 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(709,a,702,b)].
% 5.86/6.07 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(709,a,703,b)].
% 5.86/6.07 710 -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].
% 5.86/6.07 Derived: class_OrderedGroup_Ocancel__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(710,a,699,b)].
% 5.86/6.09 Derived: class_OrderedGroup_Ocancel__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(710,a,700,b)].
% 5.86/6.09 Derived: class_OrderedGroup_Ocancel__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(710,a,701,b)].
% 5.86/6.09 Derived: class_OrderedGroup_Ocancel__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(710,a,702,b)].
% 5.86/6.09 Derived: class_OrderedGroup_Ocancel__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(710,a,703,b)].
% 5.86/6.09 711 -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].
% 5.86/6.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(711,a,702,b)].
% 5.86/6.09 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(711,a,703,b)].
% 5.86/6.09 712 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) # label(axiom). [assumption].
% 5.86/6.09 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(712,a,702,b)].
% 5.86/6.09 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(712,a,703,b)].
% 5.86/6.09 713 -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].
% 5.86/6.09 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(713,b,690,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(713,b,691,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(713,b,692,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(713,b,693,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(713,b,694,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(713,b,695,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(713,b,696,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(713,b,697,a)].
% 5.86/6.09 714 -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].
% 5.86/6.09 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(714,b,690,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(714,b,691,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(714,b,692,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(714,b,693,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(714,b,694,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(714,b,695,a)].
% 5.86/6.09 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(714,b,696,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(714,b,697,a)].
% 5.86/6.11 715 -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].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(715,b,690,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(715,b,691,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(715,b,692,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(715,b,693,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(715,b,694,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(715,b,695,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(715,b,696,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(715,b,697,a)].
% 5.86/6.11 716 -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].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(716,b,690,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(716,b,691,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(716,b,692,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(716,b,693,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(716,b,694,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(716,b,695,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(716,b,696,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(716,b,697,a)].
% 5.86/6.11 717 -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].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(717,b,690,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(717,b,691,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(717,b,692,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(717,b,693,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(717,b,694,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(717,b,695,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(717,b,696,a)].
% 5.86/6.11 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(717,b,697,a)].
% 6.01/6.22 718 -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].
% 6.01/6.22 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(718,b,690,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(718,b,691,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(718,b,692,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(718,b,693,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(718,b,694,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(718,b,695,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(718,b,696,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(718,b,697,a)].
% 6.01/6.22 719 -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].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(719,b,690,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(719,b,691,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(719,b,692,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(719,b,693,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(719,b,694,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(719,b,695,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(719,b,696,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(719,b,697,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(719,b,705,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A). [resolve(719,b,706,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A). [resolve(719,b,707,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(719,b,709,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(719,b,711,a)].
% 6.01/6.22 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(719,b,712,a)].
% 6.01/6.22 720 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint). [resolve(367,a,318,a)].
% 6.01/6.22 Derived: class_Orderings_Oorder(tc_IntDef_Oint). [resolve(720,a,706,a)].
% 6.01/6.22 Derived: class_Orderings_Oord(tc_IntDef_Oint). [resolve(720,a,707,a)].
% 6.01/6.22 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(720,a,708,a)].
% 6.01/6.22 Derived: class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint). [resolve(720,a,710,a)].
% 6.01/6.22 721 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). [resolve(367,a,343,a)].
% 6.01/6.22 Derived: class_Orderings_Oorder(tc_nat). [resolve(721,a,706,a)].
% 6.26/6.47 Derived: class_Orderings_Oord(tc_nat). [resolve(721,a,707,a)].
% 6.26/6.47 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat). [resolve(721,a,708,a)].
% 6.26/6.47 Derived: class_OrderedGroup_Ocancel__semigroup__add(tc_nat). [resolve(721,a,710,a)].
% 6.26/6.47 722 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(367,a,344,b)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(722,a,708,a)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(722,a,709,a)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(722,a,710,a)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(722,a,711,a)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__field(A) | class_HOL_Oplus(A). [resolve(722,a,712,a)].
% 6.26/6.47 723 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(367,a,345,b)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(723,a,708,a)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(723,a,710,a)].
% 6.26/6.47 724 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A). [resolve(638,b,631,a)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oorder(A). [resolve(724,b,706,a)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A). [resolve(724,b,707,a)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(724,b,708,a)].
% 6.26/6.47 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(724,b,710,a)].
% 6.26/6.47 725 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_15) # label(axiom). [assumption].
% 6.26/6.47 726 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D # label(cls_OrderedGroup_Oadd__left__cancel_0) # label(axiom). [assumption].
% 6.26/6.47 727 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D # label(cls_OrderedGroup_Oadd__right__cancel_0) # label(axiom). [assumption].
% 6.26/6.47 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(725,a,726,a)].
% 6.26/6.47 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(725,a,727,a)].
% 6.26/6.47 728 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat_27) # label(axiom). [assumption].
% 6.26/6.47 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(728,a,726,a)].
% 6.26/6.47 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(728,a,727,a)].
% 6.26/6.47 729 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_7) # label(axiom). [assumption].
% 6.26/6.47 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(729,b,726,a)].
% 6.26/6.47 Derived: -class_OrderedGroup_Oab__group__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(729,b,727,a)].
% 6.26/6.47 730 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 6.26/6.47 Derived: -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(730,b,726,a)].
% 6.26/6.47 Derived: -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(730,b,727,a)].
% 6.26/6.47 731 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_0) # label(axiom). [assumption].
% 6.26/6.47 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(731,a,730,b)].
% 6.26/6.49 732 -class_OrderedGroup_Ocancel__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__semigroup__add_1) # label(axiom). [assumption].
% 6.26/6.49 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(732,a,730,b)].
% 6.26/6.49 733 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_12) # label(axiom). [assumption].
% 6.26/6.49 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(733,b,726,a)].
% 6.26/6.49 Derived: -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(733,b,727,a)].
% 6.26/6.49 734 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_12) # label(axiom). [assumption].
% 6.26/6.49 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(734,b,726,a)].
% 6.26/6.49 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(734,b,727,a)].
% 6.26/6.49 735 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_12) # label(axiom). [assumption].
% 6.26/6.49 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(735,b,726,a)].
% 6.26/6.49 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(735,b,727,a)].
% 6.26/6.49 736 -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].
% 6.26/6.49 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(736,b,726,a)].
% 6.26/6.49 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(736,b,727,a)].
% 6.26/6.49 737 -class_OrderedGroup_Opordered__ab__group__add(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_6) # label(axiom). [assumption].
% 6.26/6.49 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(737,b,726,a)].
% 6.26/6.49 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(737,b,727,a)].
% 6.26/6.49 738 -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].
% 6.26/6.49 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(738,b,726,a)].
% 6.26/6.49 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(738,b,727,a)].
% 6.26/6.49 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(738,b,731,a)].
% 6.26/6.49 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A). [resolve(738,b,732,a)].
% 6.26/6.49 739 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Power_Orecpower_19) # label(axiom). [assumption].
% 6.26/6.49 Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(739,b,726,a)].
% 6.26/6.49 Derived: -class_Power_Orecpower(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(739,b,727,a)].
% 6.26/6.49 740 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_15) # label(axiom). [assumption].
% 6.26/6.49 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(740,b,726,a)].
% 6.26/6.49 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(740,b,727,a)].
% 6.26/6.49 741 -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].
% 6.31/6.51 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(741,b,726,a)].
% 6.31/6.51 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(741,b,727,a)].
% 6.31/6.51 742 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_27) # label(axiom). [assumption].
% 6.31/6.51 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(742,b,726,a)].
% 6.31/6.51 Derived: -class_Ring__and__Field_Ofield(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(742,b,727,a)].
% 6.31/6.51 743 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_27) # label(axiom). [assumption].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(743,b,726,a)].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(743,b,727,a)].
% 6.31/6.51 744 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_21) # label(axiom). [assumption].
% 6.31/6.51 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(744,b,726,a)].
% 6.31/6.51 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(744,b,727,a)].
% 6.31/6.51 745 -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].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(745,b,726,a)].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(745,b,727,a)].
% 6.31/6.51 746 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__field_28) # label(axiom). [assumption].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(746,b,726,a)].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oordered__field(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(746,b,727,a)].
% 6.31/6.51 747 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oordered__idom_27) # label(axiom). [assumption].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(747,b,726,a)].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(747,b,727,a)].
% 6.31/6.51 748 -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].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(748,b,726,a)].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(748,b,727,a)].
% 6.31/6.51 749 -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].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(749,b,726,a)].
% 6.31/6.51 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(749,b,727,a)].
% 6.31/6.51 750 -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].
% 6.31/6.51 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(750,b,726,a)].
% 6.45/6.61 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(750,b,727,a)].
% 6.45/6.61 751 -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].
% 6.45/6.61 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(751,b,726,a)].
% 6.45/6.61 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(751,b,727,a)].
% 6.45/6.61 752 -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].
% 6.45/6.61 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(752,b,726,a)].
% 6.45/6.61 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(752,b,727,a)].
% 6.45/6.61 753 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_5) # label(axiom). [assumption].
% 6.45/6.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(753,b,726,a)].
% 6.45/6.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(753,b,727,a)].
% 6.45/6.61 754 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_11) # label(axiom). [assumption].
% 6.45/6.61 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(754,b,726,a)].
% 6.45/6.61 Derived: -class_Ring__and__Field_Oring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(754,b,727,a)].
% 6.45/6.61 755 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Ocancel__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_5) # label(axiom). [assumption].
% 6.45/6.61 Derived: -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(755,b,726,a)].
% 6.45/6.61 Derived: -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(755,b,727,a)].
% 6.45/6.61 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(755,b,731,a)].
% 6.45/6.61 Derived: -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A). [resolve(755,b,732,a)].
% 6.45/6.61 756 -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].
% 6.45/6.61 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(756,b,726,a)].
% 6.45/6.61 Derived: -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(756,b,727,a)].
% 6.45/6.61 757 -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].
% 6.45/6.61 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(757,b,726,a)].
% 6.45/6.61 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(757,b,727,a)].
% 6.45/6.61 758 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint). [resolve(149,a,74,a)].
% 6.45/6.61 759 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(226,b,204,a)].
% 6.45/6.61 760 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint). [resolve(228,a,204,a)].
% 6.45/6.61 761 class_OrderedGroup_Ocancel__semigroup__add(tc_nat). [resolve(253,a,240,a)].
% 6.45/6.61 762 class_OrderedGroup_Ocancel__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(253,a,241,b)].
% 6.45/6.61 763 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(265,b,253,a)].
% 6.45/6.61 764 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(266,b,253,a)].
% 6.45/6.61 765 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(268,b,253,a)].
% 6.68/6.88 766 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint). [resolve(271,a,253,a)].
% 6.68/6.88 767 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(635,b,621,a)].
% 6.68/6.88 768 class_OrderedGroup_Ocancel__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(710,a,699,b)].
% 6.68/6.88 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(768,a,731,a)].
% 6.68/6.88 Derived: -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A). [resolve(768,a,732,a)].
% 6.68/6.88 769 class_OrderedGroup_Ocancel__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(710,a,700,b)].
% 6.68/6.88 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(769,a,731,a)].
% 6.68/6.88 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_HOL_Oplus(A). [resolve(769,a,732,a)].
% 6.68/6.88 770 class_OrderedGroup_Ocancel__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(710,a,701,b)].
% 6.68/6.88 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(770,a,731,a)].
% 6.68/6.88 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_HOL_Oplus(A). [resolve(770,a,732,a)].
% 6.68/6.88 771 class_OrderedGroup_Ocancel__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(710,a,702,b)].
% 6.68/6.88 772 class_OrderedGroup_Ocancel__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(710,a,703,b)].
% 6.68/6.88 773 class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint). [resolve(720,a,710,a)].
% 6.68/6.88 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(773,a,731,a)].
% 6.68/6.88 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(773,a,732,a)].
% 6.68/6.88 774 class_OrderedGroup_Ocancel__semigroup__add(tc_nat). [resolve(721,a,710,a)].
% 6.68/6.88 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(774,a,731,a)].
% 6.68/6.88 Derived: class_HOL_Oplus(tc_nat). [resolve(774,a,732,a)].
% 6.68/6.88 775 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(722,a,710,a)].
% 6.68/6.88 776 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(723,a,710,a)].
% 6.68/6.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(776,b,731,a)].
% 6.68/6.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Oplus(A). [resolve(776,b,732,a)].
% 6.68/6.88 777 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocancel__semigroup__add(A). [resolve(724,b,710,a)].
% 6.68/6.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(777,b,731,a)].
% 6.68/6.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(777,b,732,a)].
% 6.68/6.88 778 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_48) # label(axiom). [assumption].
% 6.68/6.88 779 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A) # label(cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 6.68/6.88 780 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A) # label(cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 6.68/6.88 781 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0 # label(cls_OrderedGroup_Ojoin__0__eq__0_0) # label(axiom). [assumption].
% 6.68/6.88 782 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0 # label(cls_OrderedGroup_Ojoin__0__eq__0_1) # label(axiom). [assumption].
% 6.68/6.88 783 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0 # label(cls_OrderedGroup_Omeet__0__eq__0_0) # label(axiom). [assumption].
% 6.68/6.88 784 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0 # label(cls_OrderedGroup_Omeet__0__eq__0_1) # label(axiom). [assumption].
% 6.68/6.89 785 -class_OrderedGroup_Olordered__ab__group(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A) # label(cls_OrderedGroup_Oneg__join__eq__meet_0) # label(axiom). [assumption].
% 6.68/6.89 786 -class_OrderedGroup_Olordered__ab__group(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A) # label(cls_OrderedGroup_Oneg__meet__eq__join_0) # label(axiom). [assumption].
% 6.68/6.89 787 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Onprt(c_0,A) = c_0 # label(cls_OrderedGroup_Onprt__0_0) # label(axiom). [assumption].
% 6.68/6.89 788 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0 # label(cls_OrderedGroup_Onprt__eq__0_0) # label(axiom). [assumption].
% 6.68/6.89 789 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B # label(cls_OrderedGroup_Onprt__eq__id_0) # label(axiom). [assumption].
% 6.68/6.89 790 -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A) # label(cls_OrderedGroup_Onprt__le__zero_0) # label(axiom). [assumption].
% 6.68/6.89 791 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A) # label(cls_OrderedGroup_Onprt__mono_0) # label(axiom). [assumption].
% 6.68/6.89 792 -class_OrderedGroup_Olordered__ab__group(A) | c_OrderedGroup_Opprt(c_0,A) = c_0 # label(cls_OrderedGroup_Opprt__0_0) # label(axiom). [assumption].
% 6.68/6.89 793 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0 # label(cls_OrderedGroup_Opprt__eq__0_0) # label(axiom). [assumption].
% 6.68/6.89 794 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B # label(cls_OrderedGroup_Opprt__eq__id_0) # label(axiom). [assumption].
% 6.68/6.89 795 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A) # label(cls_OrderedGroup_Opprt__mono_0) # label(axiom). [assumption].
% 6.68/6.89 796 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A) # label(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 6.68/6.89 797 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A) # label(cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 6.68/6.89 798 -class_OrderedGroup_Olordered__ab__group(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A) # label(cls_OrderedGroup_Ozero__le__pprt_0) # label(axiom). [assumption].
% 6.68/6.89 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(778,a,779,a)].
% 6.68/6.89 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(778,a,780,a)].
% 6.68/6.89 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(778,a,781,a)].
% 6.68/6.89 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(778,a,782,a)].
% 6.68/6.89 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(778,a,783,a)].
% 6.68/6.89 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(778,a,784,a)].
% 6.68/6.89 Derived: c_uminus(c_LOrder_Ojoin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Omeet(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(778,a,785,a)].
% 6.68/6.89 Derived: c_uminus(c_LOrder_Omeet(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Ojoin(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(778,a,786,a)].
% 6.68/6.89 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(778,a,787,a)].
% 6.68/6.89 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(778,a,788,a)].
% 6.68/6.89 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(778,a,789,a)].
% 6.68/6.89 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(778,a,790,a)].
% 6.68/6.90 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_OrderedGroup_Onprt(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(778,a,791,a)].
% 6.68/6.90 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(778,a,792,a)].
% 6.68/6.90 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(778,a,793,a)].
% 6.68/6.90 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(778,a,794,a)].
% 6.68/6.90 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Opprt(A,tc_IntDef_Oint),c_OrderedGroup_Opprt(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(778,a,795,a)].
% 6.68/6.90 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(778,a,796,a)].
% 6.68/6.90 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(778,a,797,a)].
% 6.68/6.90 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(778,a,798,a)].
% 6.68/6.90 799 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_0) # label(axiom). [assumption].
% 6.68/6.90 800 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_1) # label(axiom). [assumption].
% 6.68/6.90 801 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_10) # label(axiom). [assumption].
% 6.68/6.90 802 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_11) # label(axiom). [assumption].
% 6.68/6.90 803 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_13) # label(axiom). [assumption].
% 6.68/6.90 804 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_14) # label(axiom). [assumption].
% 6.68/6.90 805 -class_OrderedGroup_Olordered__ab__group(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_15) # label(axiom). [assumption].
% 6.68/6.90 806 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ominus(A) # label(clsrel_OrderedGroup_Olordered__ab__group_2) # label(axiom). [assumption].
% 6.68/6.90 807 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Ozero(A) # label(clsrel_OrderedGroup_Olordered__ab__group_4) # label(axiom). [assumption].
% 6.68/6.90 808 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_6) # label(axiom). [assumption].
% 6.68/6.90 809 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group_7) # label(axiom). [assumption].
% 6.68/6.90 810 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group_8) # label(axiom). [assumption].
% 6.68/6.90 811 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group_9) # label(axiom). [assumption].
% 6.68/6.90 812 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_16) # label(axiom). [assumption].
% 6.68/6.90 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(812,b,779,a)].
% 6.68/6.90 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(812,b,780,a)].
% 6.68/6.90 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(812,b,781,a)].
% 6.68/6.90 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(812,b,782,a)].
% 6.68/6.90 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(812,b,783,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(812,b,784,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(812,b,785,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(812,b,786,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(812,b,787,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(812,b,788,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(812,b,789,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(812,b,790,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(812,b,791,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(812,b,792,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(812,b,793,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(812,b,794,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(812,b,795,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(812,b,796,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(812,b,797,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(812,b,798,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(812,b,799,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(812,b,800,a)].
% 6.68/6.91 813 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_16) # label(axiom). [assumption].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(813,b,779,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(813,b,780,a)].
% 6.68/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(813,b,781,a)].
% 6.75/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(813,b,782,a)].
% 6.75/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(813,b,783,a)].
% 6.75/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(813,b,784,a)].
% 6.75/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(813,b,785,a)].
% 6.75/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(813,b,786,a)].
% 6.75/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(813,b,787,a)].
% 6.75/6.91 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(813,b,788,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(813,b,789,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(813,b,790,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(813,b,791,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(813,b,792,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(813,b,793,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(813,b,794,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(813,b,795,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(813,b,796,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(813,b,797,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(813,b,798,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(813,b,799,a)].
% 6.75/6.93 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(813,b,800,a)].
% 6.75/6.93 814 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Olordered__ring_25) # label(axiom). [assumption].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(814,b,779,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(814,b,780,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(814,b,781,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(814,b,782,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(814,b,783,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(814,b,784,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(814,b,785,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(814,b,786,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(814,b,787,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(814,b,788,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(814,b,789,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(814,b,790,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(814,b,791,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(814,b,792,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(814,b,793,a)].
% 6.75/6.93 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(814,b,794,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(814,b,795,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(814,b,796,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(814,b,797,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(814,b,798,a)].
% 6.75/6.95 815 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__field_50) # label(axiom). [assumption].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(815,b,779,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(815,b,780,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(815,b,781,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(815,b,782,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(815,b,783,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(815,b,784,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(815,b,785,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(815,b,786,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(815,b,787,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(815,b,788,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(815,b,789,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(815,b,790,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(815,b,791,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(815,b,792,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(815,b,793,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(815,b,794,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(815,b,795,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(815,b,796,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(815,b,797,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(815,b,798,a)].
% 6.75/6.95 816 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Olordered__ab__group(A) # label(clsrel_Ring__and__Field_Oordered__idom_53) # label(axiom). [assumption].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(816,b,779,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(816,b,780,a)].
% 6.75/6.95 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(816,b,781,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(816,b,782,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(816,b,783,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(816,b,784,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(816,b,785,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(816,b,786,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(816,b,787,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(816,b,788,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(816,b,789,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(816,b,790,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(816,b,791,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(816,b,792,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(816,b,793,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(816,b,794,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(816,b,795,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(816,b,796,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(816,b,797,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(816,b,798,a)].
% 6.79/6.97 817 -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].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(817,b,779,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(817,b,780,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(817,b,781,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(817,b,782,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(817,b,783,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(817,b,784,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(817,b,785,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(817,b,786,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(817,b,787,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(817,b,788,a)].
% 6.79/6.97 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(817,b,789,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(817,b,790,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(817,b,791,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(817,b,792,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(817,b,793,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(817,b,794,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(817,b,795,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(817,b,796,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(817,b,797,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(817,b,798,a)].
% 7.00/7.19 818 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(278,b,273,a)].
% 7.00/7.19 819 -class_OrderedGroup_Olordered__ab__group(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(301,b,296,a)].
% 7.00/7.19 820 class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint). [resolve(618,a,602,a)].
% 7.00/7.19 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(820,a,800,a)].
% 7.00/7.19 Derived: class_LOrder_Olorder(tc_IntDef_Oint). [resolve(820,a,805,a)].
% 7.00/7.19 Derived: class_HOL_Ominus(tc_IntDef_Oint). [resolve(820,a,806,a)].
% 7.00/7.19 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(820,a,808,a)].
% 7.00/7.19 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(820,a,809,a)].
% 7.00/7.19 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(820,a,818,a)].
% 7.00/7.19 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(820,a,819,a)].
% 7.00/7.19 821 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Olordered__ab__group(A). [resolve(638,b,618,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(821,b,818,a)].
% 7.00/7.19 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(821,b,819,a)].
% 7.00/7.19 822 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,c_0,A) = B. [resolve(650,b,642,a)].
% 7.00/7.19 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(822,a,778,a)].
% 7.00/7.19 823 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(c_0,B,A) = B. [resolve(650,b,643,a)].
% 7.00/7.19 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(823,a,778,a)].
% 7.00/7.19 824 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(650,b,647,a)].
% 7.00/7.19 825 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(650,b,648,a)].
% 7.00/7.19 826 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A). [resolve(650,b,649,a)].
% 7.00/7.19 827 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(699,b,690,a)].
% 7.00/7.19 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(827,a,778,a)].
% 7.00/7.19 828 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(699,b,691,a)].
% 7.00/7.19 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(828,a,778,a)].
% 7.00/7.19 829 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(699,b,692,a)].
% 7.00/7.19 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(829,a,778,a)].
% 7.00/7.21 830 -class_OrderedGroup_Olordered__ab__group(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(699,b,693,a)].
% 7.00/7.21 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(830,a,778,a)].
% 7.00/7.21 831 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(699,b,694,a)].
% 7.00/7.21 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(831,a,778,a)].
% 7.00/7.21 832 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(699,b,695,a)].
% 7.00/7.21 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(832,a,778,a)].
% 7.00/7.21 833 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(699,b,696,a)].
% 7.00/7.21 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(833,a,778,a)].
% 7.00/7.21 834 -class_OrderedGroup_Olordered__ab__group(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(699,b,697,a)].
% 7.00/7.21 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(834,a,778,a)].
% 7.00/7.21 835 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(704,a,699,b)].
% 7.00/7.21 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(835,b,814,b)].
% 7.00/7.21 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(835,b,815,b)].
% 7.00/7.21 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(835,b,816,b)].
% 7.00/7.21 Derived: class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(835,b,817,b)].
% 7.00/7.21 836 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(705,a,699,b)].
% 7.00/7.21 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(836,b,814,b)].
% 7.00/7.21 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(836,b,815,b)].
% 7.00/7.21 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(836,b,816,b)].
% 7.00/7.21 Derived: class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(836,b,817,b)].
% 7.00/7.21 837 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(706,a,699,b)].
% 7.00/7.21 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(837,b,814,b)].
% 7.00/7.21 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(837,b,815,b)].
% 7.00/7.21 Derived: class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(837,b,816,b)].
% 7.00/7.21 838 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(707,a,699,b)].
% 7.00/7.21 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(838,b,814,b)].
% 7.00/7.21 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(838,b,815,b)].
% 7.00/7.21 Derived: class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(838,b,816,b)].
% 7.00/7.21 839 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group(A). [resolve(708,a,699,b)].
% 7.00/7.21 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(839,b,814,b)].
% 7.00/7.21 840 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(733,b,726,a)].
% 7.00/7.21 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(840,a,778,a)].
% 7.20/7.37 841 -class_OrderedGroup_Olordered__ab__group(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(733,b,727,a)].
% 7.20/7.37 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(841,a,778,a)].
% 7.20/7.37 842 -class_OrderedGroup_Olordered__ab__group(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(768,a,731,a)].
% 7.20/7.37 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(842,a,814,b)].
% 7.20/7.37 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(842,a,815,b)].
% 7.20/7.37 843 -class_OrderedGroup_Olordered__ab__group(A) | class_HOL_Oplus(A). [resolve(768,a,732,a)].
% 7.20/7.37 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(843,a,814,b)].
% 7.20/7.37 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(843,a,815,b)].
% 7.20/7.37 844 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_23) # label(axiom). [assumption].
% 7.20/7.37 845 -class_OrderedGroup_Omonoid__mult(A) | c_times(c_1,B,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) # label(axiom). [assumption].
% 7.20/7.37 846 -class_OrderedGroup_Omonoid__mult(A) | c_times(B,c_1,A) = B # label(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) # label(axiom). [assumption].
% 7.20/7.37 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(844,a,845,a)].
% 7.20/7.37 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(844,a,846,a)].
% 7.20/7.37 847 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat_23) # label(axiom). [assumption].
% 7.20/7.37 Derived: c_times(c_1,A,tc_nat) = A. [resolve(847,a,845,a)].
% 7.20/7.37 Derived: c_times(A,c_1,tc_nat) = A. [resolve(847,a,846,a)].
% 7.20/7.37 848 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_4) # label(axiom). [assumption].
% 7.20/7.37 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(c_1,B,A) = B. [resolve(848,b,845,a)].
% 7.20/7.37 Derived: -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(B,c_1,A) = B. [resolve(848,b,846,a)].
% 7.20/7.37 849 -class_OrderedGroup_Omonoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Omonoid__mult_1) # label(axiom). [assumption].
% 7.20/7.37 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(849,a,848,b)].
% 7.20/7.37 850 -class_OrderedGroup_Omonoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Omonoid__mult_2) # label(axiom). [assumption].
% 7.20/7.37 Derived: class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(850,a,848,b)].
% 7.20/7.37 851 -class_Power_Orecpower(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Power_Orecpower_15) # label(axiom). [assumption].
% 7.20/7.37 Derived: -class_Power_Orecpower(A) | c_times(c_1,B,A) = B. [resolve(851,b,845,a)].
% 7.20/7.37 Derived: -class_Power_Orecpower(A) | c_times(B,c_1,A) = B. [resolve(851,b,846,a)].
% 7.20/7.37 852 -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].
% 7.20/7.37 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B. [resolve(852,b,845,a)].
% 7.20/7.37 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B. [resolve(852,b,846,a)].
% 7.20/7.37 853 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_12) # label(axiom). [assumption].
% 7.20/7.37 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_1,B,A) = B. [resolve(853,b,845,a)].
% 7.20/7.37 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_1,A) = B. [resolve(853,b,846,a)].
% 7.20/7.37 854 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_12) # label(axiom). [assumption].
% 7.20/7.37 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B. [resolve(854,b,845,a)].
% 7.20/7.37 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B. [resolve(854,b,846,a)].
% 7.20/7.37 855 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_15) # label(axiom). [assumption].
% 7.20/7.37 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_1,B,A) = B. [resolve(855,b,845,a)].
% 7.39/7.56 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_1,A) = B. [resolve(855,b,846,a)].
% 7.39/7.56 856 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_12) # label(axiom). [assumption].
% 7.39/7.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_1,B,A) = B. [resolve(856,b,845,a)].
% 7.39/7.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_1,A) = B. [resolve(856,b,846,a)].
% 7.39/7.56 857 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Oring__1_17) # label(axiom). [assumption].
% 7.39/7.56 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B. [resolve(857,b,845,a)].
% 7.39/7.56 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B. [resolve(857,b,846,a)].
% 7.39/7.56 858 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Omonoid__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_11) # label(axiom). [assumption].
% 7.39/7.56 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B. [resolve(858,b,845,a)].
% 7.39/7.56 Derived: -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B. [resolve(858,b,846,a)].
% 7.39/7.56 859 -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].
% 7.39/7.56 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(859,b,845,a)].
% 7.39/7.56 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(859,b,846,a)].
% 7.39/7.56 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(859,b,849,a)].
% 7.39/7.56 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(859,b,850,a)].
% 7.39/7.56 860 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint). [resolve(159,a,74,a)].
% 7.39/7.56 861 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Omonoid__mult(A). [resolve(226,b,212,a)].
% 7.39/7.56 Derived: -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(861,b,849,a)].
% 7.39/7.56 862 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint). [resolve(228,a,212,a)].
% 7.39/7.56 863 class_OrderedGroup_Omonoid__mult(tc_nat). [resolve(248,a,240,a)].
% 7.39/7.56 864 class_OrderedGroup_Omonoid__mult(A) | -class_Power_Orecpower(A). [resolve(248,a,241,b)].
% 7.39/7.56 865 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Omonoid__mult(A). [resolve(265,b,248,a)].
% 7.39/7.56 866 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Omonoid__mult(A). [resolve(266,b,248,a)].
% 7.39/7.56 867 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Omonoid__mult(A). [resolve(268,b,248,a)].
% 7.39/7.56 868 class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint). [resolve(271,a,248,a)].
% 7.39/7.56 869 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(582,b,570,a)].
% 7.39/7.56 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_1 | A = c_uminus(c_1,tc_IntDef_Oint). [resolve(869,a,844,a)].
% 7.39/7.56 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(A,tc_nat) != c_1 | A = c_uminus(c_1,tc_nat). [resolve(869,a,847,a)].
% 7.39/7.56 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(869,a,848,b)].
% 7.39/7.56 870 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(582,b,571,a)].
% 7.39/7.56 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) = c_1. [resolve(870,a,844,a)].
% 7.39/7.56 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(c_uminus(c_1,tc_nat),tc_nat) = c_1. [resolve(870,a,847,a)].
% 7.39/7.56 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(870,a,848,b)].
% 7.39/7.56 871 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(582,b,572,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(871,a,844,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat) | c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(871,a,847,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(871,a,848,b)].
% 7.39/7.57 872 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(582,b,573,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(872,a,844,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat) | c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(872,a,847,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(872,a,848,b)].
% 7.39/7.57 873 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(582,b,574,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(873,a,844,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_1,c_uminus(A,tc_nat),tc_nat) | c_less(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(873,a,847,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(873,a,848,b)].
% 7.39/7.57 874 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(582,b,575,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(874,a,844,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_uminus(c_1,tc_nat),tc_nat) | c_less(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(874,a,847,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(874,a,848,b)].
% 7.39/7.57 875 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(582,b,576,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(875,a,844,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat) | c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(875,a,847,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(875,a,848,b)].
% 7.39/7.57 876 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(582,b,577,a)].
% 7.39/7.57 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(876,a,844,a)].
% 7.61/7.78 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat) | c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(876,a,847,a)].
% 7.61/7.78 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(876,a,848,b)].
% 7.61/7.78 877 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(582,b,578,a)].
% 7.61/7.78 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(877,a,844,a)].
% 7.61/7.78 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(A,tc_nat),c_1,tc_nat) | c_less(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(877,a,847,a)].
% 7.61/7.78 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(877,a,848,b)].
% 7.61/7.78 878 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(582,b,579,a)].
% 7.61/7.78 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(878,a,844,a)].
% 7.61/7.78 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(c_1,tc_nat),A,tc_nat) | c_less(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(878,a,847,a)].
% 7.61/7.78 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(878,a,848,b)].
% 7.61/7.78 879 class_Orderings_Oorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_31) # label(axiom). [assumption].
% 7.61/7.78 880 -class_Orderings_Oorder(A) | -c_less(B,B,A) # label(cls_Orderings_Oorder__less__irrefl_0) # label(axiom). [assumption].
% 7.61/7.78 881 -class_Orderings_Oorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset # label(cls_SetInterval_OatLeastAtMost__empty_0) # label(axiom). [assumption].
% 7.61/7.78 882 -class_Orderings_Oorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A) # label(cls_SetInterval_OatLeastAtMost__singleton_0) # label(axiom). [assumption].
% 7.61/7.78 883 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset # label(cls_SetInterval_OatLeastLessThan__empty_0) # label(axiom). [assumption].
% 7.61/7.78 884 -class_Orderings_Oorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeast__subset__iff_0) # label(axiom). [assumption].
% 7.61/7.78 885 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)) # label(cls_SetInterval_OatLeast__subset__iff_1) # label(axiom). [assumption].
% 7.61/7.78 886 -class_Orderings_Oorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A) # label(cls_SetInterval_OatMost__subset__iff_0) # label(axiom). [assumption].
% 7.61/7.78 887 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) # label(cls_SetInterval_OatMost__subset__iff_1) # label(axiom). [assumption].
% 7.61/7.78 888 -class_Orderings_Oorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset # label(cls_SetInterval_OgreaterThanAtMost__empty_0) # label(axiom). [assumption].
% 7.61/7.78 889 -class_Orderings_Oorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A) # label(cls_SetInterval_Osingle__Diff__lessThan_0) # label(axiom). [assumption].
% 7.61/7.78 890 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_Orderings_Oorder__class_Oaxioms__1_0) # label(axiom). [assumption].
% 7.61/7.79 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(879,a,880,a)].
% 7.61/7.79 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(879,a,881,a)].
% 7.61/7.79 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(879,a,882,a)].
% 7.61/7.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(879,a,883,a)].
% 7.61/7.79 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(879,a,884,a)].
% 7.61/7.79 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(879,a,885,a)].
% 7.61/7.79 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(879,a,886,a)].
% 7.61/7.79 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(879,a,887,a)].
% 7.61/7.79 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(879,a,888,a)].
% 7.61/7.79 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(879,a,889,a)].
% 7.61/7.79 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(879,a,890,a)].
% 7.61/7.79 891 class_Orderings_Oorder(tc_nat) # label(clsarity_nat_3) # label(axiom). [assumption].
% 7.61/7.79 Derived: -c_less(A,A,tc_nat). [resolve(891,a,880,a)].
% 7.61/7.79 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(891,a,881,a)].
% 7.61/7.79 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(891,a,882,a)].
% 7.61/7.79 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(891,a,883,a)].
% 7.61/7.79 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(891,a,884,a)].
% 7.61/7.79 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(891,a,885,a)].
% 7.61/7.79 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(891,a,886,a)].
% 7.61/7.79 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(891,a,887,a)].
% 7.61/7.79 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(891,a,888,a)].
% 7.61/7.79 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(891,a,889,a)].
% 7.61/7.79 Derived: c_lessequals(A,A,tc_nat). [resolve(891,a,890,a)].
% 7.61/7.79 892 class_Orderings_Oorder(tc_set(A)) # label(clsarity_set_2) # label(axiom). [assumption].
% 7.61/7.79 Derived: -c_less(A,A,tc_set(B)). [resolve(892,a,880,a)].
% 7.61/7.79 Derived: -c_less(A,B,tc_set(C)) | c_SetInterval_OatLeastAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(892,a,881,a)].
% 7.61/7.79 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_set(B)) = c_insert(A,c_emptyset,tc_set(B)). [resolve(892,a,882,a)].
% 7.61/7.79 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OatLeastLessThan(B,A,tc_set(C)) = c_emptyset. [resolve(892,a,883,a)].
% 7.61/7.79 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(892,a,884,a)].
% 7.61/7.79 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(892,a,885,a)].
% 7.61/7.79 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(892,a,886,a)].
% 7.61/7.81 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(892,a,887,a)].
% 7.61/7.81 Derived: -c_lessequals(A,B,tc_set(C)) | c_SetInterval_OgreaterThanAtMost(B,A,tc_set(C)) = c_emptyset. [resolve(892,a,888,a)].
% 7.61/7.81 Derived: c_minus(c_insert(A,c_emptyset,tc_set(B)),c_SetInterval_OlessThan(A,tc_set(B)),tc_set(tc_set(B))) = c_insert(A,c_emptyset,tc_set(B)). [resolve(892,a,889,a)].
% 7.61/7.81 Derived: c_lessequals(A,A,tc_set(B)). [resolve(892,a,890,a)].
% 7.61/7.81 893 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A) # label(clsrel_LOrder_Olorder_2) # label(axiom). [assumption].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | -c_less(B,B,A). [resolve(893,b,880,a)].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(893,b,881,a)].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(893,b,882,a)].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(893,b,883,a)].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(893,b,884,a)].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(893,b,885,a)].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(893,b,886,a)].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(893,b,887,a)].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(893,b,888,a)].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(893,b,889,a)].
% 7.61/7.81 Derived: -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(893,b,890,a)].
% 7.61/7.81 894 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_8) # label(axiom). [assumption].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A). [resolve(894,b,880,a)].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(894,b,881,a)].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(894,b,882,a)].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(894,b,883,a)].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(894,b,884,a)].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(894,b,885,a)].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(894,b,886,a)].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(894,b,887,a)].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(894,b,888,a)].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(894,b,889,a)].
% 7.61/7.81 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(894,b,890,a)].
% 7.61/7.82 895 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_8) # label(axiom). [assumption].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A). [resolve(895,b,880,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(895,b,881,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(895,b,882,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(895,b,883,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(895,b,884,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(895,b,885,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(895,b,886,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(895,b,887,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(895,b,888,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(895,b,889,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(895,b,890,a)].
% 7.61/7.82 896 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(896,b,880,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(896,b,881,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(896,b,882,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(896,b,883,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(896,b,884,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(896,b,885,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(896,b,886,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(896,b,887,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(896,b,888,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(896,b,889,a)].
% 7.61/7.82 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(896,b,890,a)].
% 7.61/7.82 897 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_10) # label(axiom). [assumption].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,B,A). [resolve(897,b,880,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(897,b,881,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(897,b,882,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(897,b,883,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(897,b,884,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(897,b,885,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(897,b,886,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(897,b,887,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(897,b,888,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(897,b,889,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,B,A). [resolve(897,b,890,a)].
% 7.67/7.83 898 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) # label(axiom). [assumption].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(898,b,880,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(898,b,881,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(898,b,882,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(898,b,883,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(898,b,884,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(898,b,885,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(898,b,886,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(898,b,887,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(898,b,888,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(898,b,889,a)].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(898,b,890,a)].
% 7.67/7.83 899 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oorder(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 7.67/7.83 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(899,b,880,a)].
% 7.70/7.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(899,b,881,a)].
% 7.70/7.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(899,b,882,a)].
% 7.70/7.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(899,b,883,a)].
% 7.70/7.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(899,b,884,a)].
% 7.70/7.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(899,b,885,a)].
% 7.70/7.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(899,b,886,a)].
% 7.70/7.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(899,b,887,a)].
% 7.70/7.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(899,b,888,a)].
% 7.70/7.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(899,b,889,a)].
% 7.70/7.85 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(899,b,890,a)].
% 7.70/7.85 900 -class_Orderings_Oorder(A) | class_Orderings_Oord(A) # label(clsrel_Orderings_Oorder_0) # label(axiom). [assumption].
% 7.70/7.85 Derived: class_Orderings_Oord(tc_set(A)). [resolve(900,a,892,a)].
% 7.70/7.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(900,a,898,b)].
% 7.70/7.85 Derived: class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(900,a,899,b)].
% 7.70/7.85 901 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_10) # label(axiom). [assumption].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A). [resolve(901,b,880,a)].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(901,b,881,a)].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(901,b,882,a)].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(901,b,883,a)].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(901,b,884,a)].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(901,b,885,a)].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(901,b,886,a)].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(901,b,887,a)].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(901,b,888,a)].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(901,b,889,a)].
% 7.70/7.85 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(901,b,890,a)].
% 7.70/7.86 902 -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].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A). [resolve(902,b,880,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(902,b,881,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(902,b,882,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(902,b,883,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(902,b,884,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(902,b,885,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(902,b,886,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(902,b,887,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(902,b,888,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(902,b,889,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(902,b,890,a)].
% 7.70/7.86 903 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__field_58) # label(axiom). [assumption].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,B,A). [resolve(903,b,880,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(903,b,881,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(903,b,882,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(903,b,883,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(903,b,884,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(903,b,885,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(903,b,886,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(903,b,887,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(903,b,888,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(903,b,889,a)].
% 7.70/7.86 Derived: -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,B,A). [resolve(903,b,890,a)].
% 7.70/7.86 904 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_44) # label(axiom). [assumption].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,B,A). [resolve(904,b,880,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(904,b,881,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(904,b,882,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(904,b,883,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(904,b,884,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(904,b,885,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(904,b,886,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(904,b,887,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(904,b,888,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(904,b,889,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,A). [resolve(904,b,890,a)].
% 7.70/7.88 905 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_26) # label(axiom). [assumption].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,B,A). [resolve(905,b,880,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(905,b,881,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(905,b,882,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(905,b,883,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(905,b,884,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(905,b,885,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(905,b,886,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(905,b,887,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(905,b,888,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(905,b,889,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,B,A). [resolve(905,b,890,a)].
% 7.70/7.88 906 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_17) # label(axiom). [assumption].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A). [resolve(906,b,880,a)].
% 7.70/7.88 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(906,b,881,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(906,b,882,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(906,b,883,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(906,b,884,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(906,b,885,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(906,b,886,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(906,b,887,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(906,b,888,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(906,b,889,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(906,b,890,a)].
% 7.70/7.89 907 -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].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A). [resolve(907,b,880,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(907,b,881,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(907,b,882,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(907,b,883,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(907,b,884,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(907,b,885,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(907,b,886,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(907,b,887,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(907,b,888,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(907,b,889,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(907,b,890,a)].
% 7.70/7.89 908 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_11) # label(axiom). [assumption].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A). [resolve(908,b,880,a)].
% 7.70/7.89 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(908,b,881,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(908,b,882,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(908,b,883,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(908,b,884,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(908,b,885,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(908,b,886,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(908,b,887,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(908,b,888,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(908,b,889,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(908,b,890,a)].
% 7.70/7.90 909 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_23) # label(axiom). [assumption].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,B,A). [resolve(909,b,880,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(909,b,881,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(909,b,882,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(909,b,883,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(909,b,884,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(909,b,885,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(909,b,886,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(909,b,887,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(909,b,888,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(909,b,889,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_lessequals(B,B,A). [resolve(909,b,890,a)].
% 7.70/7.90 910 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_13) # label(axiom). [assumption].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A). [resolve(910,b,880,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(910,b,881,a)].
% 7.70/7.90 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(910,b,882,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(910,b,883,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(910,b,884,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(910,b,885,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(910,b,886,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(910,b,887,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(910,b,888,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(910,b,889,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(910,b,890,a)].
% 7.70/7.91 911 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__ring_17) # label(axiom). [assumption].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A). [resolve(911,b,880,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(911,b,881,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(911,b,882,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(911,b,883,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(911,b,884,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(911,b,885,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(911,b,886,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(911,b,887,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(911,b,888,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(911,b,889,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(911,b,890,a)].
% 7.70/7.91 912 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oorder(A) # label(clsrel_Ring__and__Field_Opordered__semiring_10) # label(axiom). [assumption].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A). [resolve(912,b,880,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(912,b,881,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(912,b,882,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(912,b,883,a)].
% 7.70/7.91 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(912,b,884,a)].
% 7.93/8.12 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(912,b,885,a)].
% 7.93/8.12 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(912,b,886,a)].
% 7.93/8.12 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(912,b,887,a)].
% 7.93/8.12 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(912,b,888,a)].
% 7.93/8.12 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(912,b,889,a)].
% 7.93/8.12 Derived: -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(912,b,890,a)].
% 7.93/8.12 913 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_1) # label(axiom). [assumption].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A). [resolve(913,b,880,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(913,b,881,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(913,b,882,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(913,b,883,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(913,b,884,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(913,b,885,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(913,b,886,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(913,b,887,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(913,b,888,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(913,b,889,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(913,b,890,a)].
% 7.93/8.12 914 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(66,a,1,a)].
% 7.93/8.12 915 class_Orderings_Oorder(tc_nat). [resolve(66,a,60,a)].
% 7.93/8.12 916 class_Orderings_Oorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(66,a,61,b)].
% 7.93/8.12 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A). [resolve(916,a,900,a)].
% 7.93/8.12 917 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oorder(A). [resolve(73,b,66,a)].
% 7.93/8.12 Derived: -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(917,b,900,a)].
% 7.93/8.12 918 -class_LOrder_Olorder(A) | class_Orderings_Oorder(A). [resolve(277,b,276,a)].
% 7.93/8.12 Derived: -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(918,b,900,a)].
% 7.93/8.12 919 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oorder(A). [resolve(283,b,276,a)].
% 7.93/8.12 920 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(374,a,344,b)].
% 7.93/8.12 921 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(374,a,345,b)].
% 7.93/8.12 922 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oorder(A). [resolve(638,b,625,a)].
% 8.28/8.46 923 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(706,a,700,b)].
% 8.28/8.46 924 class_Orderings_Oorder(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(706,a,701,b)].
% 8.28/8.46 925 class_Orderings_Oorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(706,a,703,b)].
% 8.28/8.46 926 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oorder(A). [resolve(719,b,706,a)].
% 8.28/8.46 927 class_Orderings_Oorder(tc_IntDef_Oint). [resolve(720,a,706,a)].
% 8.28/8.46 928 class_Orderings_Oorder(tc_nat). [resolve(721,a,706,a)].
% 8.28/8.46 929 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oorder(A). [resolve(724,b,706,a)].
% 8.28/8.46 930 class_Orderings_Oorder(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(837,b,814,b)].
% 8.28/8.46 931 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(837,b,815,b)].
% 8.28/8.46 932 class_Orderings_Oorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(837,b,816,b)].
% 8.28/8.46 933 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_22) # label(axiom). [assumption].
% 8.28/8.46 934 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | c_0 != c_1 # label(cls_Ring__and__Field_Oaxclass__0__neq__1__class_Oaxioms_0) # label(axiom). [assumption].
% 8.28/8.46 935 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | c_1 != c_0 # label(cls_Ring__and__Field_Oone__neq__zero_0) # label(axiom). [assumption].
% 8.28/8.46 Derived: c_0 != c_1. [resolve(933,a,934,a)].
% 8.28/8.46 Derived: c_1 != c_0. [resolve(933,a,935,a)].
% 8.28/8.46 936 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) # label(clsarity_nat_13) # label(axiom). [assumption].
% 8.28/8.46 937 -class_Power_Orecpower(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A) # label(clsrel_Power_Orecpower_3) # label(axiom). [assumption].
% 8.28/8.46 938 -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].
% 8.28/8.46 939 -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].
% 8.28/8.46 940 -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].
% 8.28/8.46 941 -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].
% 8.28/8.46 942 -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].
% 8.28/8.46 943 -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].
% 8.28/8.46 944 -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].
% 8.28/8.46 Derived: -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A). [resolve(944,b,938,a)].
% 8.28/8.46 945 -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].
% 8.28/8.46 946 -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].
% 8.28/8.46 947 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint). [resolve(158,a,74,a)].
% 8.28/8.46 948 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(226,b,211,a)].
% 8.28/8.46 949 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint). [resolve(228,a,211,a)].
% 8.28/8.46 950 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat). [resolve(261,a,240,a)].
% 8.28/8.46 951 class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_Power_Orecpower(A). [resolve(261,a,241,b)].
% 8.28/8.46 952 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(265,b,261,a)].
% 8.28/8.46 953 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(266,b,261,a)].
% 8.59/8.81 954 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oaxclass__0__neq__1(A). [resolve(268,b,261,a)].
% 8.59/8.81 955 class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint). [resolve(271,a,261,a)].
% 8.59/8.81 956 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(584,b,570,a)].
% 8.59/8.81 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Power_Orecpower(A). [resolve(956,a,937,b)].
% 8.59/8.81 957 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(584,b,571,a)].
% 8.59/8.81 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Power_Orecpower(A). [resolve(957,a,937,b)].
% 8.59/8.81 958 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(584,b,572,a)].
% 8.59/8.81 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(958,a,937,b)].
% 8.59/8.81 959 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(584,b,573,a)].
% 8.59/8.81 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(959,a,937,b)].
% 8.59/8.81 960 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(584,b,574,a)].
% 8.59/8.81 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(960,a,937,b)].
% 8.59/8.81 961 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(584,b,575,a)].
% 8.59/8.81 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(961,a,937,b)].
% 8.59/8.81 962 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(584,b,576,a)].
% 8.59/8.81 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(962,a,937,b)].
% 8.59/8.81 963 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(584,b,577,a)].
% 8.59/8.81 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(963,a,937,b)].
% 8.59/8.81 964 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(584,b,578,a)].
% 8.59/8.81 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(964,a,937,b)].
% 8.59/8.81 965 -class_Ring__and__Field_Oaxclass__0__neq__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(584,b,579,a)].
% 8.59/8.81 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(965,a,937,b)].
% 8.59/8.81 966 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_18) # label(axiom). [assumption].
% 8.59/8.81 967 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_times(c_0,B,A) = c_0 # label(cls_Ring__and__Field_Omult__zero__left_0) # label(axiom). [assumption].
% 8.69/8.84 968 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_times(B,c_0,A) = c_0 # label(cls_Ring__and__Field_Omult__zero__right_0) # label(axiom). [assumption].
% 8.69/8.84 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(966,a,967,a)].
% 8.69/8.84 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(966,a,968,a)].
% 8.69/8.84 969 class_Ring__and__Field_Osemiring__0__cancel(tc_nat) # label(clsarity_nat_29) # label(axiom). [assumption].
% 8.69/8.84 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(969,a,967,a)].
% 8.69/8.84 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(969,a,968,a)].
% 8.69/8.84 970 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Power_Orecpower_21) # label(axiom). [assumption].
% 8.69/8.84 Derived: -class_Power_Orecpower(A) | c_times(c_0,B,A) = c_0. [resolve(970,b,967,a)].
% 8.69/8.84 Derived: -class_Power_Orecpower(A) | c_times(B,c_0,A) = c_0. [resolve(970,b,968,a)].
% 8.69/8.84 971 -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].
% 8.69/8.84 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(971,b,967,a)].
% 8.69/8.84 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(971,b,968,a)].
% 8.69/8.84 972 -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].
% 8.69/8.84 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(972,b,967,a)].
% 8.69/8.84 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(972,b,968,a)].
% 8.69/8.84 973 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Ofield_18) # label(axiom). [assumption].
% 8.69/8.84 Derived: -class_Ring__and__Field_Ofield(A) | c_times(c_0,B,A) = c_0. [resolve(973,b,967,a)].
% 8.69/8.84 Derived: -class_Ring__and__Field_Ofield(A) | c_times(B,c_0,A) = c_0. [resolve(973,b,968,a)].
% 8.69/8.84 974 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oidom_18) # label(axiom). [assumption].
% 8.69/8.84 Derived: -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0. [resolve(974,b,967,a)].
% 8.69/8.84 Derived: -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0. [resolve(974,b,968,a)].
% 8.69/8.84 975 -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].
% 8.69/8.84 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(975,b,967,a)].
% 8.69/8.84 Derived: -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(975,b,968,a)].
% 8.69/8.84 976 -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].
% 8.69/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(976,b,967,a)].
% 8.69/8.84 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(976,b,968,a)].
% 8.69/8.84 977 -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].
% 8.69/8.84 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(c_0,B,A) = c_0. [resolve(977,b,967,a)].
% 8.69/8.84 Derived: -class_Ring__and__Field_Oordered__field(A) | c_times(B,c_0,A) = c_0. [resolve(977,b,968,a)].
% 8.69/8.84 978 -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].
% 8.69/8.84 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(c_0,B,A) = c_0. [resolve(978,b,967,a)].
% 8.69/8.84 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_times(B,c_0,A) = c_0. [resolve(978,b,968,a)].
% 8.69/8.84 979 -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].
% 8.69/8.86 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(979,b,967,a)].
% 8.69/8.86 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(979,b,968,a)].
% 8.69/8.86 980 -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].
% 8.69/8.86 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(980,b,967,a)].
% 8.69/8.86 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(980,b,968,a)].
% 8.69/8.86 981 -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].
% 8.69/8.86 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(981,b,967,a)].
% 8.69/8.86 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(981,b,968,a)].
% 8.69/8.86 982 -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].
% 8.69/8.86 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(982,b,967,a)].
% 8.69/8.86 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(982,b,968,a)].
% 8.69/8.86 983 -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].
% 8.69/8.86 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(983,b,967,a)].
% 8.69/8.86 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(983,b,968,a)].
% 8.69/8.86 984 -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].
% 8.69/8.86 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(984,b,967,a)].
% 8.69/8.86 Derived: -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(984,b,968,a)].
% 8.69/8.86 985 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0__cancel(A) # label(clsrel_Ring__and__Field_Oring_12) # label(axiom). [assumption].
% 8.69/8.86 Derived: -class_Ring__and__Field_Oring(A) | c_times(c_0,B,A) = c_0. [resolve(985,b,967,a)].
% 8.69/8.86 Derived: -class_Ring__and__Field_Oring(A) | c_times(B,c_0,A) = c_0. [resolve(985,b,968,a)].
% 8.69/8.86 986 -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].
% 8.69/8.86 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0. [resolve(986,b,967,a)].
% 8.69/8.86 Derived: -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0. [resolve(986,b,968,a)].
% 8.69/8.86 987 -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].
% 8.69/8.86 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(987,a,971,b)].
% 8.69/8.86 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(987,a,972,b)].
% 8.69/8.86 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(987,a,975,b)].
% 8.69/8.86 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(987,a,976,b)].
% 8.69/8.86 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(987,a,979,b)].
% 8.69/8.86 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(987,a,980,b)].
% 8.69/8.86 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(987,a,981,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(987,a,982,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(987,a,983,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(987,a,984,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Oring(A). [resolve(987,a,985,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Oring__1(A). [resolve(987,a,986,b)].
% 8.69/8.87 988 -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].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(988,a,971,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(988,a,972,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(988,a,975,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(988,a,976,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(988,a,979,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(988,a,980,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(988,a,981,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(988,a,982,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(988,a,983,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(988,a,984,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oring(A). [resolve(988,a,985,b)].
% 8.69/8.87 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oring__1(A). [resolve(988,a,986,b)].
% 8.69/8.87 989 -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].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(989,a,971,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(989,a,972,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(989,a,975,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(989,a,976,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(989,a,979,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(989,a,980,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(989,a,981,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(989,a,982,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(989,a,983,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(989,a,984,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring(A). [resolve(989,a,985,b)].
% 8.69/8.87 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(989,a,986,b)].
% 8.69/8.87 990 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_3) # label(axiom). [assumption].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(990,a,971,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(990,a,972,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(990,a,975,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(990,a,976,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(990,a,979,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(990,a,980,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(990,a,981,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(990,a,982,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(990,a,983,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(990,a,984,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring(A). [resolve(990,a,985,b)].
% 8.69/8.89 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(990,a,986,b)].
% 8.69/8.89 991 -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].
% 8.69/8.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(991,a,971,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(991,a,972,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(991,a,976,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(991,a,980,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(991,a,982,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(991,a,983,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(991,a,986,b)].
% 8.69/8.89 992 -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].
% 8.69/8.89 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(992,a,971,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(992,a,972,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(992,a,976,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(992,a,980,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(992,a,982,b)].
% 8.69/8.89 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(992,a,983,b)].
% 8.69/8.89 993 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_7) # label(axiom). [assumption].
% 8.69/8.89 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(993,a,980,b)].
% 8.69/8.89 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(993,a,983,b)].
% 8.69/8.89 994 -class_Ring__and__Field_Osemiring__0__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0__cancel_8) # label(axiom). [assumption].
% 8.69/8.89 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(994,a,980,b)].
% 8.69/8.89 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(994,a,981,b)].
% 8.83/8.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(994,a,982,b)].
% 8.83/8.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(994,a,983,b)].
% 8.83/8.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(994,a,984,b)].
% 8.83/8.98 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring(A). [resolve(994,a,985,b)].
% 8.83/8.98 995 -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].
% 8.83/8.98 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(995,a,971,b)].
% 8.83/8.98 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(995,a,972,b)].
% 8.83/8.98 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(995,a,976,b)].
% 8.83/8.98 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(995,a,980,b)].
% 8.83/8.98 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(995,a,981,b)].
% 8.83/8.98 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(995,a,982,b)].
% 8.83/8.98 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(995,a,983,b)].
% 8.83/8.98 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(995,a,984,b)].
% 8.83/8.98 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(995,a,985,b)].
% 8.83/8.98 Derived: class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(995,a,986,b)].
% 8.83/8.98 996 -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].
% 8.83/8.98 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(996,b,967,a)].
% 8.83/8.98 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(996,b,968,a)].
% 8.83/8.98 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(996,b,995,a)].
% 8.83/8.98 997 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint). [resolve(152,a,74,a)].
% 8.83/8.98 998 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(226,b,222,a)].
% 8.83/8.98 Derived: -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring(A). [resolve(998,b,988,a)].
% 8.83/8.98 999 class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint). [resolve(228,a,222,a)].
% 8.83/8.98 1000 class_Ring__and__Field_Osemiring__0__cancel(tc_nat). [resolve(256,a,240,a)].
% 8.83/8.98 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1000,a,989,a)].
% 8.83/8.98 Derived: class_HOL_Otimes(tc_nat). [resolve(1000,a,990,a)].
% 8.83/8.98 1001 class_Ring__and__Field_Osemiring__0__cancel(A) | -class_Power_Orecpower(A). [resolve(256,a,241,b)].
% 8.83/8.98 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(1001,a,989,a)].
% 8.83/8.98 Derived: -class_Power_Orecpower(A) | class_HOL_Otimes(A). [resolve(1001,a,990,a)].
% 8.83/8.98 Derived: -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(1001,a,995,a)].
% 8.83/8.98 1002 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(265,b,256,a)].
% 8.83/8.98 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(1002,b,989,a)].
% 8.83/8.98 Derived: -class_Ring__and__Field_Ofield(A) | class_HOL_Otimes(A). [resolve(1002,b,990,a)].
% 8.83/8.98 Derived: -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(1002,b,995,a)].
% 8.83/8.98 1003 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(266,b,256,a)].
% 8.83/8.98 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(1003,b,989,a)].
% 8.96/9.10 Derived: -class_Ring__and__Field_Oidom(A) | class_HOL_Otimes(A). [resolve(1003,b,990,a)].
% 8.96/9.10 Derived: -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(1003,b,995,a)].
% 8.96/9.10 1004 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__0__cancel(A). [resolve(268,b,256,a)].
% 8.96/9.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(1004,b,989,a)].
% 8.96/9.10 Derived: -class_Ring__and__Field_Oordered__idom(A) | class_HOL_Otimes(A). [resolve(1004,b,990,a)].
% 8.96/9.10 1005 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,c_0,A) = B. [resolve(676,b,642,a)].
% 8.96/9.10 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(1005,a,969,a)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(1005,a,970,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1005,a,971,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(1005,a,972,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(1005,a,973,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1005,a,974,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1005,a,975,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1005,a,976,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1005,a,977,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1005,a,978,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1005,a,979,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1005,a,980,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1005,a,981,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1005,a,982,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1005,a,983,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1005,a,984,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring(B). [resolve(1005,a,985,b)].
% 8.96/9.10 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(1005,a,986,b)].
% 8.96/9.10 1006 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(c_0,B,A) = B. [resolve(676,b,643,a)].
% 8.96/9.10 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(1006,a,969,a)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(1006,a,970,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1006,a,971,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(1006,a,972,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(1006,a,973,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1006,a,974,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1006,a,975,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1006,a,976,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1006,a,977,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1006,a,978,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1006,a,979,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1006,a,980,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1006,a,981,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1006,a,982,b)].
% 8.96/9.10 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1006,a,983,b)].
% 9.00/9.14 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1006,a,984,b)].
% 9.00/9.14 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring(B). [resolve(1006,a,985,b)].
% 9.00/9.14 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(1006,a,986,b)].
% 9.00/9.14 1007 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(756,b,726,a)].
% 9.00/9.14 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1007,a,969,a)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(1007,a,970,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(1007,a,971,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(1007,a,972,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(1007,a,973,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(1007,a,974,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1007,a,975,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1007,a,976,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1007,a,977,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1007,a,978,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1007,a,979,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1007,a,980,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1007,a,981,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1007,a,982,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1007,a,983,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(1007,a,984,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring(C). [resolve(1007,a,985,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(1007,a,986,b)].
% 9.00/9.14 1008 -class_Ring__and__Field_Osemiring__0__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(756,b,727,a)].
% 9.00/9.14 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1008,a,969,a)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(1008,a,970,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(1008,a,971,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(1008,a,972,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(1008,a,973,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(1008,a,974,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1008,a,975,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1008,a,976,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1008,a,977,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1008,a,978,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1008,a,979,b)].
% 9.00/9.14 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1008,a,980,b)].
% 9.13/9.35 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1008,a,981,b)].
% 9.13/9.35 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1008,a,982,b)].
% 9.13/9.35 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1008,a,983,b)].
% 9.13/9.35 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(1008,a,984,b)].
% 9.13/9.35 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring(C). [resolve(1008,a,985,b)].
% 9.13/9.35 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(1008,a,986,b)].
% 9.13/9.35 1009 class_Orderings_Oord(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_5) # label(axiom). [assumption].
% 9.13/9.35 1010 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeastAtMost__iff_0) # label(axiom). [assumption].
% 9.13/9.35 1011 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A) # label(cls_SetInterval_OatLeastAtMost__iff_1) # label(axiom). [assumption].
% 9.13/9.35 1012 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A) # label(cls_SetInterval_OatLeastAtMost__iff_2) # label(axiom). [assumption].
% 9.13/9.35 1013 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeastLessThan__iff_0) # label(axiom). [assumption].
% 9.13/9.35 1014 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A) # label(cls_SetInterval_OatLeastLessThan__iff_1) # label(axiom). [assumption].
% 9.13/9.35 1015 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A) # label(cls_SetInterval_OatLeastLessThan__iff_2) # label(axiom). [assumption].
% 9.13/9.35 1016 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A) # label(cls_SetInterval_OatLeast__iff_0) # label(axiom). [assumption].
% 9.13/9.35 1017 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A) # label(cls_SetInterval_OatLeast__iff_1) # label(axiom). [assumption].
% 9.13/9.35 1018 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A) # label(cls_SetInterval_OatMost__iff_0) # label(axiom). [assumption].
% 9.13/9.35 1019 -class_Orderings_Oord(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A) # label(cls_SetInterval_OatMost__iff_1) # label(axiom). [assumption].
% 9.13/9.35 1020 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThanAtMost__iff_0) # label(axiom). [assumption].
% 9.13/9.35 1021 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A) # label(cls_SetInterval_OgreaterThanAtMost__iff_1) # label(axiom). [assumption].
% 9.13/9.35 1022 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A) # label(cls_SetInterval_OgreaterThanAtMost__iff_2) # label(axiom). [assumption].
% 9.13/9.35 1023 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThanLessThan__iff_0) # label(axiom). [assumption].
% 9.13/9.35 1024 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A) # label(cls_SetInterval_OgreaterThanLessThan__iff_1) # label(axiom). [assumption].
% 9.13/9.35 1025 -class_Orderings_Oord(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A) # label(cls_SetInterval_OgreaterThanLessThan__iff_2) # label(axiom). [assumption].
% 9.13/9.35 1026 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A) # label(cls_SetInterval_OgreaterThan__iff_0) # label(axiom). [assumption].
% 9.13/9.35 1027 -class_Orderings_Oord(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A) # label(cls_SetInterval_OgreaterThan__iff_1) # label(axiom). [assumption].
% 9.23/9.37 1028 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A) # label(cls_SetInterval_OlessThan__iff_0) # label(axiom). [assumption].
% 9.23/9.37 1029 -class_Orderings_Oord(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A) # label(cls_SetInterval_OlessThan__iff_1) # label(axiom). [assumption].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1009,a,1010,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1009,a,1011,a)].
% 9.23/9.37 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1009,a,1012,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1009,a,1013,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1009,a,1014,a)].
% 9.23/9.37 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1009,a,1015,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1009,a,1016,a)].
% 9.23/9.37 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1009,a,1017,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1009,a,1018,a)].
% 9.23/9.37 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1009,a,1019,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1009,a,1020,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1009,a,1021,a)].
% 9.23/9.37 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1009,a,1022,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1009,a,1023,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1009,a,1024,a)].
% 9.23/9.37 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1009,a,1025,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1009,a,1026,a)].
% 9.23/9.37 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1009,a,1027,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1009,a,1028,a)].
% 9.23/9.37 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1009,a,1029,a)].
% 9.23/9.37 1030 class_Orderings_Oord(tc_nat) # label(clsarity_nat_2) # label(axiom). [assumption].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1030,a,1010,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1030,a,1011,a)].
% 9.23/9.37 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(1030,a,1012,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1030,a,1013,a)].
% 9.23/9.37 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1030,a,1014,a)].
% 9.23/9.37 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(1030,a,1015,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1030,a,1016,a)].
% 9.23/9.39 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1030,a,1017,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1030,a,1018,a)].
% 9.23/9.39 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1030,a,1019,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1030,a,1020,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1030,a,1021,a)].
% 9.23/9.39 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(1030,a,1022,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1030,a,1023,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1030,a,1024,a)].
% 9.23/9.39 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(1030,a,1025,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1030,a,1026,a)].
% 9.23/9.39 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1030,a,1027,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1030,a,1028,a)].
% 9.23/9.39 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1030,a,1029,a)].
% 9.23/9.39 1031 class_Orderings_Oord(tc_set(A)) # label(clsarity_set_1) # label(axiom). [assumption].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(1031,a,1010,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(1031,a,1011,a)].
% 9.23/9.39 Derived: -c_lessequals(A,B,tc_set(C)) | -c_lessequals(D,A,tc_set(C)) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,tc_set(C)),tc_set(C)). [resolve(1031,a,1012,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_lessequals(B,A,tc_set(D)). [resolve(1031,a,1013,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(1031,a,1014,a)].
% 9.23/9.39 Derived: -c_less(A,B,tc_set(C)) | -c_lessequals(D,A,tc_set(C)) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,tc_set(C)),tc_set(C)). [resolve(1031,a,1015,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_set(C)),tc_set(C)) | c_lessequals(B,A,tc_set(C)). [resolve(1031,a,1016,a)].
% 9.23/9.39 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(B,c_SetInterval_OatLeast(A,tc_set(C)),tc_set(C)). [resolve(1031,a,1017,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)) | c_lessequals(A,B,tc_set(C)). [resolve(1031,a,1018,a)].
% 9.23/9.39 Derived: -c_lessequals(A,B,tc_set(C)) | c_in(A,c_SetInterval_OatMost(B,tc_set(C)),tc_set(C)). [resolve(1031,a,1019,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(1031,a,1020,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_set(D)),tc_set(D)) | c_lessequals(A,C,tc_set(D)). [resolve(1031,a,1021,a)].
% 9.23/9.39 Derived: -c_less(A,B,tc_set(C)) | -c_lessequals(B,D,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,tc_set(C)),tc_set(C)). [resolve(1031,a,1022,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(B,A,tc_set(D)). [resolve(1031,a,1023,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_set(D)),tc_set(D)) | c_less(A,C,tc_set(D)). [resolve(1031,a,1024,a)].
% 9.23/9.39 Derived: -c_less(A,B,tc_set(C)) | -c_less(D,A,tc_set(C)) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,tc_set(C)),tc_set(C)). [resolve(1031,a,1025,a)].
% 9.23/9.39 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_set(C)),tc_set(C)) | c_less(B,A,tc_set(C)). [resolve(1031,a,1026,a)].
% 9.23/9.40 Derived: -c_less(A,B,tc_set(C)) | c_in(B,c_SetInterval_OgreaterThan(A,tc_set(C)),tc_set(C)). [resolve(1031,a,1027,a)].
% 9.23/9.40 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)) | c_less(A,B,tc_set(C)). [resolve(1031,a,1028,a)].
% 9.23/9.40 Derived: -c_less(A,B,tc_set(C)) | c_in(A,c_SetInterval_OlessThan(B,tc_set(C)),tc_set(C)). [resolve(1031,a,1029,a)].
% 9.23/9.40 1032 -class_LOrder_Olorder(A) | class_Orderings_Oord(A) # label(clsrel_LOrder_Olorder_1) # label(axiom). [assumption].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1032,b,1010,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1032,b,1011,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1032,b,1012,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1032,b,1013,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1032,b,1014,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1032,b,1015,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1032,b,1016,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1032,b,1017,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1032,b,1018,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1032,b,1019,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1032,b,1020,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1032,b,1021,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1032,b,1022,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1032,b,1023,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1032,b,1024,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1032,b,1025,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1032,b,1026,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1032,b,1027,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1032,b,1028,a)].
% 9.23/9.40 Derived: -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1032,b,1029,a)].
% 9.23/9.40 1033 -class_OrderedGroup_Olordered__ab__group__join(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_9) # label(axiom). [assumption].
% 9.23/9.40 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1033,b,1010,a)].
% 9.23/9.40 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1033,b,1011,a)].
% 9.23/9.40 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1033,b,1012,a)].
% 9.23/9.40 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1033,b,1013,a)].
% 9.23/9.40 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1033,b,1014,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1033,b,1015,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1033,b,1016,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1033,b,1017,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1033,b,1018,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1033,b,1019,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1033,b,1020,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1033,b,1021,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1033,b,1022,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1033,b,1023,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1033,b,1024,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1033,b,1025,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1033,b,1026,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1033,b,1027,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1033,b,1028,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1033,b,1029,a)].
% 9.27/9.42 1034 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_9) # label(axiom). [assumption].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1034,b,1010,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1034,b,1011,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1034,b,1012,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1034,b,1013,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1034,b,1014,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1034,b,1015,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1034,b,1016,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1034,b,1017,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1034,b,1018,a)].
% 9.27/9.42 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1034,b,1019,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1034,b,1020,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1034,b,1021,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1034,b,1022,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1034,b,1023,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1034,b,1024,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1034,b,1025,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1034,b,1026,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1034,b,1027,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1034,b,1028,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1034,b,1029,a)].
% 9.27/9.43 1035 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) # label(axiom). [assumption].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1035,b,1010,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1035,b,1011,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1035,b,1012,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1035,b,1013,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1035,b,1014,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1035,b,1015,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1035,b,1016,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1035,b,1017,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1035,b,1018,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1035,b,1019,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1035,b,1020,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1035,b,1021,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1035,b,1022,a)].
% 9.27/9.43 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1035,b,1023,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1035,b,1024,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1035,b,1025,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1035,b,1026,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1035,b,1027,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1035,b,1028,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1035,b,1029,a)].
% 9.31/9.44 1036 -class_OrderedGroup_Opordered__ab__group__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__group__add_11) # label(axiom). [assumption].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1036,b,1010,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1036,b,1011,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1036,b,1012,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1036,b,1013,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1036,b,1014,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1036,b,1015,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1036,b,1016,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1036,b,1017,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1036,b,1018,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1036,b,1019,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1036,b,1020,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1036,b,1021,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1036,b,1022,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1036,b,1023,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1036,b,1024,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1036,b,1025,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1036,b,1026,a)].
% 9.31/9.44 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1036,b,1027,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1036,b,1028,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1036,b,1029,a)].
% 9.31/9.45 1037 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) # label(axiom). [assumption].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1037,b,1010,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1037,b,1011,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1037,b,1012,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1037,b,1013,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1037,b,1014,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1037,b,1015,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1037,b,1016,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1037,b,1017,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1037,b,1018,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1037,b,1019,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1037,b,1020,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1037,b,1021,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1037,b,1022,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1037,b,1023,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1037,b,1024,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1037,b,1025,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1037,b,1026,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1037,b,1027,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1037,b,1028,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1037,b,1029,a)].
% 9.31/9.45 1038 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A) # label(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1038,b,1010,a)].
% 9.31/9.45 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1038,b,1011,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1038,b,1012,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1038,b,1013,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1038,b,1014,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1038,b,1015,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1038,b,1016,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1038,b,1017,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1038,b,1018,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1038,b,1019,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1038,b,1020,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1038,b,1021,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1038,b,1022,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1038,b,1023,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1038,b,1024,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1038,b,1025,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1038,b,1026,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1038,b,1027,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1038,b,1028,a)].
% 9.31/9.47 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1038,b,1029,a)].
% 9.31/9.47 1039 -class_Ring__and__Field_Oaxclass__abs__if(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oaxclass__abs__if_1) # label(axiom). [assumption].
% 9.31/9.47 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1039,b,1010,a)].
% 9.31/9.47 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1039,b,1011,a)].
% 9.31/9.47 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1039,b,1012,a)].
% 9.31/9.47 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1039,b,1013,a)].
% 9.31/9.47 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1039,b,1014,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1039,b,1015,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1039,b,1016,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1039,b,1017,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1039,b,1018,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1039,b,1019,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1039,b,1020,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1039,b,1021,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1039,b,1022,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1039,b,1023,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1039,b,1024,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1039,b,1025,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1039,b,1026,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1039,b,1027,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1039,b,1028,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1039,b,1029,a)].
% 9.31/9.49 1040 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Olordered__ring_11) # label(axiom). [assumption].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1040,b,1010,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1040,b,1011,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1040,b,1012,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1040,b,1013,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1040,b,1014,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1040,b,1015,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1040,b,1016,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1040,b,1017,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1040,b,1018,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1040,b,1019,a)].
% 9.31/9.49 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1040,b,1020,a)].
% 9.31/9.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1040,b,1021,a)].
% 9.31/9.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1040,b,1022,a)].
% 9.31/9.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1040,b,1023,a)].
% 9.31/9.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1040,b,1024,a)].
% 9.31/9.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1040,b,1025,a)].
% 9.31/9.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1040,b,1026,a)].
% 9.31/9.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1040,b,1027,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1040,b,1028,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1040,b,1029,a)].
% 9.38/9.50 1041 -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].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1041,b,1010,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1041,b,1011,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1041,b,1012,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1041,b,1013,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1041,b,1014,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1041,b,1015,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1041,b,1016,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1041,b,1017,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1041,b,1018,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1041,b,1019,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1041,b,1020,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1041,b,1021,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1041,b,1022,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1041,b,1023,a)].
% 9.38/9.50 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1041,b,1024,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1041,b,1025,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1041,b,1026,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1041,b,1027,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1041,b,1028,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1041,b,1029,a)].
% 9.38/9.52 1042 -class_Ring__and__Field_Oordered__field(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__field_59) # label(axiom). [assumption].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1042,b,1010,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1042,b,1011,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1042,b,1012,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1042,b,1013,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1042,b,1014,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1042,b,1015,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1042,b,1016,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1042,b,1017,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1042,b,1018,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1042,b,1019,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1042,b,1020,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1042,b,1021,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1042,b,1022,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1042,b,1023,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1042,b,1024,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1042,b,1025,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1042,b,1026,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1042,b,1027,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1042,b,1028,a)].
% 9.38/9.52 Derived: -class_Ring__and__Field_Oordered__field(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1042,b,1029,a)].
% 9.38/9.52 1043 -class_Ring__and__Field_Oordered__idom(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__idom_45) # label(axiom). [assumption].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1043,b,1010,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1043,b,1011,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1043,b,1012,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1043,b,1013,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1043,b,1014,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1043,b,1015,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1043,b,1016,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1043,b,1017,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1043,b,1018,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1043,b,1019,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1043,b,1020,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1043,b,1021,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1043,b,1022,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1043,b,1023,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1043,b,1024,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1043,b,1025,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1043,b,1026,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1043,b,1027,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1043,b,1028,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1043,b,1029,a)].
% 9.38/9.53 1044 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_27) # label(axiom). [assumption].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1044,b,1010,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1044,b,1011,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1044,b,1012,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1044,b,1013,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1044,b,1014,a)].
% 9.38/9.53 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1044,b,1015,a)].
% 9.38/9.54 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1044,b,1016,a)].
% 9.38/9.54 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1044,b,1017,a)].
% 9.38/9.54 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1044,b,1018,a)].
% 9.38/9.54 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1044,b,1019,a)].
% 9.38/9.54 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1044,b,1020,a)].
% 9.38/9.54 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1044,b,1021,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1044,b,1022,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1044,b,1023,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1044,b,1024,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1044,b,1025,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1044,b,1026,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1044,b,1027,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1044,b,1028,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1044,b,1029,a)].
% 9.38/9.55 1045 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_18) # label(axiom). [assumption].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1045,b,1010,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1045,b,1011,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1045,b,1012,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1045,b,1013,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1045,b,1014,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1045,b,1015,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1045,b,1016,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1045,b,1017,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1045,b,1018,a)].
% 9.38/9.55 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1045,b,1019,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1045,b,1020,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1045,b,1021,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1045,b,1022,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1045,b,1023,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1045,b,1024,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1045,b,1025,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1045,b,1026,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1045,b,1027,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1045,b,1028,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1045,b,1029,a)].
% 9.43/9.56 1046 -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].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1046,b,1010,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1046,b,1011,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1046,b,1012,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1046,b,1013,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1046,b,1014,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1046,b,1015,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1046,b,1016,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1046,b,1017,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1046,b,1018,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1046,b,1019,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1046,b,1020,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1046,b,1021,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1046,b,1022,a)].
% 9.43/9.56 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1046,b,1023,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1046,b,1024,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1046,b,1025,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1046,b,1026,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1046,b,1027,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1046,b,1028,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1046,b,1029,a)].
% 9.43/9.57 1047 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__cancel__semiring_12) # label(axiom). [assumption].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1047,b,1010,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1047,b,1011,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1047,b,1012,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1047,b,1013,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1047,b,1014,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1047,b,1015,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1047,b,1016,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1047,b,1017,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1047,b,1018,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1047,b,1019,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1047,b,1020,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1047,b,1021,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1047,b,1022,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1047,b,1023,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1047,b,1024,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1047,b,1025,a)].
% 9.43/9.57 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1047,b,1026,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1047,b,1027,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1047,b,1028,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1047,b,1029,a)].
% 9.43/9.58 1048 -class_Ring__and__Field_Opordered__comm__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__ring_24) # label(axiom). [assumption].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1048,b,1010,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1048,b,1011,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1048,b,1012,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1048,b,1013,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1048,b,1014,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1048,b,1015,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1048,b,1016,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1048,b,1017,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1048,b,1018,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1048,b,1019,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1048,b,1020,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1048,b,1021,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1048,b,1022,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1048,b,1023,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1048,b,1024,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1048,b,1025,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1048,b,1026,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1048,b,1027,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1048,b,1028,a)].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1048,b,1029,a)].
% 9.43/9.58 1049 -class_Ring__and__Field_Opordered__comm__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__comm__semiring_14) # label(axiom). [assumption].
% 9.43/9.58 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1049,b,1010,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1049,b,1011,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1049,b,1012,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1049,b,1013,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1049,b,1014,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1049,b,1015,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1049,b,1016,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1049,b,1017,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1049,b,1018,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1049,b,1019,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1049,b,1020,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1049,b,1021,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1049,b,1022,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1049,b,1023,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1049,b,1024,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1049,b,1025,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1049,b,1026,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1049,b,1027,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1049,b,1028,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1049,b,1029,a)].
% 9.43/9.60 1050 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__ring_18) # label(axiom). [assumption].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1050,b,1010,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1050,b,1011,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1050,b,1012,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1050,b,1013,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1050,b,1014,a)].
% 9.43/9.60 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1050,b,1015,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1050,b,1016,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1050,b,1017,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1050,b,1018,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1050,b,1019,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1050,b,1020,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1050,b,1021,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1050,b,1022,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1050,b,1023,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1050,b,1024,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1050,b,1025,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1050,b,1026,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1050,b,1027,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1050,b,1028,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1050,b,1029,a)].
% 9.43/9.61 1051 -class_Ring__and__Field_Opordered__semiring(A) | class_Orderings_Oord(A) # label(clsrel_Ring__and__Field_Opordered__semiring_11) # label(axiom). [assumption].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1051,b,1010,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1051,b,1011,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1051,b,1012,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1051,b,1013,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1051,b,1014,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1051,b,1015,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1051,b,1016,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1051,b,1017,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1051,b,1018,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1051,b,1019,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1051,b,1020,a)].
% 9.43/9.61 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1051,b,1021,a)].
% 9.43/9.63 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1051,b,1022,a)].
% 9.43/9.63 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1051,b,1023,a)].
% 9.43/9.63 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1051,b,1024,a)].
% 9.43/9.63 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1051,b,1025,a)].
% 9.43/9.63 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1051,b,1026,a)].
% 9.43/9.63 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1051,b,1027,a)].
% 9.43/9.63 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1051,b,1028,a)].
% 9.43/9.63 Derived: -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1051,b,1029,a)].
% 9.43/9.63 1052 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A) # label(clsrel_Wellfounded__Recursion_Owellorder_0) # label(axiom). [assumption].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1052,b,1010,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1052,b,1011,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1052,b,1012,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1052,b,1013,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1052,b,1014,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1052,b,1015,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1052,b,1016,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1052,b,1017,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1052,b,1018,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1052,b,1019,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1052,b,1020,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1052,b,1021,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1052,b,1022,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1052,b,1023,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1052,b,1024,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1052,b,1025,a)].
% 9.43/9.63 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1052,b,1026,a)].
% 11.20/11.34 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1052,b,1027,a)].
% 11.20/11.34 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1052,b,1028,a)].
% 11.20/11.34 Derived: -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1052,b,1029,a)].
% 11.20/11.34 1053 class_Orderings_Oord(tc_IntDef_Oint). [resolve(65,a,1,a)].
% 11.20/11.34 1054 class_Orderings_Oord(tc_nat). [resolve(65,a,60,a)].
% 11.20/11.34 1055 class_Orderings_Oord(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(65,a,61,b)].
% 11.20/11.34 1056 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(73,b,65,a)].
% 11.20/11.34 1057 -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(277,b,275,a)].
% 11.20/11.34 1058 -class_Ring__and__Field_Olordered__ring(A) | class_Orderings_Oord(A). [resolve(283,b,275,a)].
% 11.20/11.34 1059 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(375,a,344,b)].
% 11.20/11.34 1060 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(375,a,345,b)].
% 11.20/11.34 1061 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A). [resolve(638,b,626,a)].
% 11.20/11.34 1062 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(707,a,700,b)].
% 11.20/11.34 1063 class_Orderings_Oord(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(707,a,701,b)].
% 11.20/11.34 1064 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(707,a,703,b)].
% 11.20/11.34 1065 -class_Ring__and__Field_Opordered__ring(A) | class_Orderings_Oord(A). [resolve(719,b,707,a)].
% 11.20/11.34 1066 class_Orderings_Oord(tc_IntDef_Oint). [resolve(720,a,707,a)].
% 11.20/11.34 1067 class_Orderings_Oord(tc_nat). [resolve(721,a,707,a)].
% 11.20/11.34 1068 -class_Ring__and__Field_Oordered__ring__strict(A) | class_Orderings_Oord(A). [resolve(724,b,707,a)].
% 11.20/11.34 1069 class_Orderings_Oord(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(838,b,814,b)].
% 11.20/11.34 1070 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(838,b,815,b)].
% 11.20/11.34 1071 class_Orderings_Oord(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(838,b,816,b)].
% 11.20/11.34 1072 class_Orderings_Oord(tc_set(A)). [resolve(900,a,892,a)].
% 11.20/11.34 1073 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(900,a,898,b)].
% 11.20/11.34 1074 class_Orderings_Oord(A) | -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(900,a,899,b)].
% 11.20/11.34 1075 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_Orderings_Oord(A). [resolve(916,a,900,a)].
% 11.20/11.34 1076 -class_Wellfounded__Recursion_Owellorder(A) | class_Orderings_Oord(A). [resolve(917,b,900,a)].
% 11.20/11.34 1077 -class_LOrder_Olorder(A) | class_Orderings_Oord(A). [resolve(918,b,900,a)].
% 11.20/11.34 1078 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_0) # label(axiom). [assumption].
% 11.20/11.34 1079 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_11) # label(axiom). [assumption].
% 11.20/11.34 1080 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat_19) # label(axiom). [assumption].
% 11.20/11.34 1081 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Power_Orecpower_11) # label(axiom). [assumption].
% 11.20/11.34 1082 -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].
% 11.20/11.34 1083 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_1) # label(axiom). [assumption].
% 11.20/11.34 1084 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_2) # label(axiom). [assumption].
% 11.20/11.34 1085 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_3) # label(axiom). [assumption].
% 11.20/11.34 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1085,a,1082,b)].
% 11.71/11.90 1086 -class_Ring__and__Field_Ocomm__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_4) # label(axiom). [assumption].
% 11.71/11.90 1087 -class_Ring__and__Field_Ocomm__semiring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_5) # label(axiom). [assumption].
% 11.71/11.90 1088 -class_Ring__and__Field_Ocomm__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__semiring_6) # label(axiom). [assumption].
% 11.71/11.90 1089 -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].
% 11.71/11.90 1090 -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].
% 11.71/11.90 1091 -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].
% 11.71/11.90 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1091,b,1078,a)].
% 11.71/11.90 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1091,b,1083,a)].
% 11.71/11.90 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Oplus(A). [resolve(1091,b,1084,a)].
% 11.71/11.90 1092 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Ofield_16) # label(axiom). [assumption].
% 11.71/11.90 1093 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A) # label(clsrel_Ring__and__Field_Oidom_16) # label(axiom). [assumption].
% 11.71/11.90 1094 -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].
% 11.71/11.90 1095 -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].
% 11.71/11.90 1096 -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].
% 11.71/11.90 1097 -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].
% 11.71/11.90 1098 -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].
% 11.71/11.90 1099 -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].
% 11.71/11.90 1100 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint). [resolve(172,a,74,a)].
% 11.71/11.90 1101 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring(A). [resolve(226,b,220,a)].
% 11.71/11.90 1102 class_Ring__and__Field_Ocomm__semiring(tc_nat). [resolve(254,a,240,a)].
% 11.71/11.90 1103 class_Ring__and__Field_Ocomm__semiring(A) | -class_Power_Orecpower(A). [resolve(254,a,241,b)].
% 11.71/11.90 1104 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring(A). [resolve(265,b,254,a)].
% 11.71/11.90 1105 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring(A). [resolve(266,b,254,a)].
% 11.71/11.90 1106 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring(A). [resolve(268,b,254,a)].
% 11.71/11.90 1107 class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint). [resolve(271,a,254,a)].
% 11.71/11.90 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1107,a,1086,a)].
% 11.71/11.90 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(1107,a,1087,a)].
% 11.71/11.90 1108 -class_Ring__and__Field_Osemiring__0(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__0_0) # label(axiom). [assumption].
% 11.71/11.90 1109 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_13) # label(axiom). [assumption].
% 11.71/11.91 1110 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat_21) # label(axiom). [assumption].
% 11.71/11.91 1111 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Power_Orecpower_13) # label(axiom). [assumption].
% 11.71/11.91 1112 -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].
% 11.71/11.91 1113 -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].
% 11.71/11.91 1114 -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].
% 11.71/11.91 1115 -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].
% 11.71/11.91 1116 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Ofield_19) # label(axiom). [assumption].
% 11.71/11.91 1117 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oidom_19) # label(axiom). [assumption].
% 11.71/11.91 1118 -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].
% 11.71/11.91 1119 -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].
% 11.71/11.91 1120 -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].
% 11.71/11.91 1121 -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].
% 11.71/11.91 1122 -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].
% 11.71/11.91 1123 -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].
% 11.71/11.91 1124 -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].
% 11.71/11.91 1125 -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].
% 11.71/11.91 1126 -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].
% 11.71/11.91 1127 -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].
% 11.71/11.91 1128 -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].
% 11.71/11.91 1129 -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].
% 11.71/11.91 1130 -class_Ring__and__Field_Oring(A) | class_Ring__and__Field_Osemiring__0(A) # label(clsrel_Ring__and__Field_Oring_13) # label(axiom). [assumption].
% 11.71/11.91 1131 -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].
% 11.71/11.91 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1108,a,1113,b)].
% 11.71/11.91 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1108,a,1115,b)].
% 11.71/11.91 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1108,a,1127,b)].
% 12.02/12.14 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1108,a,1129,b)].
% 12.02/12.14 1132 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_1) # label(axiom). [assumption].
% 12.02/12.14 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1132,a,1127,b)].
% 12.02/12.14 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1132,a,1129,b)].
% 12.02/12.14 1133 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__0_2) # label(axiom). [assumption].
% 12.02/12.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1133,a,1127,b)].
% 12.02/12.14 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1133,a,1129,b)].
% 12.02/12.14 1134 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Osemiring__0_3) # label(axiom). [assumption].
% 12.02/12.14 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1134,a,1129,b)].
% 12.02/12.14 1135 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__0_4) # label(axiom). [assumption].
% 12.02/12.14 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1135,a,1113,b)].
% 12.02/12.14 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1135,a,1115,b)].
% 12.02/12.14 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1135,a,1127,b)].
% 12.02/12.14 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1135,a,1129,b)].
% 12.02/12.14 1136 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__0_5) # label(axiom). [assumption].
% 12.02/12.14 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1136,a,1113,b)].
% 12.02/12.14 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1136,a,1115,b)].
% 12.02/12.14 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1136,a,1127,b)].
% 12.02/12.14 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1136,a,1129,b)].
% 12.02/12.14 1137 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__0_7) # label(axiom). [assumption].
% 12.02/12.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1137,a,1113,b)].
% 12.02/12.14 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1137,a,1129,b)].
% 12.02/12.14 1138 -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].
% 12.02/12.14 1139 -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].
% 12.02/12.14 1140 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint). [resolve(146,a,74,a)].
% 12.02/12.14 1141 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__0(A). [resolve(226,b,223,a)].
% 12.02/12.14 1142 class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint). [resolve(228,a,223,a)].
% 12.02/12.14 1143 class_Ring__and__Field_Osemiring__0(tc_nat). [resolve(262,a,240,a)].
% 12.02/12.14 1144 class_Ring__and__Field_Osemiring__0(A) | -class_Power_Orecpower(A). [resolve(262,a,241,b)].
% 12.02/12.14 1145 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__0(A). [resolve(265,b,262,a)].
% 12.02/12.14 1146 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__0(A). [resolve(266,b,262,a)].
% 12.02/12.14 1147 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__0(A). [resolve(268,b,262,a)].
% 12.02/12.14 1148 -class_Ring__and__Field_Osemiring__0(A) | c_plus(B,c_0,A) = B. [resolve(675,b,642,a)].
% 12.12/12.27 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(1148,a,1113,b)].
% 12.12/12.27 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(1148,a,1115,b)].
% 12.12/12.27 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1148,a,1127,b)].
% 12.12/12.27 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(1148,a,1129,b)].
% 12.12/12.27 1149 -class_Ring__and__Field_Osemiring__0(A) | c_plus(c_0,B,A) = B. [resolve(675,b,643,a)].
% 12.12/12.27 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(1149,a,1113,b)].
% 12.12/12.27 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(1149,a,1115,b)].
% 12.12/12.27 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1149,a,1127,b)].
% 12.12/12.27 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(1149,a,1129,b)].
% 12.12/12.27 1150 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(675,b,647,a)].
% 12.12/12.27 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1150,a,1113,b)].
% 12.12/12.27 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1150,a,1124,b)].
% 12.12/12.27 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(1150,a,1130,b)].
% 12.12/12.27 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(1150,a,1138,b)].
% 12.12/12.27 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(1150,a,1139,b)].
% 12.12/12.27 1151 -class_Ring__and__Field_Osemiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(675,b,648,a)].
% 12.12/12.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1151,a,1113,b)].
% 12.12/12.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1151,a,1124,b)].
% 12.12/12.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(1151,a,1130,b)].
% 12.12/12.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(1151,a,1138,b)].
% 12.12/12.27 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(1151,a,1139,b)].
% 12.12/12.27 1152 -class_Ring__and__Field_Osemiring__0(A) | class_HOL_Oplus(A). [resolve(675,b,649,a)].
% 12.12/12.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1152,a,1112,b)].
% 12.12/12.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1152,a,1113,b)].
% 12.12/12.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1152,a,1114,b)].
% 12.12/12.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1152,a,1119,b)].
% 12.12/12.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1152,a,1124,b)].
% 12.12/12.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(1152,a,1125,b)].
% 12.12/12.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1152,a,1127,b)].
% 12.12/12.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oring(A). [resolve(1152,a,1130,b)].
% 12.12/12.27 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(1152,a,1139,b)].
% 12.12/12.27 1153 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(987,a,971,b)].
% 12.12/12.27 Derived: -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(1153,a,1137,a)].
% 12.12/12.27 1154 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(987,a,972,b)].
% 12.12/12.27 Derived: -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(1154,a,1137,a)].
% 12.12/12.27 1155 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(987,a,975,b)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1155,a,1132,a)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1155,a,1133,a)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Oplus(A). [resolve(1155,a,1134,a)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Olordered__ring(A) | class_HOL_Ozero(A). [resolve(1155,a,1137,a)].
% 12.37/12.52 1156 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(987,a,976,b)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_HOL_Ozero(A). [resolve(1156,a,1137,a)].
% 12.37/12.52 1157 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(987,a,979,b)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1157,a,1132,a)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1157,a,1133,a)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Oplus(A). [resolve(1157,a,1134,a)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Oordered__ring__strict(A) | class_HOL_Ozero(A). [resolve(1157,a,1137,a)].
% 12.37/12.52 1158 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(987,a,980,b)].
% 12.37/12.52 1159 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(987,a,981,b)].
% 12.37/12.52 1160 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(987,a,982,b)].
% 12.37/12.52 1161 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(987,a,983,b)].
% 12.37/12.52 1162 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(987,a,984,b)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1162,a,1132,a)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1162,a,1133,a)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Opordered__ring(A) | class_HOL_Oplus(A). [resolve(1162,a,1134,a)].
% 12.37/12.52 1163 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Oring(A). [resolve(987,a,985,b)].
% 12.37/12.52 1164 class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Oring__1(A). [resolve(987,a,986,b)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1164,a,1133,a)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Oring__1(A) | class_HOL_Oplus(A). [resolve(1164,a,1134,a)].
% 12.37/12.52 Derived: -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A). [resolve(1164,a,1137,a)].
% 12.37/12.52 1165 -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].
% 12.37/12.52 1166 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_14) # label(axiom). [assumption].
% 12.37/12.52 1167 class_Ring__and__Field_Ocomm__semiring__0(tc_nat) # label(clsarity_nat_22) # label(axiom). [assumption].
% 12.37/12.52 1168 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Power_Orecpower_14) # label(axiom). [assumption].
% 12.37/12.52 1169 -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].
% 12.37/12.52 1170 -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].
% 12.37/12.52 1171 -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].
% 12.37/12.52 1172 -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].
% 12.37/12.52 1173 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_5) # label(axiom). [assumption].
% 12.79/12.93 1174 -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].
% 12.79/12.93 1175 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_7) # label(axiom). [assumption].
% 12.79/12.93 1176 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__0_9) # label(axiom). [assumption].
% 12.79/12.93 1177 -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].
% 12.79/12.93 1178 -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].
% 12.79/12.93 1179 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Ofield_15) # label(axiom). [assumption].
% 12.79/12.93 1180 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsrel_Ring__and__Field_Oidom_15) # label(axiom). [assumption].
% 12.79/12.93 1181 -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].
% 12.79/12.93 1182 -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].
% 12.79/12.93 1183 -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].
% 12.79/12.93 1184 -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].
% 12.79/12.93 1185 -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].
% 12.79/12.93 1186 -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].
% 12.79/12.93 1187 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint). [resolve(147,a,74,a)].
% 12.79/12.93 1188 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(226,b,219,a)].
% 12.79/12.93 1189 class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint). [resolve(228,a,219,a)].
% 12.79/12.93 1190 class_Ring__and__Field_Ocomm__semiring__0(tc_nat). [resolve(243,a,240,a)].
% 12.79/12.93 1191 class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Orecpower(A). [resolve(243,a,241,b)].
% 12.79/12.93 1192 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(265,b,243,a)].
% 12.79/12.93 1193 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(266,b,243,a)].
% 12.79/12.93 1194 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(268,b,243,a)].
% 12.79/12.93 1195 -class_Ring__and__Field_Ocomm__semiring__0(A) | c_plus(B,c_0,A) = B. [resolve(656,b,642,a)].
% 12.79/12.93 1196 -class_Ring__and__Field_Ocomm__semiring__0(A) | c_plus(c_0,B,A) = B. [resolve(656,b,643,a)].
% 12.79/12.93 1197 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(656,b,647,a)].
% 12.79/12.93 1198 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(656,b,648,a)].
% 12.79/12.93 1199 -class_Ring__and__Field_Ocomm__semiring__0(A) | class_HOL_Oplus(A). [resolve(656,b,649,a)].
% 12.79/12.93 1200 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1108,a,1113,b)].
% 12.79/12.93 Derived: class_Ring__and__Field_Osemiring(tc_IntDef_Oint). [resolve(1200,b,1166,a)].
% 12.79/12.93 Derived: class_Ring__and__Field_Osemiring(tc_nat). [resolve(1200,b,1167,a)].
% 12.79/12.94 Derived: class_Ring__and__Field_Osemiring(A) | -class_Power_Orecpower(A). [resolve(1200,b,1168,b)].
% 12.79/12.94 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1200,b,1169,b)].
% 12.79/12.94 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1200,b,1177,b)].
% 12.79/12.94 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ofield(A). [resolve(1200,b,1179,b)].
% 12.79/12.94 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oidom(A). [resolve(1200,b,1180,b)].
% 12.79/12.94 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1200,b,1181,b)].
% 12.79/12.94 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1200,b,1182,b)].
% 12.79/12.94 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1200,b,1183,b)].
% 12.79/12.94 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1200,b,1184,b)].
% 12.79/12.94 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1200,b,1185,b)].
% 12.79/12.94 1201 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1135,a,1113,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1201,b,1166,a)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1201,b,1167,a)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(1201,b,1168,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1201,b,1169,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1201,b,1177,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(1201,b,1179,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(1201,b,1180,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1201,b,1181,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1201,b,1182,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1201,b,1183,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1201,b,1184,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1201,b,1185,b)].
% 12.79/12.94 1202 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1136,a,1113,b)].
% 12.79/12.94 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(1202,b,1166,a)].
% 12.79/12.94 Derived: class_HOL_Otimes(tc_nat). [resolve(1202,b,1167,a)].
% 12.79/12.94 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(1202,b,1168,b)].
% 12.79/12.94 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1202,b,1169,b)].
% 12.79/12.94 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1202,b,1177,b)].
% 12.79/12.94 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(1202,b,1179,b)].
% 12.79/12.94 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(1202,b,1180,b)].
% 12.79/12.94 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1202,b,1181,b)].
% 12.79/12.94 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1202,b,1182,b)].
% 12.79/12.94 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1202,b,1183,b)].
% 12.79/12.94 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1202,b,1184,b)].
% 12.79/12.94 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1202,b,1185,b)].
% 12.79/12.94 1203 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1137,a,1113,b)].
% 12.79/12.94 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1203,b,1166,a)].
% 12.79/12.94 Derived: class_HOL_Ozero(tc_nat). [resolve(1203,b,1167,a)].
% 12.79/12.94 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(1203,b,1168,b)].
% 12.79/12.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1203,b,1178,b)].
% 12.79/12.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(1203,b,1179,b)].
% 12.79/12.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(1203,b,1180,b)].
% 12.79/12.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1203,b,1182,b)].
% 12.79/12.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1203,b,1183,b)].
% 12.79/12.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1203,b,1184,b)].
% 12.79/12.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1203,b,1185,b)].
% 12.79/12.94 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1203,b,1186,b)].
% 12.79/12.94 1204 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(1148,a,1113,b)].
% 12.79/12.94 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(1204,b,1166,a)].
% 12.79/12.94 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(1204,b,1167,a)].
% 12.79/12.94 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(1204,b,1168,b)].
% 12.79/12.94 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1204,b,1169,b)].
% 12.79/12.94 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(1204,b,1177,b)].
% 12.79/12.94 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(1204,b,1179,b)].
% 12.79/12.94 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1204,b,1180,b)].
% 12.79/12.94 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1204,b,1181,b)].
% 12.79/12.94 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1204,b,1182,b)].
% 12.79/12.94 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1204,b,1183,b)].
% 12.79/12.94 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1204,b,1184,b)].
% 12.79/12.94 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1204,b,1185,b)].
% 12.79/12.94 1205 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0(B). [resolve(1149,a,1113,b)].
% 12.79/12.94 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(1205,b,1166,a)].
% 12.79/12.94 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(1205,b,1167,a)].
% 12.79/12.94 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(1205,b,1168,b)].
% 12.79/12.94 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1205,b,1169,b)].
% 12.79/12.94 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(1205,b,1177,b)].
% 12.79/12.94 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(1205,b,1179,b)].
% 12.79/12.94 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1205,b,1180,b)].
% 12.79/12.94 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1205,b,1181,b)].
% 12.79/12.94 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1205,b,1182,b)].
% 12.79/12.94 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1205,b,1183,b)].
% 12.79/12.94 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1205,b,1184,b)].
% 12.79/12.94 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1205,b,1185,b)].
% 12.79/12.94 1206 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1150,a,1113,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1206,b,1166,a)].
% 12.79/12.94 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1206,b,1167,a)].
% 12.79/12.94 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(1206,b,1168,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1206,b,1169,b)].
% 12.79/12.94 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1206,b,1177,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1206,b,1178,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1206,b,1179,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1206,b,1180,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1206,b,1181,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1206,b,1182,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1206,b,1183,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1206,b,1185,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1206,b,1186,b)].
% 12.97/13.10 1207 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1151,a,1113,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1207,b,1166,a)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1207,b,1167,a)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(1207,b,1168,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1207,b,1169,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1207,b,1177,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1207,b,1178,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1207,b,1179,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1207,b,1180,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1207,b,1181,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1207,b,1182,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1207,b,1183,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1207,b,1185,b)].
% 12.97/13.10 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1207,b,1186,b)].
% 12.97/13.10 1208 class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__0(A). [resolve(1152,a,1113,b)].
% 12.97/13.10 Derived: class_HOL_Oplus(tc_IntDef_Oint). [resolve(1208,b,1166,a)].
% 12.97/13.10 Derived: class_HOL_Oplus(tc_nat). [resolve(1208,b,1167,a)].
% 12.97/13.10 Derived: class_HOL_Oplus(A) | -class_Power_Orecpower(A). [resolve(1208,b,1168,b)].
% 12.97/13.10 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1208,b,1169,b)].
% 12.97/13.10 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1208,b,1178,b)].
% 12.97/13.10 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Ofield(A). [resolve(1208,b,1179,b)].
% 12.97/13.10 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oidom(A). [resolve(1208,b,1180,b)].
% 12.97/13.10 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1208,b,1182,b)].
% 12.97/13.10 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1208,b,1183,b)].
% 12.97/13.10 Derived: class_HOL_Oplus(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1208,b,1185,b)].
% 12.97/13.10 1209 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) # label(axiom). [assumption].
% 12.97/13.10 1210 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_16) # label(axiom). [assumption].
% 12.97/13.10 1211 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_28) # label(axiom). [assumption].
% 12.97/13.12 1212 -class_OrderedGroup_Oab__group__add(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_OrderedGroup_Oab__group__add_6) # label(axiom). [assumption].
% 12.97/13.12 1213 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) # label(axiom). [assumption].
% 12.97/13.12 1214 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # label(clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) # label(axiom). [assumption].
% 12.97/13.12 1215 -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].
% 12.97/13.12 1216 -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].
% 12.97/13.12 1217 -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].
% 12.97/13.12 1218 -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].
% 12.97/13.12 1219 -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].
% 12.97/13.12 Derived: -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1219,b,1209,a)].
% 12.97/13.12 1220 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Power_Orecpower_20) # label(axiom). [assumption].
% 12.97/13.12 1221 -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].
% 12.97/13.12 1222 -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].
% 12.97/13.12 1223 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ofield_25) # label(axiom). [assumption].
% 12.97/13.12 1224 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_25) # label(axiom). [assumption].
% 12.97/13.12 1225 -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].
% 12.97/13.12 1226 -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].
% 12.97/13.12 1227 -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].
% 12.97/13.12 1228 -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].
% 12.97/13.12 1229 -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].
% 12.97/13.12 1230 -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].
% 12.97/13.12 1231 -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].
% 12.97/13.12 1232 -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].
% 13.14/13.34 1233 -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].
% 13.14/13.34 1234 -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].
% 13.14/13.34 1235 -class_Ring__and__Field_Oring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring_10) # label(axiom). [assumption].
% 13.14/13.34 1236 -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].
% 13.14/13.34 1237 -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].
% 13.14/13.34 1238 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(150,a,74,a)].
% 13.14/13.34 1239 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(226,b,202,a)].
% 13.14/13.34 1240 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(228,a,202,a)].
% 13.14/13.34 1241 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat). [resolve(252,a,240,a)].
% 13.14/13.34 1242 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(252,a,241,b)].
% 13.14/13.34 1243 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(265,b,252,a)].
% 13.14/13.34 1244 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(266,b,252,a)].
% 13.14/13.34 1245 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(268,b,252,a)].
% 13.14/13.34 1246 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(271,a,252,a)].
% 13.14/13.34 1247 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(635,b,634,a)].
% 13.14/13.34 1248 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(708,a,700,b)].
% 13.14/13.34 Derived: -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1248,a,1209,a)].
% 13.14/13.34 1249 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(708,a,701,b)].
% 13.14/13.34 Derived: -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1249,a,1209,a)].
% 13.14/13.34 1250 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(708,a,702,b)].
% 13.14/13.34 1251 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(708,a,703,b)].
% 13.14/13.34 1252 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(720,a,708,a)].
% 13.14/13.34 1253 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat). [resolve(721,a,708,a)].
% 13.14/13.34 1254 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(722,a,708,a)].
% 13.14/13.34 1255 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(723,a,708,a)].
% 13.14/13.34 1256 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(724,b,708,a)].
% 13.14/13.34 1257 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(730,b,726,a)].
% 13.14/13.34 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oab__group__add(C). [resolve(1257,a,1212,b)].
% 13.14/13.34 1258 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(730,b,727,a)].
% 13.14/13.34 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oab__group__add(C). [resolve(1258,a,1212,b)].
% 13.14/13.34 1259 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(731,a,730,b)].
% 13.14/13.34 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(1259,b,1212,b)].
% 14.06/14.24 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1259,b,1217,b)].
% 14.06/14.24 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1259,b,1218,b)].
% 14.06/14.24 1260 class_HOL_Oplus(A) | -class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(732,a,730,b)].
% 14.06/14.24 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oab__group__add(A). [resolve(1260,b,1212,b)].
% 14.06/14.24 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1260,b,1217,b)].
% 14.06/14.24 Derived: class_HOL_Oplus(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1260,b,1218,b)].
% 14.06/14.24 1261 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(839,b,814,b)].
% 14.06/14.24 1262 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(995,a,971,b)].
% 14.06/14.24 1263 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(995,a,972,b)].
% 14.06/14.24 1264 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(995,a,976,b)].
% 14.06/14.24 1265 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(995,a,980,b)].
% 14.06/14.24 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1265,a,1209,a)].
% 14.06/14.24 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1265,a,1213,a)].
% 14.06/14.24 Derived: -class_Ring__and__Field_Oordered__semiring__strict(A) | class_HOL_Oplus(A). [resolve(1265,a,1214,a)].
% 14.06/14.24 1266 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(995,a,981,b)].
% 14.06/14.24 1267 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(995,a,982,b)].
% 14.06/14.24 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1267,a,1209,a)].
% 14.06/14.24 Derived: -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1267,a,1213,a)].
% 14.06/14.24 1268 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(995,a,983,b)].
% 14.06/14.24 1269 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(995,a,984,b)].
% 14.06/14.24 1270 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oring(A). [resolve(995,a,985,b)].
% 14.06/14.24 1271 class_OrderedGroup_Ocancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(995,a,986,b)].
% 14.06/14.24 Derived: -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1271,a,1209,a)].
% 14.06/14.24 1272 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(996,b,995,a)].
% 14.06/14.24 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1272,b,1257,a)].
% 14.06/14.24 Derived: -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1272,b,1258,a)].
% 14.06/14.24 1273 -class_Power_Orecpower(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(1001,a,995,a)].
% 14.06/14.24 1274 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(1002,b,995,a)].
% 14.06/14.24 1275 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A). [resolve(1003,b,995,a)].
% 14.06/14.24 1276 -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].
% 14.06/14.24 1277 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_20) # label(axiom). [assumption].
% 14.06/14.24 1278 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) # label(clsarity_nat_31) # label(axiom). [assumption].
% 14.37/14.53 1279 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A) # label(clsrel_Power_Orecpower_23) # label(axiom). [assumption].
% 14.37/14.53 1280 -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].
% 14.37/14.53 1281 -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].
% 14.37/14.53 1282 -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].
% 14.37/14.53 1283 -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].
% 14.37/14.53 1284 -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].
% 14.37/14.53 1285 -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].
% 14.37/14.53 1286 -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].
% 14.37/14.53 1287 -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].
% 14.37/14.53 1288 -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].
% 14.37/14.53 1289 -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].
% 14.37/14.53 1290 -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].
% 14.37/14.53 1291 -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].
% 14.37/14.53 1292 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint). [resolve(154,a,74,a)].
% 14.37/14.53 1293 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(226,b,218,a)].
% 14.37/14.53 1294 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint). [resolve(228,a,218,a)].
% 14.37/14.53 1295 class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat). [resolve(257,a,240,a)].
% 14.37/14.53 1296 class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | -class_Power_Orecpower(A). [resolve(257,a,241,b)].
% 14.37/14.53 1297 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(265,b,257,a)].
% 14.37/14.53 1298 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(266,b,257,a)].
% 14.37/14.53 1299 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(268,b,257,a)].
% 14.37/14.53 1300 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,c_0,A) = B. [resolve(657,b,642,a)].
% 14.37/14.53 1301 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(c_0,B,A) = B. [resolve(657,b,643,a)].
% 14.37/14.53 1302 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(657,b,646,a)].
% 14.37/14.53 1303 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(741,b,726,a)].
% 14.37/14.53 1304 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(741,b,727,a)].
% 14.37/14.53 1305 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(972,b,967,a)].
% 14.37/14.53 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1305,a,1277,a)].
% 14.37/14.53 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(1305,a,1278,a)].
% 14.52/14.66 Derived: c_times(c_0,A,B) = c_0 | -class_Power_Orecpower(B). [resolve(1305,a,1279,b)].
% 14.52/14.66 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1305,a,1280,b)].
% 14.52/14.66 1306 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(972,b,968,a)].
% 14.52/14.66 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1306,a,1277,a)].
% 14.52/14.66 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(1306,a,1278,a)].
% 14.52/14.66 Derived: c_times(A,c_0,B) = c_0 | -class_Power_Orecpower(B). [resolve(1306,a,1279,b)].
% 14.52/14.66 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1306,a,1280,b)].
% 14.52/14.66 1307 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(988,a,972,b)].
% 14.52/14.66 1308 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(989,a,972,b)].
% 14.52/14.66 1309 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(990,a,972,b)].
% 14.52/14.66 1310 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(991,a,972,b)].
% 14.52/14.66 1311 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(992,a,972,b)].
% 14.52/14.66 1312 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(1005,a,972,b)].
% 14.52/14.66 1313 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(1006,a,972,b)].
% 14.52/14.66 1314 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(1007,a,972,b)].
% 14.52/14.66 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1314,c,1277,a)].
% 14.52/14.66 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1314,c,1278,a)].
% 14.52/14.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Power_Orecpower(C). [resolve(1314,c,1279,b)].
% 14.52/14.66 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(1314,c,1280,b)].
% 14.52/14.66 1315 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__semiring__0__cancel(C). [resolve(1008,a,972,b)].
% 14.52/14.66 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1315,c,1277,a)].
% 14.52/14.66 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1315,c,1278,a)].
% 14.52/14.66 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Power_Orecpower(C). [resolve(1315,c,1279,b)].
% 14.52/14.66 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(1315,c,1280,b)].
% 14.52/14.66 1316 -class_Ring__and__Field_Ocomm__semiring__0__cancel(A) | class_HOL_Ozero(A). [resolve(1154,a,1137,a)].
% 14.52/14.66 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1316,a,1280,b)].
% 14.52/14.66 1317 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1200,b,1177,b)].
% 14.52/14.66 Derived: class_Ring__and__Field_Osemiring(tc_IntDef_Oint). [resolve(1317,b,1277,a)].
% 14.52/14.66 Derived: class_Ring__and__Field_Osemiring(tc_nat). [resolve(1317,b,1278,a)].
% 14.52/14.66 Derived: class_Ring__and__Field_Osemiring(A) | -class_Power_Orecpower(A). [resolve(1317,b,1279,b)].
% 14.52/14.66 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1317,b,1280,b)].
% 14.52/14.66 1318 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1201,b,1177,b)].
% 14.52/14.66 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1318,b,1277,a)].
% 14.52/14.66 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(1318,b,1278,a)].
% 14.52/14.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Power_Orecpower(A). [resolve(1318,b,1279,b)].
% 14.52/14.66 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1318,b,1280,b)].
% 14.52/14.66 1319 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1202,b,1177,b)].
% 14.52/14.66 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(1319,b,1277,a)].
% 14.52/14.66 Derived: class_HOL_Otimes(tc_nat). [resolve(1319,b,1278,a)].
% 14.52/14.66 Derived: class_HOL_Otimes(A) | -class_Power_Orecpower(A). [resolve(1319,b,1279,b)].
% 14.67/14.81 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1319,b,1280,b)].
% 14.67/14.81 1320 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(1204,b,1177,b)].
% 14.67/14.81 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(1320,b,1277,a)].
% 14.67/14.81 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(1320,b,1278,a)].
% 14.67/14.81 Derived: c_plus(A,c_0,B) = A | -class_Power_Orecpower(B). [resolve(1320,b,1279,b)].
% 14.67/14.81 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1320,b,1280,b)].
% 14.67/14.81 1321 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__0__cancel(B). [resolve(1205,b,1177,b)].
% 14.67/14.81 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(1321,b,1277,a)].
% 14.67/14.81 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(1321,b,1278,a)].
% 14.67/14.81 Derived: c_plus(c_0,A,B) = A | -class_Power_Orecpower(B). [resolve(1321,b,1279,b)].
% 14.67/14.81 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1321,b,1280,b)].
% 14.67/14.81 1322 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1206,b,1177,b)].
% 14.67/14.81 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1322,b,1277,a)].
% 14.67/14.81 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1322,b,1278,a)].
% 14.67/14.81 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Power_Orecpower(A). [resolve(1322,b,1279,b)].
% 14.67/14.81 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1322,b,1280,b)].
% 14.67/14.81 1323 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__0__cancel(A). [resolve(1207,b,1177,b)].
% 14.67/14.81 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1323,b,1277,a)].
% 14.67/14.81 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(1323,b,1278,a)].
% 14.67/14.81 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Power_Orecpower(A). [resolve(1323,b,1279,b)].
% 14.67/14.81 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1323,b,1280,b)].
% 14.67/14.81 1324 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__ring_11) # label(axiom). [assumption].
% 14.67/14.81 1325 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_21) # label(axiom). [assumption].
% 14.67/14.81 1326 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_12) # label(axiom). [assumption].
% 14.67/14.81 1327 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_16) # label(axiom). [assumption].
% 14.67/14.81 1328 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_2) # label(axiom). [assumption].
% 14.67/14.81 1329 -class_Ring__and__Field_Ocomm__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Ocomm__ring_4) # label(axiom). [assumption].
% 14.67/14.81 1330 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Ocomm__ring_5) # label(axiom). [assumption].
% 14.67/14.81 1331 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__ring_6) # label(axiom). [assumption].
% 14.67/14.81 1332 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_8) # label(axiom). [assumption].
% 14.67/14.81 1333 -class_Ring__and__Field_Ocomm__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Ocomm__ring_9) # label(axiom). [assumption].
% 14.67/14.81 1334 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Ofield_1) # label(axiom). [assumption].
% 14.67/14.81 1335 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__ring(A) # label(clsrel_Ring__and__Field_Oidom_1) # label(axiom). [assumption].
% 14.67/14.81 1336 -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].
% 14.67/14.81 1337 -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].
% 15.09/15.21 1338 -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].
% 15.09/15.21 1339 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint). [resolve(155,a,74,a)].
% 15.09/15.21 1340 class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint). [resolve(228,a,195,a)].
% 15.09/15.21 1341 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,c_0,A) = B. [resolve(655,b,642,a)].
% 15.09/15.21 1342 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(c_0,B,A) = B. [resolve(655,b,643,a)].
% 15.09/15.21 1343 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(655,b,646,a)].
% 15.09/15.21 1344 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(740,b,726,a)].
% 15.09/15.21 1345 -class_Ring__and__Field_Ocomm__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(740,b,727,a)].
% 15.09/15.21 1346 -class_Ring__and__Field_Ocomm__ring(A) | c_times(c_0,B,A) = c_0. [resolve(971,b,967,a)].
% 15.09/15.21 1347 -class_Ring__and__Field_Ocomm__ring(A) | c_times(B,c_0,A) = c_0. [resolve(971,b,968,a)].
% 15.09/15.21 1348 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(988,a,971,b)].
% 15.09/15.21 1349 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(989,a,971,b)].
% 15.09/15.21 1350 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(990,a,971,b)].
% 15.09/15.21 1351 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(991,a,971,b)].
% 15.09/15.21 1352 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(992,a,971,b)].
% 15.09/15.21 1353 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1005,a,971,b)].
% 15.09/15.21 1354 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1006,a,971,b)].
% 15.09/15.21 1355 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(1007,a,971,b)].
% 15.09/15.21 1356 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(1008,a,971,b)].
% 15.09/15.21 1357 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1085,a,1082,b)].
% 15.09/15.21 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(1357,b,1325,a)].
% 15.09/15.21 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(1357,b,1334,b)].
% 15.09/15.21 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(1357,b,1335,b)].
% 15.09/15.21 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1357,b,1336,b)].
% 15.09/15.21 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1357,b,1337,b)].
% 15.09/15.21 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1357,b,1338,b)].
% 15.09/15.21 1358 -class_Ring__and__Field_Ocomm__ring(A) | class_HOL_Ozero(A). [resolve(1153,a,1137,a)].
% 15.09/15.21 1359 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1200,b,1169,b)].
% 15.09/15.21 1360 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1201,b,1169,b)].
% 15.09/15.21 1361 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1202,b,1169,b)].
% 15.09/15.21 1362 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1204,b,1169,b)].
% 15.09/15.21 1363 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1205,b,1169,b)].
% 15.09/15.21 1364 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1206,b,1169,b)].
% 15.09/15.21 1365 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1207,b,1169,b)].
% 15.09/15.21 1366 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1305,a,1280,b)].
% 15.09/15.21 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1366,b,1325,a)].
% 15.09/15.21 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(1366,b,1334,b)].
% 15.09/15.21 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(1366,b,1335,b)].
% 15.09/15.21 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(1366,b,1336,b)].
% 15.09/15.21 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1366,b,1337,b)].
% 15.09/15.21 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1366,b,1338,b)].
% 15.09/15.21 1367 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1306,a,1280,b)].
% 15.09/15.21 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1367,b,1325,a)].
% 15.09/15.21 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(1367,b,1334,b)].
% 15.09/15.21 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(1367,b,1335,b)].
% 15.09/15.21 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(1367,b,1336,b)].
% 15.09/15.21 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1367,b,1337,b)].
% 15.09/15.21 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1367,b,1338,b)].
% 15.09/15.21 1368 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(1314,c,1280,b)].
% 15.09/15.21 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1368,c,1325,a)].
% 15.09/15.21 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(1368,c,1334,b)].
% 15.09/15.21 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(1368,c,1335,b)].
% 15.09/15.21 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1368,c,1336,b)].
% 15.09/15.21 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1368,c,1337,b)].
% 15.09/15.21 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1368,c,1338,b)].
% 15.09/15.21 1369 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ocomm__ring(C). [resolve(1315,c,1280,b)].
% 15.09/15.21 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1369,c,1325,a)].
% 15.09/15.21 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(1369,c,1334,b)].
% 15.09/15.21 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(1369,c,1335,b)].
% 15.09/15.21 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1369,c,1336,b)].
% 15.09/15.21 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1369,c,1337,b)].
% 15.09/15.21 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1369,c,1338,b)].
% 15.09/15.21 1370 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1316,a,1280,b)].
% 15.09/15.21 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1370,b,1325,a)].
% 15.09/15.21 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(1370,b,1334,b)].
% 15.09/15.21 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(1370,b,1335,b)].
% 15.09/15.21 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1370,b,1336,b)].
% 15.09/15.21 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1370,b,1337,b)].
% 15.09/15.21 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1370,b,1338,b)].
% 15.09/15.21 1371 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1317,b,1280,b)].
% 15.09/15.21 Derived: class_Ring__and__Field_Osemiring(tc_IntDef_Oint). [resolve(1371,b,1325,a)].
% 15.09/15.21 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ofield(A). [resolve(1371,b,1334,b)].
% 15.09/15.21 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oidom(A). [resolve(1371,b,1335,b)].
% 15.09/15.21 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1371,b,1336,b)].
% 15.09/15.21 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1371,b,1337,b)].
% 15.09/15.21 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1371,b,1338,b)].
% 15.09/15.21 1372 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1318,b,1280,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(1372,b,1325,a)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(1372,b,1334,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(1372,b,1335,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1372,b,1336,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1372,b,1337,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1372,b,1338,b)].
% 15.09/15.22 1373 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1319,b,1280,b)].
% 15.09/15.22 Derived: class_HOL_Otimes(tc_IntDef_Oint). [resolve(1373,b,1325,a)].
% 15.09/15.22 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Ofield(A). [resolve(1373,b,1334,b)].
% 15.09/15.22 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oidom(A). [resolve(1373,b,1335,b)].
% 15.09/15.22 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1373,b,1336,b)].
% 15.09/15.22 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1373,b,1337,b)].
% 15.09/15.22 Derived: class_HOL_Otimes(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1373,b,1338,b)].
% 15.09/15.22 1374 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1320,b,1280,b)].
% 15.09/15.22 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(1374,b,1325,a)].
% 15.09/15.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(1374,b,1334,b)].
% 15.09/15.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1374,b,1335,b)].
% 15.09/15.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1374,b,1336,b)].
% 15.09/15.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1374,b,1337,b)].
% 15.09/15.22 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1374,b,1338,b)].
% 15.09/15.22 1375 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__ring(B). [resolve(1321,b,1280,b)].
% 15.09/15.22 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(1375,b,1325,a)].
% 15.09/15.22 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(1375,b,1334,b)].
% 15.09/15.22 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1375,b,1335,b)].
% 15.09/15.22 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1375,b,1336,b)].
% 15.09/15.22 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1375,b,1337,b)].
% 15.09/15.22 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1375,b,1338,b)].
% 15.09/15.22 1376 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1322,b,1280,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1376,b,1325,a)].
% 15.09/15.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1376,b,1334,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1376,b,1335,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1376,b,1336,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1376,b,1337,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1376,b,1338,b)].
% 15.09/15.22 1377 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__ring(A). [resolve(1323,b,1280,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(1377,b,1325,a)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1377,b,1334,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1377,b,1335,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1377,b,1336,b)].
% 15.09/15.22 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1377,b,1337,b)].
% 15.40/15.51 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(1377,b,1338,b)].
% 15.40/15.51 1378 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_1) # label(axiom). [assumption].
% 15.40/15.51 1379 class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_24) # label(axiom). [assumption].
% 15.40/15.51 1380 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat_24) # label(axiom). [assumption].
% 15.40/15.51 1381 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_2) # label(axiom). [assumption].
% 15.40/15.51 1382 -class_OrderedGroup_Ocomm__monoid__mult(A) | class_HOL_Otimes(A) # label(clsrel_OrderedGroup_Ocomm__monoid__mult_3) # label(axiom). [assumption].
% 15.40/15.51 1383 -class_Power_Orecpower(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Power_Orecpower_16) # label(axiom). [assumption].
% 15.40/15.51 1384 -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].
% 15.40/15.51 1385 -class_Ring__and__Field_Ofield(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Ofield_8) # label(axiom). [assumption].
% 15.40/15.51 1386 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oidom_8) # label(axiom). [assumption].
% 15.40/15.51 1387 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__field_11) # label(axiom). [assumption].
% 15.40/15.51 1388 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocomm__monoid__mult(A) # label(clsrel_Ring__and__Field_Oordered__idom_8) # label(axiom). [assumption].
% 15.40/15.51 1389 class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(160,a,74,a)].
% 15.40/15.51 1390 -class_Ring__and__Field_Oordered__field(A) | class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(226,b,209,a)].
% 15.40/15.51 1391 class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(228,a,209,a)].
% 15.40/15.51 1392 class_OrderedGroup_Ocomm__monoid__mult(tc_nat). [resolve(258,a,240,a)].
% 15.40/15.51 1393 class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Power_Orecpower(A). [resolve(258,a,241,b)].
% 15.40/15.51 1394 class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint). [resolve(271,a,258,a)].
% 15.40/15.51 1395 class_OrderedGroup_Ocomm__monoid__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(357,a,345,b)].
% 15.40/15.51 1396 -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(581,b,570,a)].
% 15.40/15.51 1397 -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(581,b,571,a)].
% 15.40/15.51 1398 -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(581,b,572,a)].
% 15.40/15.51 1399 -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(581,b,573,a)].
% 15.40/15.51 1400 -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(581,b,574,a)].
% 15.40/15.51 1401 -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(581,b,575,a)].
% 15.40/15.51 1402 -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(581,b,576,a)].
% 15.40/15.51 1403 -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(581,b,577,a)].
% 15.40/15.51 1404 -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(581,b,578,a)].
% 15.44/15.60 1405 -class_OrderedGroup_Ocomm__monoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(581,b,579,a)].
% 15.44/15.60 1406 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(c_1,B,A) = B. [resolve(848,b,845,a)].
% 15.44/15.60 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(1406,a,1379,a)].
% 15.44/15.60 Derived: c_times(c_1,A,tc_nat) = A. [resolve(1406,a,1380,a)].
% 15.44/15.60 1407 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_times(B,c_1,A) = B. [resolve(848,b,846,a)].
% 15.44/15.60 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(1407,a,1379,a)].
% 15.44/15.60 Derived: c_times(A,c_1,tc_nat) = A. [resolve(1407,a,1380,a)].
% 15.44/15.60 1408 class_OrderedGroup_Osemigroup__mult(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(849,a,848,b)].
% 15.44/15.60 1409 class_HOL_Otimes(A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(850,a,848,b)].
% 15.44/15.60 1410 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(869,a,848,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_1 | A = c_uminus(c_1,tc_IntDef_Oint). [resolve(1410,d,1379,a)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(A,tc_nat) != c_1 | A = c_uminus(c_1,tc_nat). [resolve(1410,d,1380,a)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1410,d,1384,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(1410,d,1385,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1410,d,1386,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1410,d,1387,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1410,d,1388,b)].
% 15.44/15.60 1411 -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(870,a,848,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) = c_1. [resolve(1411,c,1379,a)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(c_uminus(c_1,tc_nat),tc_nat) = c_1. [resolve(1411,c,1380,a)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1411,c,1384,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(1411,c,1385,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(1411,c,1386,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(1411,c,1387,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(1411,c,1388,b)].
% 15.44/15.60 1412 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(871,a,848,b)].
% 15.44/15.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1412,d,1379,a)].
% 15.44/15.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat) | c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(1412,d,1380,a)].
% 15.44/15.60 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1412,d,1384,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(1412,d,1385,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1412,d,1386,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1412,d,1387,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1412,d,1388,b)].
% 15.44/15.61 1413 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(872,a,848,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1413,d,1379,a)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat) | c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(1413,d,1380,a)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1413,d,1384,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(1413,d,1385,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1413,d,1386,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1413,d,1387,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1413,d,1388,b)].
% 15.44/15.61 1414 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(873,a,848,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1414,d,1379,a)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_1,c_uminus(A,tc_nat),tc_nat) | c_less(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(1414,d,1380,a)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1414,d,1384,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(1414,d,1385,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1414,d,1386,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1414,d,1387,b)].
% 15.44/15.61 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1414,d,1388,b)].
% 15.44/15.62 1415 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(874,a,848,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1415,d,1379,a)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_uminus(c_1,tc_nat),tc_nat) | c_less(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(1415,d,1380,a)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1415,d,1384,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(1415,d,1385,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1415,d,1386,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1415,d,1387,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1415,d,1388,b)].
% 15.44/15.62 1416 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(875,a,848,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(1416,d,1379,a)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat) | c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(1416,d,1380,a)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1416,d,1384,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(1416,d,1385,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(1416,d,1386,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1416,d,1387,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1416,d,1388,b)].
% 15.44/15.62 1417 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(876,a,848,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(1417,d,1379,a)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat) | c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(1417,d,1380,a)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1417,d,1384,b)].
% 15.44/15.62 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(1417,d,1385,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1417,d,1386,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1417,d,1387,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1417,d,1388,b)].
% 15.84/15.95 1418 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(877,a,848,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(1418,d,1379,a)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(A,tc_nat),c_1,tc_nat) | c_less(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(1418,d,1380,a)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1418,d,1384,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(1418,d,1385,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(1418,d,1386,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1418,d,1387,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1418,d,1388,b)].
% 15.84/15.95 1419 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_OrderedGroup_Ocomm__monoid__mult(A). [resolve(878,a,848,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(1419,d,1379,a)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(c_1,tc_nat),A,tc_nat) | c_less(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(1419,d,1380,a)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1419,d,1384,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(1419,d,1385,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1419,d,1386,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1419,d,1387,b)].
% 15.84/15.95 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1419,d,1388,b)].
% 15.84/15.95 1420 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1_1) # label(axiom). [assumption].
% 15.84/15.95 1421 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_25) # label(axiom). [assumption].
% 15.84/15.95 1422 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat_25) # label(axiom). [assumption].
% 15.84/15.95 1423 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Power_Orecpower_17) # label(axiom). [assumption].
% 15.97/16.12 1424 -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].
% 15.97/16.12 1425 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Ofield_10) # label(axiom). [assumption].
% 15.97/16.12 1426 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A) # label(clsrel_Ring__and__Field_Oidom_10) # label(axiom). [assumption].
% 15.97/16.12 1427 -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].
% 15.97/16.12 1428 -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].
% 15.97/16.12 1429 -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].
% 15.97/16.12 1430 -class_Ring__and__Field_Osemiring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Osemiring__1_4) # label(axiom). [assumption].
% 15.97/16.12 1431 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Osemiring__1_5) # label(axiom). [assumption].
% 15.97/16.12 1432 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1_6) # label(axiom). [assumption].
% 15.97/16.12 1433 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_8) # label(axiom). [assumption].
% 15.97/16.12 1434 -class_Ring__and__Field_Osemiring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Osemiring__1_9) # label(axiom). [assumption].
% 15.97/16.12 1435 -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].
% 15.97/16.12 1436 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint). [resolve(161,a,74,a)].
% 15.97/16.12 1437 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__1(A). [resolve(226,b,210,a)].
% 15.97/16.12 1438 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint). [resolve(228,a,210,a)].
% 15.97/16.12 1439 class_Ring__and__Field_Osemiring__1(tc_nat). [resolve(260,a,240,a)].
% 15.97/16.12 1440 class_Ring__and__Field_Osemiring__1(A) | -class_Power_Orecpower(A). [resolve(260,a,241,b)].
% 15.97/16.12 1441 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1(A). [resolve(265,b,260,a)].
% 15.97/16.12 1442 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1(A). [resolve(266,b,260,a)].
% 15.97/16.12 1443 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Osemiring__1(A). [resolve(268,b,260,a)].
% 15.97/16.12 1444 class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint). [resolve(271,a,260,a)].
% 15.97/16.12 1445 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(591,b,570,a)].
% 15.97/16.12 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(1445,a,1429,b)].
% 15.97/16.12 1446 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(591,b,571,a)].
% 15.97/16.12 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Oring__1(A). [resolve(1446,a,1429,b)].
% 15.97/16.12 1447 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(591,b,572,a)].
% 15.97/16.12 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(1447,a,1429,b)].
% 15.97/16.12 1448 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(591,b,573,a)].
% 16.10/16.22 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(1448,a,1429,b)].
% 16.10/16.22 1449 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(591,b,574,a)].
% 16.10/16.22 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(1449,a,1429,b)].
% 16.10/16.22 1450 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(591,b,575,a)].
% 16.10/16.22 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(1450,a,1429,b)].
% 16.10/16.22 1451 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(591,b,576,a)].
% 16.10/16.22 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(1451,a,1429,b)].
% 16.10/16.22 1452 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(591,b,577,a)].
% 16.10/16.22 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(1452,a,1429,b)].
% 16.10/16.22 1453 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(591,b,578,a)].
% 16.10/16.22 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(1453,a,1429,b)].
% 16.10/16.22 1454 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(591,b,579,a)].
% 16.10/16.22 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(1454,a,1429,b)].
% 16.10/16.22 1455 -class_Ring__and__Field_Osemiring__1(A) | c_plus(B,c_0,A) = B. [resolve(677,b,642,a)].
% 16.10/16.22 1456 -class_Ring__and__Field_Osemiring__1(A) | c_plus(c_0,B,A) = B. [resolve(677,b,643,a)].
% 16.10/16.22 1457 -class_Ring__and__Field_Osemiring__1(A) | class_HOL_Ozero(A). [resolve(677,b,646,a)].
% 16.10/16.22 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(1457,a,1435,b)].
% 16.10/16.22 1458 -class_Ring__and__Field_Osemiring__1(A) | c_times(c_1,B,A) = B. [resolve(858,b,845,a)].
% 16.10/16.22 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(1458,a,1423,b)].
% 16.10/16.22 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(1458,a,1424,b)].
% 16.10/16.22 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(1458,a,1425,b)].
% 16.10/16.22 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1458,a,1426,b)].
% 16.10/16.22 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1458,a,1427,b)].
% 16.10/16.22 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1458,a,1428,b)].
% 16.10/16.22 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(1458,a,1429,b)].
% 16.10/16.22 1459 -class_Ring__and__Field_Osemiring__1(A) | c_times(B,c_1,A) = B. [resolve(858,b,846,a)].
% 16.10/16.22 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(1459,a,1423,b)].
% 16.10/16.22 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(1459,a,1424,b)].
% 16.10/16.22 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(1459,a,1425,b)].
% 16.10/16.22 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1459,a,1426,b)].
% 16.56/16.69 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1459,a,1427,b)].
% 16.56/16.69 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1459,a,1428,b)].
% 16.56/16.69 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(1459,a,1429,b)].
% 16.56/16.69 1460 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(1150,a,1138,b)].
% 16.56/16.69 1461 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1(A). [resolve(1151,a,1138,b)].
% 16.56/16.69 1462 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_1) # label(axiom). [assumption].
% 16.56/16.69 1463 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_26) # label(axiom). [assumption].
% 16.56/16.69 1464 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat_26) # label(axiom). [assumption].
% 16.56/16.69 1465 -class_Power_Orecpower(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Power_Orecpower_18) # label(axiom). [assumption].
% 16.56/16.69 1466 -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].
% 16.56/16.69 1467 -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].
% 16.56/16.69 1468 -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].
% 16.56/16.69 1469 -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].
% 16.56/16.69 1470 -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].
% 16.56/16.69 1471 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Ocomm__semiring__1_9) # label(axiom). [assumption].
% 16.56/16.69 1472 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Ofield_7) # label(axiom). [assumption].
% 16.56/16.69 1473 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsrel_Ring__and__Field_Oidom_7) # label(axiom). [assumption].
% 16.56/16.69 1474 -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].
% 16.56/16.69 1475 -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].
% 16.56/16.69 1476 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint). [resolve(162,a,74,a)].
% 16.56/16.69 1477 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(226,b,208,a)].
% 16.56/16.69 1478 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint). [resolve(228,a,208,a)].
% 16.56/16.69 1479 class_Ring__and__Field_Ocomm__semiring__1(tc_nat). [resolve(242,a,240,a)].
% 16.56/16.69 1480 class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Power_Orecpower(A). [resolve(242,a,241,b)].
% 16.56/16.69 1481 class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint). [resolve(271,a,242,a)].
% 16.56/16.69 1482 class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(346,a,345,b)].
% 16.56/16.69 1483 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(585,b,570,a)].
% 16.56/16.69 1484 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(585,b,571,a)].
% 16.56/16.69 1485 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(585,b,572,a)].
% 16.56/16.69 1486 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(585,b,573,a)].
% 16.85/16.95 1487 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(585,b,574,a)].
% 16.85/16.95 1488 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(585,b,575,a)].
% 16.85/16.95 1489 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(585,b,576,a)].
% 16.85/16.95 1490 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(585,b,577,a)].
% 16.85/16.95 1491 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(585,b,578,a)].
% 16.85/16.95 1492 -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(585,b,579,a)].
% 16.85/16.95 1493 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_plus(B,c_0,A) = B. [resolve(658,b,642,a)].
% 16.85/16.95 1494 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_plus(c_0,B,A) = B. [resolve(658,b,643,a)].
% 16.85/16.95 1495 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_HOL_Ozero(A). [resolve(658,b,646,a)].
% 16.85/16.95 1496 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(c_1,B,A) = B. [resolve(852,b,845,a)].
% 16.85/16.95 1497 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_times(B,c_1,A) = B. [resolve(852,b,846,a)].
% 16.85/16.95 1498 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1091,b,1078,a)].
% 16.85/16.95 1499 -class_Ring__and__Field_Ocomm__semiring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1091,b,1083,a)].
% 16.85/16.95 1500 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1108,a,1115,b)].
% 16.85/16.95 1501 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1135,a,1115,b)].
% 16.85/16.95 1502 class_HOL_Otimes(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1136,a,1115,b)].
% 16.85/16.95 1503 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(1148,a,1115,b)].
% 16.85/16.95 1504 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(1149,a,1115,b)].
% 16.85/16.95 1505 class_HOL_Ozero(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1203,b,1178,b)].
% 16.85/16.95 Derived: class_HOL_Ozero(tc_nat). [resolve(1505,b,1464,a)].
% 16.85/16.95 Derived: class_HOL_Ozero(A) | -class_Power_Orecpower(A). [resolve(1505,b,1465,b)].
% 16.85/16.95 1506 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1206,b,1178,b)].
% 16.85/16.95 1507 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1207,b,1178,b)].
% 16.85/16.95 1508 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1410,d,1384,b)].
% 16.85/16.95 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_1 | A = c_uminus(c_1,tc_IntDef_Oint). [resolve(1508,d,1463,a)].
% 16.85/16.95 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(A,tc_nat) != c_1 | A = c_uminus(c_1,tc_nat). [resolve(1508,d,1464,a)].
% 16.85/16.95 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Power_Orecpower(A). [resolve(1508,d,1465,b)].
% 16.85/16.95 1509 -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1411,c,1384,b)].
% 16.85/16.95 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) = c_1. [resolve(1509,c,1463,a)].
% 16.85/16.95 Derived: -class_OrderedGroup_Oab__group__add(tc_nat) | c_uminus(c_uminus(c_1,tc_nat),tc_nat) = c_1. [resolve(1509,c,1464,a)].
% 16.85/16.95 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Power_Orecpower(A). [resolve(1509,c,1465,b)].
% 16.85/16.96 1510 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1412,d,1384,b)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1510,d,1463,a)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat) | c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(1510,d,1464,a)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(1510,d,1465,b)].
% 16.85/16.96 1511 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1413,d,1384,b)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1511,d,1463,a)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(A,c_uminus(c_1,tc_nat),tc_nat) | c_lessequals(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(1511,d,1464,a)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(1511,d,1465,b)].
% 16.85/16.96 1512 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1414,d,1384,b)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1512,d,1463,a)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_1,c_uminus(A,tc_nat),tc_nat) | c_less(A,c_uminus(c_1,tc_nat),tc_nat). [resolve(1512,d,1464,a)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Power_Orecpower(A). [resolve(1512,d,1465,b)].
% 16.85/16.96 1513 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1415,d,1384,b)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1513,d,1463,a)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_uminus(c_1,tc_nat),tc_nat) | c_less(c_1,c_uminus(A,tc_nat),tc_nat). [resolve(1513,d,1464,a)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Power_Orecpower(A). [resolve(1513,d,1465,b)].
% 16.85/16.96 1514 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1416,d,1384,b)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(1514,d,1463,a)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat) | c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(1514,d,1464,a)].
% 16.85/16.96 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(1514,d,1465,b)].
% 16.85/16.96 1515 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1417,d,1384,b)].
% 17.01/17.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(1515,d,1463,a)].
% 17.01/17.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_lessequals(c_uminus(c_1,tc_nat),A,tc_nat) | c_lessequals(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(1515,d,1464,a)].
% 17.01/17.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(1515,d,1465,b)].
% 17.01/17.11 1516 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1418,d,1384,b)].
% 17.01/17.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(1516,d,1463,a)].
% 17.01/17.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(A,tc_nat),c_1,tc_nat) | c_less(c_uminus(c_1,tc_nat),A,tc_nat). [resolve(1516,d,1464,a)].
% 17.01/17.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Power_Orecpower(A). [resolve(1516,d,1465,b)].
% 17.01/17.11 1517 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ocomm__semiring__1(A). [resolve(1419,d,1384,b)].
% 17.01/17.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(1517,d,1463,a)].
% 17.01/17.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_uminus(c_1,tc_nat),A,tc_nat) | c_less(c_uminus(A,tc_nat),c_1,tc_nat). [resolve(1517,d,1464,a)].
% 17.01/17.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Power_Orecpower(A). [resolve(1517,d,1465,b)].
% 17.01/17.11 1518 c_times(c_1,A,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(1458,a,1424,b)].
% 17.01/17.11 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(1518,b,1463,a)].
% 17.01/17.11 Derived: c_times(c_1,A,tc_nat) = A. [resolve(1518,b,1464,a)].
% 17.01/17.11 Derived: c_times(c_1,A,B) = A | -class_Power_Orecpower(B). [resolve(1518,b,1465,b)].
% 17.01/17.11 1519 c_times(A,c_1,B) = A | -class_Ring__and__Field_Ocomm__semiring__1(B). [resolve(1459,a,1424,b)].
% 17.01/17.11 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(1519,b,1463,a)].
% 17.01/17.11 Derived: c_times(A,c_1,tc_nat) = A. [resolve(1519,b,1464,a)].
% 17.01/17.11 Derived: c_times(A,c_1,B) = A | -class_Power_Orecpower(B). [resolve(1519,b,1465,b)].
% 17.01/17.11 1520 -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].
% 17.01/17.11 1521 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_27) # label(axiom). [assumption].
% 17.01/17.11 1522 class_Ring__and__Field_Osemiring__1__cancel(tc_nat) # label(clsarity_nat_30) # label(axiom). [assumption].
% 17.01/17.11 1523 -class_Power_Orecpower(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Power_Orecpower_22) # label(axiom). [assumption].
% 17.01/17.11 1524 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Ofield_9) # label(axiom). [assumption].
% 17.01/17.11 1525 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring__1__cancel(A) # label(clsrel_Ring__and__Field_Oidom_9) # label(axiom). [assumption].
% 17.01/17.11 1526 -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].
% 17.01/17.11 1527 -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].
% 17.19/17.33 1528 -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].
% 17.19/17.33 1529 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_12) # label(axiom). [assumption].
% 17.19/17.33 1530 -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].
% 17.19/17.33 1531 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Osemiring__1__cancel_5) # label(axiom). [assumption].
% 17.19/17.33 1532 -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].
% 17.19/17.33 1533 -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].
% 17.19/17.33 1534 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint). [resolve(163,a,74,a)].
% 17.19/17.33 1535 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(226,b,215,a)].
% 17.19/17.33 1536 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint). [resolve(228,a,215,a)].
% 17.19/17.33 1537 class_Ring__and__Field_Osemiring__1__cancel(tc_nat). [resolve(255,a,240,a)].
% 17.19/17.33 1538 class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Power_Orecpower(A). [resolve(255,a,241,b)].
% 17.19/17.33 1539 class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint). [resolve(271,a,255,a)].
% 17.19/17.33 1540 class_Ring__and__Field_Osemiring__1__cancel(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(366,a,345,b)].
% 17.19/17.33 1541 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(592,b,570,a)].
% 17.19/17.33 1542 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(592,b,571,a)].
% 17.19/17.33 1543 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(592,b,572,a)].
% 17.19/17.33 1544 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(592,b,573,a)].
% 17.19/17.33 1545 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(592,b,574,a)].
% 17.19/17.33 1546 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(592,b,575,a)].
% 17.19/17.33 1547 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(592,b,576,a)].
% 17.19/17.33 1548 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(592,b,577,a)].
% 17.19/17.33 1549 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(592,b,578,a)].
% 17.19/17.33 1550 -class_Ring__and__Field_Osemiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(592,b,579,a)].
% 17.19/17.33 1551 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,c_0,A) = B. [resolve(678,b,642,a)].
% 17.19/17.33 1552 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(c_0,B,A) = B. [resolve(678,b,643,a)].
% 17.19/17.33 1553 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(757,b,726,a)].
% 17.19/17.33 1554 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(757,b,727,a)].
% 17.56/17.69 1555 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_1,B,A) = B. [resolve(859,b,845,a)].
% 17.56/17.69 1556 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_1,A) = B. [resolve(859,b,846,a)].
% 17.56/17.69 1557 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(859,b,849,a)].
% 17.56/17.69 1558 -class_Ring__and__Field_Osemiring__1__cancel(A) | class_HOL_Otimes(A). [resolve(859,b,850,a)].
% 17.56/17.69 1559 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(c_0,B,A) = c_0. [resolve(996,b,967,a)].
% 17.56/17.69 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(1559,a,1528,b)].
% 17.56/17.69 1560 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_times(B,c_0,A) = c_0. [resolve(996,b,968,a)].
% 17.56/17.69 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(1560,a,1528,b)].
% 17.56/17.69 1561 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(1150,a,1139,b)].
% 17.56/17.69 1562 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(1151,a,1139,b)].
% 17.56/17.69 1563 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(1272,b,1257,a)].
% 17.56/17.69 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(1563,a,1528,b)].
% 17.56/17.69 1564 -class_Ring__and__Field_Osemiring__1__cancel(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(1272,b,1258,a)].
% 17.56/17.69 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(1564,a,1528,b)].
% 17.56/17.69 1565 class_HOL_Ozero(A) | -class_Ring__and__Field_Osemiring__1__cancel(A). [resolve(1457,a,1435,b)].
% 17.56/17.69 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1565,b,1521,a)].
% 17.56/17.69 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(1565,b,1524,b)].
% 17.56/17.69 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(1565,b,1525,b)].
% 17.56/17.69 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1565,b,1526,b)].
% 17.56/17.69 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1565,b,1527,b)].
% 17.56/17.69 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(1565,b,1528,b)].
% 17.56/17.69 1566 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oring__1_0) # label(axiom). [assumption].
% 17.56/17.69 1567 class_Ring__and__Field_Oring__1(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_28) # label(axiom). [assumption].
% 17.56/17.69 1568 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Ofield_2) # label(axiom). [assumption].
% 17.56/17.69 1569 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring__1(A) # label(clsrel_Ring__and__Field_Oidom_2) # label(axiom). [assumption].
% 17.56/17.69 1570 -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].
% 17.56/17.69 1571 -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].
% 17.56/17.69 Derived: class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Ofield(A). [resolve(1566,a,1568,b)].
% 17.56/17.69 Derived: class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Oidom(A). [resolve(1566,a,1569,b)].
% 17.56/17.69 Derived: class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1566,a,1570,b)].
% 17.56/17.69 Derived: class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1566,a,1571,b)].
% 17.56/17.69 1572 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oring__1_1) # label(axiom). [assumption].
% 17.56/17.69 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(1572,a,1568,b)].
% 17.56/17.69 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1572,a,1569,b)].
% 17.56/17.69 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1572,a,1570,b)].
% 17.56/17.69 1573 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_11) # label(axiom). [assumption].
% 17.85/17.96 1574 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oring__1_12) # label(axiom). [assumption].
% 17.85/17.96 1575 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A) # label(clsrel_Ring__and__Field_Oring__1_14) # label(axiom). [assumption].
% 17.85/17.96 1576 -class_Ring__and__Field_Oring__1(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oring__1_7) # label(axiom). [assumption].
% 17.85/17.96 1577 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oring__1_8) # label(axiom). [assumption].
% 17.85/17.96 1578 -class_Ring__and__Field_Oring__1(A) | class_HOL_Otimes(A) # label(clsrel_Ring__and__Field_Oring__1_9) # label(axiom). [assumption].
% 17.85/17.96 1579 class_Ring__and__Field_Oring__1(tc_IntDef_Oint). [resolve(164,a,74,a)].
% 17.85/17.96 1580 class_Ring__and__Field_Oring__1(tc_IntDef_Oint). [resolve(228,a,214,a)].
% 17.85/17.96 Derived: class_Ring__and__Field_Oring(tc_IntDef_Oint). [resolve(1580,a,1566,a)].
% 17.85/17.96 1581 -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(590,b,570,a)].
% 17.85/17.96 1582 -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(590,b,571,a)].
% 17.85/17.96 1583 -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(590,b,572,a)].
% 17.85/17.96 1584 -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(590,b,573,a)].
% 17.85/17.96 1585 -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(590,b,574,a)].
% 17.85/17.96 1586 -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(590,b,575,a)].
% 17.85/17.96 1587 -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(590,b,576,a)].
% 17.85/17.96 1588 -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(590,b,577,a)].
% 17.85/17.96 1589 -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(590,b,578,a)].
% 17.85/17.96 1590 -class_Ring__and__Field_Oring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(590,b,579,a)].
% 17.85/17.96 1591 -class_Ring__and__Field_Oring__1(A) | c_plus(B,c_0,A) = B. [resolve(674,b,642,a)].
% 17.85/17.96 1592 -class_Ring__and__Field_Oring__1(A) | c_plus(c_0,B,A) = B. [resolve(674,b,643,a)].
% 17.85/17.96 1593 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(755,b,726,a)].
% 17.85/17.96 1594 -class_Ring__and__Field_Oring__1(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(755,b,727,a)].
% 17.85/17.96 1595 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(755,b,731,a)].
% 17.85/17.96 1596 -class_Ring__and__Field_Oring__1(A) | c_times(c_1,B,A) = B. [resolve(857,b,845,a)].
% 17.85/17.96 1597 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_1,A) = B. [resolve(857,b,846,a)].
% 17.85/17.96 1598 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A). [resolve(944,b,938,a)].
% 17.85/17.96 1599 -class_Ring__and__Field_Oring__1(A) | c_times(c_0,B,A) = c_0. [resolve(986,b,967,a)].
% 17.85/17.96 1600 -class_Ring__and__Field_Oring__1(A) | c_times(B,c_0,A) = c_0. [resolve(986,b,968,a)].
% 17.85/17.96 1601 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oring__1(A). [resolve(988,a,986,b)].
% 17.85/17.96 1602 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oring__1(A). [resolve(989,a,986,b)].
% 17.85/17.96 1603 class_HOL_Otimes(A) | -class_Ring__and__Field_Oring__1(A). [resolve(990,a,986,b)].
% 17.94/18.10 1604 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oring__1(A). [resolve(991,a,986,b)].
% 17.94/18.10 1605 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(1005,a,986,b)].
% 17.94/18.10 1606 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(1006,a,986,b)].
% 17.94/18.10 1607 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(1007,a,986,b)].
% 17.94/18.10 1608 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(1008,a,986,b)].
% 17.94/18.10 1609 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1164,a,1133,a)].
% 17.94/18.10 1610 -class_Ring__and__Field_Oring__1(A) | class_HOL_Ozero(A). [resolve(1164,a,1137,a)].
% 17.94/18.10 1611 -class_Ring__and__Field_Oring__1(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1271,a,1209,a)].
% 17.94/18.10 1612 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(1445,a,1429,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(1612,d,1568,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1612,d,1569,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1612,d,1570,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1612,d,1571,b)].
% 17.94/18.10 1613 -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Oring__1(A). [resolve(1446,a,1429,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(1613,c,1568,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(1613,c,1569,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Oordered__field(A). [resolve(1613,c,1570,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Oordered__idom(A). [resolve(1613,c,1571,b)].
% 17.94/18.10 1614 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(1447,a,1429,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(1614,d,1568,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1614,d,1569,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1614,d,1570,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1614,d,1571,b)].
% 17.94/18.10 1615 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(1448,a,1429,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(1615,d,1568,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1615,d,1569,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1615,d,1570,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1615,d,1571,b)].
% 17.94/18.10 1616 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(1449,a,1429,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(1616,d,1568,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1616,d,1569,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1616,d,1570,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1616,d,1571,b)].
% 17.94/18.10 1617 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oring__1(A). [resolve(1450,a,1429,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(1617,d,1568,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1617,d,1569,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1617,d,1570,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1617,d,1571,b)].
% 17.94/18.10 1618 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(1451,a,1429,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(1618,d,1568,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(1618,d,1569,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1618,d,1570,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1618,d,1571,b)].
% 17.94/18.10 1619 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(1452,a,1429,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(1619,d,1568,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1619,d,1569,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1619,d,1570,b)].
% 17.94/18.10 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1619,d,1571,b)].
% 17.94/18.11 1620 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oring__1(A). [resolve(1453,a,1429,b)].
% 17.94/18.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(1620,d,1568,b)].
% 17.94/18.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(1620,d,1569,b)].
% 17.94/18.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1620,d,1570,b)].
% 17.94/18.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1620,d,1571,b)].
% 17.94/18.11 1621 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oring__1(A). [resolve(1454,a,1429,b)].
% 17.94/18.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(1621,d,1568,b)].
% 17.94/18.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1621,d,1569,b)].
% 17.94/18.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1621,d,1570,b)].
% 17.94/18.11 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1621,d,1571,b)].
% 17.94/18.11 1622 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(1458,a,1429,b)].
% 17.94/18.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(1622,b,1568,b)].
% 17.94/18.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1622,b,1569,b)].
% 17.94/18.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1622,b,1570,b)].
% 17.94/18.11 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1622,b,1571,b)].
% 17.94/18.11 1623 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oring__1(B). [resolve(1459,a,1429,b)].
% 17.94/18.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(1623,b,1568,b)].
% 17.94/18.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1623,b,1569,b)].
% 17.94/18.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(1623,b,1570,b)].
% 17.94/18.11 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(1623,b,1571,b)].
% 17.94/18.11 1624 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(1559,a,1528,b)].
% 17.94/18.11 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(1624,b,1567,a)].
% 17.94/18.11 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(1624,b,1568,b)].
% 17.94/18.11 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(1624,b,1569,b)].
% 17.94/18.11 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(1624,b,1570,b)].
% 17.94/18.11 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1624,b,1571,b)].
% 17.94/18.11 1625 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oring__1(B). [resolve(1560,a,1528,b)].
% 17.94/18.11 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(1625,b,1567,a)].
% 17.94/18.11 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(1625,b,1568,b)].
% 17.94/18.11 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(1625,b,1569,b)].
% 17.94/18.11 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(1625,b,1570,b)].
% 17.94/18.11 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(1625,b,1571,b)].
% 17.94/18.11 1626 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oring__1(C). [resolve(1563,a,1528,b)].
% 17.94/18.11 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1626,c,1567,a)].
% 18.69/18.85 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(1626,c,1568,b)].
% 18.69/18.85 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(1626,c,1569,b)].
% 18.69/18.85 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1626,c,1570,b)].
% 18.69/18.85 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1626,c,1571,b)].
% 18.69/18.85 1627 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oring__1(C). [resolve(1564,a,1528,b)].
% 18.69/18.85 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1627,c,1567,a)].
% 18.69/18.85 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(1627,c,1568,b)].
% 18.69/18.85 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(1627,c,1569,b)].
% 18.69/18.85 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1627,c,1570,b)].
% 18.69/18.85 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1627,c,1571,b)].
% 18.69/18.85 1628 class_HOL_Ozero(A) | -class_Ring__and__Field_Oring__1(A). [resolve(1565,b,1528,b)].
% 18.69/18.85 Derived: class_HOL_Ozero(tc_IntDef_Oint). [resolve(1628,b,1567,a)].
% 18.69/18.85 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Ofield(A). [resolve(1628,b,1568,b)].
% 18.69/18.85 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oidom(A). [resolve(1628,b,1569,b)].
% 18.69/18.85 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1628,b,1570,b)].
% 18.69/18.85 Derived: class_HOL_Ozero(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1628,b,1571,b)].
% 18.69/18.85 1629 -class_LOrder_Olorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(277,b,273,a)].
% 18.69/18.85 1630 class_LOrder_Olorder(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_34) # label(axiom). [assumption].
% 18.69/18.85 1631 class_LOrder_Olorder(tc_nat) # label(clsarity_nat_6) # label(axiom). [assumption].
% 18.69/18.85 1632 -class_OrderedGroup_Olordered__ab__group__join(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_17) # label(axiom). [assumption].
% 18.69/18.85 1633 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_17) # label(axiom). [assumption].
% 18.69/18.85 1634 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | class_LOrder_Olorder(A) # label(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) # label(axiom). [assumption].
% 18.69/18.85 1635 -class_Ring__and__Field_Olordered__ring(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Olordered__ring_26) # label(axiom). [assumption].
% 18.69/18.85 1636 -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].
% 18.69/18.85 1637 -class_Ring__and__Field_Oordered__field(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__field_51) # label(axiom). [assumption].
% 18.69/18.85 1638 -class_Ring__and__Field_Oordered__idom(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__idom_34) # label(axiom). [assumption].
% 18.69/18.85 1639 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__ring__strict_18) # label(axiom). [assumption].
% 18.69/18.85 1640 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_LOrder_Olorder(A) # label(clsrel_Ring__and__Field_Oordered__semiring__strict_11) # label(axiom). [assumption].
% 18.69/18.85 1641 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A) # label(clsrel_Wellfounded__Recursion_Owellorder_4) # label(axiom). [assumption].
% 18.69/18.85 1642 class_LOrder_Olorder(tc_IntDef_Oint). [resolve(62,a,1,a)].
% 18.69/18.85 1643 class_LOrder_Olorder(tc_nat). [resolve(62,a,60,a)].
% 18.69/18.85 1644 class_LOrder_Olorder(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(62,a,61,b)].
% 18.69/18.85 1645 -class_Wellfounded__Recursion_Owellorder(A) | class_LOrder_Olorder(A). [resolve(73,b,62,a)].
% 18.69/18.85 1646 -class_LOrder_Olorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(298,b,296,a)].
% 18.84/19.01 1647 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(365,a,344,b)].
% 18.84/19.01 1648 class_LOrder_Olorder(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(365,a,345,b)].
% 18.84/19.01 1649 -class_Ring__and__Field_Oordered__ring__strict(A) | class_LOrder_Olorder(A). [resolve(638,b,624,a)].
% 18.84/19.01 1650 class_LOrder_Olorder(tc_IntDef_Oint). [resolve(820,a,805,a)].
% 18.84/19.01 1651 -class_LOrder_Olorder(A) | -c_less(B,B,A). [resolve(893,b,880,a)].
% 18.84/19.01 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1651,a,1630,a)].
% 18.84/19.01 Derived: -c_less(A,A,tc_nat). [resolve(1651,a,1631,a)].
% 18.84/19.01 1652 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(893,b,881,a)].
% 18.84/19.01 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1652,a,1630,a)].
% 18.84/19.01 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1652,a,1631,a)].
% 18.84/19.01 1653 -class_LOrder_Olorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(893,b,882,a)].
% 18.84/19.01 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1653,a,1630,a)].
% 18.84/19.01 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1653,a,1631,a)].
% 18.84/19.01 1654 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(893,b,883,a)].
% 18.84/19.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1654,a,1630,a)].
% 18.84/19.01 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1654,a,1631,a)].
% 18.84/19.01 1655 -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(893,b,884,a)].
% 18.84/19.01 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1655,a,1630,a)].
% 18.84/19.01 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(1655,a,1631,a)].
% 18.84/19.01 1656 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(893,b,885,a)].
% 18.84/19.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1656,a,1630,a)].
% 18.84/19.01 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(1656,a,1631,a)].
% 18.84/19.01 1657 -class_LOrder_Olorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(893,b,886,a)].
% 18.84/19.01 Derived: -c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1657,a,1630,a)].
% 18.84/19.01 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(1657,a,1631,a)].
% 18.84/19.01 1658 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(893,b,887,a)].
% 18.84/19.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatMost(A,tc_IntDef_Oint),c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1658,a,1630,a)].
% 18.84/19.01 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(1658,a,1631,a)].
% 18.84/19.01 1659 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(893,b,888,a)].
% 18.84/19.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1659,a,1630,a)].
% 18.84/19.01 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1659,a,1631,a)].
% 18.94/19.08 1660 -class_LOrder_Olorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(893,b,889,a)].
% 18.94/19.08 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1660,a,1630,a)].
% 18.94/19.08 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(1660,a,1631,a)].
% 18.94/19.08 1661 -class_LOrder_Olorder(A) | c_lessequals(B,B,A). [resolve(893,b,890,a)].
% 18.94/19.08 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1661,a,1630,a)].
% 18.94/19.08 Derived: c_lessequals(A,A,tc_nat). [resolve(1661,a,1631,a)].
% 18.94/19.08 1662 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1032,b,1010,a)].
% 18.94/19.08 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1662,a,1630,a)].
% 18.94/19.08 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1662,a,1631,a)].
% 18.94/19.08 1663 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1032,b,1011,a)].
% 18.94/19.08 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1663,a,1630,a)].
% 18.94/19.08 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1663,a,1631,a)].
% 18.94/19.08 1664 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1032,b,1012,a)].
% 18.94/19.08 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1664,a,1630,a)].
% 18.94/19.08 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(1664,a,1631,a)].
% 18.94/19.08 1665 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1032,b,1013,a)].
% 18.94/19.08 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1665,a,1630,a)].
% 18.94/19.08 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1665,a,1631,a)].
% 18.94/19.08 1666 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1032,b,1014,a)].
% 18.94/19.08 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1666,a,1630,a)].
% 18.94/19.08 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1666,a,1631,a)].
% 18.94/19.08 1667 -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1032,b,1015,a)].
% 18.94/19.08 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1667,a,1630,a)].
% 18.94/19.08 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(1667,a,1631,a)].
% 18.94/19.08 1668 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1032,b,1016,a)].
% 18.94/19.08 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1668,a,1630,a)].
% 18.94/19.08 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1668,a,1631,a)].
% 18.94/19.08 1669 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1032,b,1017,a)].
% 18.94/19.08 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1669,a,1630,a)].
% 18.94/19.08 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1669,a,1631,a)].
% 18.94/19.08 1670 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1032,b,1018,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1670,a,1630,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1670,a,1631,a)].
% 18.94/19.09 1671 -class_LOrder_Olorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1032,b,1019,a)].
% 18.94/19.09 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1671,a,1630,a)].
% 18.94/19.09 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1671,a,1631,a)].
% 18.94/19.09 1672 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1032,b,1020,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1672,a,1630,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1672,a,1631,a)].
% 18.94/19.09 1673 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1032,b,1021,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1673,a,1630,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1673,a,1631,a)].
% 18.94/19.09 1674 -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1032,b,1022,a)].
% 18.94/19.09 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1674,a,1630,a)].
% 18.94/19.09 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(1674,a,1631,a)].
% 18.94/19.09 1675 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1032,b,1023,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1675,a,1630,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1675,a,1631,a)].
% 18.94/19.09 1676 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1032,b,1024,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1676,a,1630,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1676,a,1631,a)].
% 18.94/19.09 1677 -class_LOrder_Olorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1032,b,1025,a)].
% 18.94/19.09 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1677,a,1630,a)].
% 18.94/19.09 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(1677,a,1631,a)].
% 18.94/19.09 1678 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1032,b,1026,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1678,a,1630,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1678,a,1631,a)].
% 18.94/19.09 1679 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1032,b,1027,a)].
% 18.94/19.09 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1679,a,1630,a)].
% 18.94/19.09 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1679,a,1631,a)].
% 18.94/19.09 1680 -class_LOrder_Olorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1032,b,1028,a)].
% 18.94/19.09 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1680,a,1630,a)].
% 19.24/19.36 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1680,a,1631,a)].
% 19.24/19.36 1681 -class_LOrder_Olorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1032,b,1029,a)].
% 19.24/19.36 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1681,a,1630,a)].
% 19.24/19.36 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1681,a,1631,a)].
% 19.24/19.36 1682 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) # label(axiom). [assumption].
% 19.24/19.36 1683 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_36) # label(axiom). [assumption].
% 19.24/19.36 1684 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat_33) # label(axiom). [assumption].
% 19.24/19.36 1685 -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].
% 19.24/19.36 1686 -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].
% 19.24/19.36 1687 -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].
% 19.24/19.36 1688 -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].
% 19.24/19.36 1689 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) # label(axiom). [assumption].
% 19.24/19.36 1690 -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].
% 19.24/19.36 1691 -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].
% 19.24/19.36 1692 -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].
% 19.24/19.36 1693 -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].
% 19.24/19.36 1694 -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].
% 19.24/19.36 1695 -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].
% 19.24/19.36 1696 -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].
% 19.24/19.36 1697 -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].
% 19.24/19.36 1698 -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].
% 19.24/19.36 1699 -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].
% 19.24/19.36 1700 -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].
% 19.46/19.58 1701 -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].
% 19.46/19.58 1702 -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].
% 19.46/19.58 1703 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(373,a,318,a)].
% 19.46/19.58 1704 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat). [resolve(373,a,343,a)].
% 19.46/19.58 1705 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(373,a,344,b)].
% 19.46/19.58 1706 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(373,a,345,b)].
% 19.46/19.58 1707 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(638,b,633,a)].
% 19.46/19.58 1708 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(705,a,700,b)].
% 19.46/19.58 1709 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(705,a,701,b)].
% 19.46/19.58 1710 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(705,a,702,b)].
% 19.46/19.58 1711 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(705,a,703,b)].
% 19.46/19.58 1712 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add(A). [resolve(719,b,705,a)].
% 19.46/19.58 1713 class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint). [resolve(820,a,809,a)].
% 19.46/19.58 1714 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(836,b,814,b)].
% 19.46/19.58 1715 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(836,b,815,b)].
% 19.46/19.58 1716 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(836,b,816,b)].
% 19.46/19.58 1717 class_OrderedGroup_Opordered__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(836,b,817,b)].
% 19.46/19.58 1718 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(898,b,880,a)].
% 19.46/19.58 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1718,a,1685,b)].
% 19.46/19.58 Derived: -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1718,a,1686,b)].
% 19.46/19.58 Derived: -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1718,a,1687,b)].
% 19.46/19.58 Derived: -c_less(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1718,a,1688,b)].
% 19.46/19.58 1719 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(898,b,881,a)].
% 19.46/19.58 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1719,a,1685,b)].
% 19.46/19.58 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1719,a,1686,b)].
% 19.46/19.58 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1719,a,1687,b)].
% 19.46/19.58 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1719,a,1688,b)].
% 19.46/19.58 1720 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(898,b,882,a)].
% 19.46/19.58 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1720,a,1685,b)].
% 19.46/19.58 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1720,a,1686,b)].
% 19.46/19.59 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1720,a,1687,b)].
% 19.46/19.59 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1720,a,1688,b)].
% 19.46/19.59 1721 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(898,b,883,a)].
% 19.46/19.59 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1721,a,1685,b)].
% 19.46/19.59 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1721,a,1686,b)].
% 19.46/19.59 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1721,a,1687,b)].
% 19.46/19.59 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1721,a,1688,b)].
% 19.46/19.59 1722 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(898,b,884,a)].
% 19.46/19.59 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(1722,a,1685,b)].
% 19.46/19.59 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(1722,a,1686,b)].
% 19.46/19.59 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(1722,a,1687,b)].
% 19.46/19.59 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(1722,a,1688,b)].
% 19.46/19.59 1723 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(898,b,885,a)].
% 19.46/19.59 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(1723,a,1685,b)].
% 19.46/19.59 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(1723,a,1686,b)].
% 19.46/19.59 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(1723,a,1687,b)].
% 19.46/19.59 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(1723,a,1688,b)].
% 19.46/19.59 1724 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(898,b,886,a)].
% 19.46/19.59 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(1724,a,1685,b)].
% 19.46/19.59 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(1724,a,1686,b)].
% 19.46/19.59 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(1724,a,1687,b)].
% 19.46/19.59 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(1724,a,1688,b)].
% 19.46/19.59 1725 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(898,b,887,a)].
% 19.57/19.66 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(1725,a,1685,b)].
% 19.57/19.66 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(1725,a,1686,b)].
% 19.57/19.66 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(1725,a,1687,b)].
% 19.57/19.66 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(1725,a,1688,b)].
% 19.57/19.66 1726 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(898,b,888,a)].
% 19.57/19.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1726,a,1685,b)].
% 19.57/19.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1726,a,1686,b)].
% 19.57/19.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1726,a,1687,b)].
% 19.57/19.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1726,a,1688,b)].
% 19.57/19.66 1727 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(898,b,889,a)].
% 19.57/19.66 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1727,a,1685,b)].
% 19.57/19.66 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1727,a,1686,b)].
% 19.57/19.66 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1727,a,1687,b)].
% 19.57/19.66 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1727,a,1688,b)].
% 19.57/19.66 1728 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(898,b,890,a)].
% 19.57/19.66 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1728,a,1685,b)].
% 19.57/19.66 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1728,a,1686,b)].
% 19.57/19.66 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1728,a,1687,b)].
% 19.57/19.66 Derived: c_lessequals(A,A,B) | -class_OrderedGroup_Opordered__ab__group__add(B). [resolve(1728,a,1688,b)].
% 19.57/19.66 1729 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1037,b,1010,a)].
% 19.57/19.66 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1729,a,1685,b)].
% 19.57/19.66 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1729,a,1686,b)].
% 19.57/19.66 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1729,a,1687,b)].
% 19.57/19.66 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1729,a,1688,b)].
% 19.57/19.66 1730 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1037,b,1011,a)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1730,a,1685,b)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1730,a,1686,b)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1730,a,1687,b)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1730,a,1688,b)].
% 19.57/19.67 1731 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1037,b,1012,a)].
% 19.57/19.67 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1731,a,1685,b)].
% 19.57/19.67 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1731,a,1686,b)].
% 19.57/19.67 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1731,a,1687,b)].
% 19.57/19.67 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1731,a,1688,b)].
% 19.57/19.67 1732 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1037,b,1013,a)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1732,a,1685,b)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1732,a,1686,b)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1732,a,1687,b)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1732,a,1688,b)].
% 19.57/19.67 1733 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1037,b,1014,a)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1733,a,1685,b)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1733,a,1686,b)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1733,a,1687,b)].
% 19.57/19.67 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1733,a,1688,b)].
% 19.57/19.67 1734 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1037,b,1015,a)].
% 19.57/19.67 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1734,a,1685,b)].
% 19.57/19.67 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1734,a,1686,b)].
% 19.57/19.67 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1734,a,1687,b)].
% 19.57/19.67 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1734,a,1688,b)].
% 19.57/19.68 1735 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1037,b,1016,a)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1735,a,1685,b)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1735,a,1686,b)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1735,a,1687,b)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1735,a,1688,b)].
% 19.57/19.68 1736 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1037,b,1017,a)].
% 19.57/19.68 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1736,a,1685,b)].
% 19.57/19.68 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1736,a,1686,b)].
% 19.57/19.68 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1736,a,1687,b)].
% 19.57/19.68 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1736,a,1688,b)].
% 19.57/19.68 1737 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1037,b,1018,a)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1737,a,1685,b)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1737,a,1686,b)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1737,a,1687,b)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1737,a,1688,b)].
% 19.57/19.68 1738 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1037,b,1019,a)].
% 19.57/19.68 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1738,a,1685,b)].
% 19.57/19.68 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1738,a,1686,b)].
% 19.57/19.68 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1738,a,1687,b)].
% 19.57/19.68 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1738,a,1688,b)].
% 19.57/19.68 1739 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1037,b,1020,a)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1739,a,1685,b)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1739,a,1686,b)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1739,a,1687,b)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1739,a,1688,b)].
% 19.57/19.68 1740 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1037,b,1021,a)].
% 19.57/19.68 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1740,a,1685,b)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1740,a,1686,b)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1740,a,1687,b)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1740,a,1688,b)].
% 19.57/19.69 1741 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1037,b,1022,a)].
% 19.57/19.69 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1741,a,1685,b)].
% 19.57/19.69 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1741,a,1686,b)].
% 19.57/19.69 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1741,a,1687,b)].
% 19.57/19.69 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1741,a,1688,b)].
% 19.57/19.69 1742 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1037,b,1023,a)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1742,a,1685,b)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1742,a,1686,b)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1742,a,1687,b)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1742,a,1688,b)].
% 19.57/19.69 1743 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1037,b,1024,a)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1743,a,1685,b)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1743,a,1686,b)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1743,a,1687,b)].
% 19.57/19.69 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Opordered__ab__group__add(D). [resolve(1743,a,1688,b)].
% 19.57/19.69 1744 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1037,b,1025,a)].
% 19.57/19.69 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1744,a,1685,b)].
% 19.57/19.69 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1744,a,1686,b)].
% 19.57/19.69 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1744,a,1687,b)].
% 19.57/19.69 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1744,a,1688,b)].
% 19.57/19.69 1745 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1037,b,1026,a)].
% 19.87/19.97 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1745,a,1685,b)].
% 19.87/19.97 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1745,a,1686,b)].
% 19.87/19.97 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1745,a,1687,b)].
% 19.87/19.97 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1745,a,1688,b)].
% 19.87/19.97 1746 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1037,b,1027,a)].
% 19.87/19.97 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1746,a,1685,b)].
% 19.87/19.97 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1746,a,1686,b)].
% 19.87/19.97 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1746,a,1687,b)].
% 19.87/19.97 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1746,a,1688,b)].
% 19.87/19.97 1747 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1037,b,1028,a)].
% 19.87/19.97 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1747,a,1685,b)].
% 19.87/19.97 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1747,a,1686,b)].
% 19.87/19.97 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1747,a,1687,b)].
% 19.87/19.97 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1747,a,1688,b)].
% 19.87/19.97 1748 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1037,b,1029,a)].
% 19.87/19.97 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1748,a,1685,b)].
% 19.87/19.97 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1748,a,1686,b)].
% 19.87/19.97 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1748,a,1687,b)].
% 19.87/19.97 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1748,a,1688,b)].
% 19.87/19.97 1749 -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].
% 19.87/19.97 1750 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_37) # label(axiom). [assumption].
% 19.87/19.97 1751 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_34) # label(axiom). [assumption].
% 19.87/19.97 1752 -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].
% 19.87/19.97 1753 -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].
% 19.87/19.97 1754 -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].
% 19.87/19.97 1755 -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].
% 19.97/20.15 1756 -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].
% 19.97/20.15 1757 -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].
% 19.97/20.15 1758 -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].
% 19.97/20.15 1759 -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].
% 19.97/20.15 1760 -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].
% 19.97/20.15 1761 -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].
% 19.97/20.15 1762 -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].
% 19.97/20.15 1763 -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].
% 19.97/20.15 1764 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(368,a,318,a)].
% 19.97/20.15 1765 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). [resolve(368,a,343,a)].
% 19.97/20.15 1766 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(368,a,344,b)].
% 19.97/20.15 1767 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(368,a,345,b)].
% 19.97/20.15 1768 -class_Ring__and__Field_Oordered__ring__strict(A) | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A). [resolve(638,b,632,a)].
% 19.97/20.15 1769 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__join(A). [resolve(704,a,700,b)].
% 19.97/20.15 1770 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Olordered__ab__group__meet(A). [resolve(704,a,701,b)].
% 19.97/20.15 1771 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(704,a,702,b)].
% 19.97/20.15 1772 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(704,a,703,b)].
% 19.97/20.15 1773 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(738,b,726,a)].
% 19.97/20.15 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1773,a,1752,b)].
% 19.97/20.15 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1773,a,1753,b)].
% 19.97/20.15 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1773,a,1754,b)].
% 19.97/20.15 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1773,a,1755,b)].
% 19.97/20.15 1774 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(738,b,727,a)].
% 19.97/20.15 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1774,a,1752,b)].
% 19.97/20.15 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1774,a,1753,b)].
% 19.97/20.15 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1774,a,1754,b)].
% 19.97/20.15 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Opordered__ab__group__add(C). [resolve(1774,a,1755,b)].
% 20.18/20.29 1775 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(738,b,731,a)].
% 20.18/20.29 1776 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(820,a,808,a)].
% 20.18/20.29 1777 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(835,b,814,b)].
% 20.18/20.29 1778 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(835,b,815,b)].
% 20.18/20.29 1779 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(835,b,816,b)].
% 20.18/20.29 1780 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(835,b,817,b)].
% 20.18/20.29 1781 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(899,b,880,a)].
% 20.18/20.29 1782 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(899,b,881,a)].
% 20.18/20.29 1783 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(899,b,882,a)].
% 20.18/20.29 1784 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(899,b,883,a)].
% 20.18/20.29 1785 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(899,b,884,a)].
% 20.18/20.29 1786 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(899,b,885,a)].
% 20.18/20.29 1787 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(899,b,886,a)].
% 20.18/20.29 1788 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(899,b,887,a)].
% 20.18/20.29 1789 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(899,b,888,a)].
% 20.18/20.29 1790 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(899,b,889,a)].
% 20.18/20.29 1791 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(899,b,890,a)].
% 20.18/20.29 1792 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1038,b,1010,a)].
% 20.18/20.29 1793 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1038,b,1011,a)].
% 20.18/20.29 1794 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1038,b,1012,a)].
% 20.18/20.29 1795 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1038,b,1013,a)].
% 20.18/20.29 1796 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1038,b,1014,a)].
% 20.18/20.29 1797 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1038,b,1015,a)].
% 20.18/20.29 1798 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1038,b,1016,a)].
% 20.18/20.29 1799 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1038,b,1017,a)].
% 20.48/20.58 1800 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1038,b,1018,a)].
% 20.48/20.58 1801 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1038,b,1019,a)].
% 20.48/20.58 1802 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1038,b,1020,a)].
% 20.48/20.58 1803 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1038,b,1021,a)].
% 20.48/20.58 1804 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1038,b,1022,a)].
% 20.48/20.58 1805 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1038,b,1023,a)].
% 20.48/20.58 1806 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1038,b,1024,a)].
% 20.48/20.58 1807 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1038,b,1025,a)].
% 20.48/20.58 1808 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1038,b,1026,a)].
% 20.48/20.58 1809 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1038,b,1027,a)].
% 20.48/20.58 1810 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1038,b,1028,a)].
% 20.48/20.58 1811 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1038,b,1029,a)].
% 20.48/20.58 1812 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1219,b,1209,a)].
% 20.48/20.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1812,a,1754,b)].
% 20.48/20.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A). [resolve(1812,a,1755,b)].
% 20.48/20.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1812,a,1757,b)].
% 20.48/20.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1812,a,1758,b)].
% 20.48/20.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1812,a,1761,b)].
% 20.48/20.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1812,a,1763,b)].
% 20.48/20.58 1813 -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].
% 20.48/20.58 1814 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_39) # label(axiom). [assumption].
% 20.48/20.58 1815 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat_36) # label(axiom). [assumption].
% 20.48/20.58 1816 -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].
% 20.48/20.58 1817 -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].
% 20.48/20.58 1818 -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].
% 20.48/20.58 1819 -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].
% 20.48/20.59 1820 -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].
% 20.48/20.59 1821 -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].
% 20.48/20.59 1822 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(61,b,2,a)].
% 20.48/20.59 1823 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(61,b,3,a)].
% 20.48/20.59 1824 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(61,b,4,a)].
% 20.48/20.59 1825 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(61,b,5,a)].
% 20.48/20.59 1826 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(61,b,6,a)].
% 20.48/20.59 1827 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(61,b,7,a)].
% 20.48/20.59 1828 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(61,b,8,a)].
% 20.48/20.59 1829 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(61,b,9,a)].
% 20.48/20.59 1830 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(61,b,10,a)].
% 20.48/20.59 1831 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(61,b,11,a)].
% 20.48/20.59 1832 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(61,b,12,a)].
% 20.48/20.59 1833 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(61,b,13,a)].
% 20.48/20.59 1834 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(61,b,14,a)].
% 20.48/20.59 1835 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(61,b,15,a)].
% 20.48/20.59 1836 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(61,b,16,a)].
% 20.48/20.59 1837 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(61,b,17,a)].
% 20.48/20.59 1838 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(61,b,18,a)].
% 20.48/20.61 1839 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(61,b,19,a)].
% 20.48/20.61 1840 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(61,b,20,a)].
% 20.48/20.61 1841 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(61,b,21,a)].
% 20.48/20.61 1842 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(61,b,22,a)].
% 20.48/20.61 1843 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(61,b,23,a)].
% 20.48/20.61 1844 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(61,b,24,a)].
% 20.48/20.61 1845 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(61,b,25,b)].
% 20.48/20.61 1846 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(61,b,26,b)].
% 20.48/20.61 1847 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(61,b,27,a)].
% 20.48/20.61 1848 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(61,b,28,a)].
% 20.48/20.61 1849 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(61,b,29,a)].
% 20.48/20.61 1850 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(61,b,30,a)].
% 20.48/20.61 1851 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(61,b,31,a)].
% 20.48/20.61 1852 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(61,b,32,a)].
% 20.48/20.61 1853 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(61,b,33,a)].
% 20.48/20.61 1854 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(61,b,34,a)].
% 20.48/20.61 1855 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(61,b,35,a)].
% 20.48/20.61 1856 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,B,A) = B. [resolve(61,b,36,a)].
% 20.48/20.61 1857 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(61,b,37,a)].
% 20.48/20.61 1858 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(61,b,38,a)].
% 20.48/20.61 1859 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(61,b,39,a)].
% 20.48/20.61 1860 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(61,b,40,a)].
% 20.48/20.61 1861 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,B,A) = B. [resolve(61,b,41,a)].
% 20.48/20.61 1862 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(61,b,42,a)].
% 20.57/20.68 1863 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(61,b,43,a)].
% 20.57/20.68 1864 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(61,b,44,a)].
% 20.57/20.68 1865 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(61,b,45,a)].
% 20.57/20.68 1866 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(61,b,46,a)].
% 20.57/20.68 1867 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(61,b,47,a)].
% 20.57/20.68 1868 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(61,b,48,a)].
% 20.57/20.68 1869 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(61,b,49,a)].
% 20.57/20.68 1870 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(61,b,50,a)].
% 20.57/20.68 1871 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(61,b,51,a)].
% 20.57/20.68 1872 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(61,b,52,a)].
% 20.57/20.68 1873 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(61,b,53,a)].
% 20.57/20.68 1874 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(61,b,54,a)].
% 20.57/20.68 1875 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(61,b,55,a)].
% 20.57/20.68 1876 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(61,b,56,a)].
% 20.57/20.68 1877 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(61,b,57,a)].
% 20.57/20.68 1878 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(61,b,58,a)].
% 20.57/20.68 1879 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(61,b,59,a)].
% 20.57/20.68 1880 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(282,b,273,a)].
% 20.57/20.68 1881 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(305,b,296,a)].
% 20.57/20.68 1882 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint). [resolve(364,a,318,a)].
% 20.57/20.68 1883 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat). [resolve(364,a,343,a)].
% 20.57/20.68 1884 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(364,a,344,b)].
% 20.57/20.68 1885 class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(364,a,345,b)].
% 20.74/20.82 1886 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(702,b,690,a)].
% 20.74/20.82 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(1886,a,1815,a)].
% 20.74/20.82 1887 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(702,b,691,a)].
% 20.74/20.82 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1887,a,1815,a)].
% 20.74/20.82 1888 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(702,b,692,a)].
% 20.74/20.82 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1888,a,1815,a)].
% 20.74/20.82 1889 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(702,b,693,a)].
% 20.74/20.82 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1889,a,1815,a)].
% 20.74/20.82 1890 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(702,b,694,a)].
% 20.74/20.82 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(1890,a,1815,a)].
% 20.74/20.82 1891 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(702,b,695,a)].
% 20.74/20.82 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(1891,a,1815,a)].
% 20.74/20.82 1892 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(702,b,696,a)].
% 20.74/20.82 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1892,a,1815,a)].
% 20.74/20.82 1893 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(702,b,697,a)].
% 20.74/20.82 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(1893,a,1815,a)].
% 20.74/20.82 1894 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(709,a,702,b)].
% 20.74/20.82 1895 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(711,a,702,b)].
% 20.74/20.82 1896 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(736,b,726,a)].
% 20.74/20.82 1897 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(736,b,727,a)].
% 20.74/20.82 1898 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,B,A). [resolve(896,b,880,a)].
% 20.74/20.82 1899 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(896,b,881,a)].
% 20.74/20.82 1900 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(896,b,882,a)].
% 20.74/20.82 1901 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(896,b,883,a)].
% 20.74/20.82 1902 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(896,b,884,a)].
% 20.74/20.82 1903 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(896,b,885,a)].
% 20.74/20.82 1904 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(896,b,886,a)].
% 20.74/20.82 1905 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(896,b,887,a)].
% 20.86/20.95 1906 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(896,b,888,a)].
% 20.86/20.95 1907 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(896,b,889,a)].
% 20.86/20.95 1908 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | c_lessequals(B,B,A). [resolve(896,b,890,a)].
% 20.86/20.95 1909 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1035,b,1010,a)].
% 20.86/20.95 1910 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1035,b,1011,a)].
% 20.86/20.95 1911 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1035,b,1012,a)].
% 20.86/20.95 1912 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1035,b,1013,a)].
% 20.86/20.95 1913 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1035,b,1014,a)].
% 20.86/20.95 1914 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1035,b,1015,a)].
% 20.86/20.95 1915 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1035,b,1016,a)].
% 20.86/20.95 1916 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1035,b,1017,a)].
% 20.86/20.95 1917 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1035,b,1018,a)].
% 20.86/20.95 1918 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1035,b,1019,a)].
% 20.86/20.95 1919 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1035,b,1020,a)].
% 20.86/20.95 1920 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1035,b,1021,a)].
% 20.86/20.95 1921 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1035,b,1022,a)].
% 20.86/20.95 1922 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1035,b,1023,a)].
% 20.86/20.95 1923 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1035,b,1024,a)].
% 20.86/20.95 1924 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1035,b,1025,a)].
% 20.86/20.95 1925 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1035,b,1026,a)].
% 20.86/20.95 1926 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1035,b,1027,a)].
% 20.86/20.95 1927 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1035,b,1028,a)].
% 20.86/20.95 1928 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1035,b,1029,a)].
% 20.86/20.95 1929 class_OrderedGroup_Osemigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1259,b,1217,b)].
% 20.86/20.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1929,b,1817,b)].
% 20.86/20.95 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(1929,b,1820,b)].
% 20.90/21.01 1930 -c_less(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1718,a,1687,b)].
% 20.90/21.01 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(1930,b,1814,a)].
% 20.90/21.01 Derived: -c_less(A,A,tc_nat). [resolve(1930,b,1815,a)].
% 20.90/21.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1930,b,1817,b)].
% 20.90/21.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1930,b,1818,b)].
% 20.90/21.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1930,b,1819,b)].
% 20.90/21.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1930,b,1820,b)].
% 20.90/21.01 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1930,b,1821,b)].
% 20.90/21.01 1931 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1719,a,1687,b)].
% 20.90/21.01 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1931,c,1814,a)].
% 20.90/21.01 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(1931,c,1815,a)].
% 20.90/21.01 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1931,c,1817,b)].
% 20.90/21.01 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1931,c,1818,b)].
% 20.90/21.01 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1931,c,1819,b)].
% 20.90/21.01 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1931,c,1820,b)].
% 20.90/21.01 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1931,c,1821,b)].
% 20.90/21.01 1932 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1720,a,1687,b)].
% 20.90/21.01 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1932,b,1814,a)].
% 20.90/21.01 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(1932,b,1815,a)].
% 20.90/21.01 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1932,b,1817,b)].
% 20.90/21.01 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1932,b,1818,b)].
% 20.90/21.01 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1932,b,1819,b)].
% 20.90/21.01 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1932,b,1820,b)].
% 20.90/21.01 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1932,b,1821,b)].
% 20.90/21.01 1933 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1721,a,1687,b)].
% 20.90/21.01 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1933,c,1814,a)].
% 20.90/21.01 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(1933,c,1815,a)].
% 20.90/21.01 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1933,c,1817,b)].
% 20.90/21.01 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1933,c,1818,b)].
% 20.90/21.01 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1933,c,1819,b)].
% 20.90/21.01 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1933,c,1820,b)].
% 20.90/21.02 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1933,c,1821,b)].
% 20.90/21.02 1934 -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(1722,a,1687,b)].
% 20.90/21.02 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_IntDef_Oint),c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1934,c,1814,a)].
% 20.90/21.02 Derived: -c_lessequals(c_SetInterval_OatLeast(A,tc_nat),c_SetInterval_OatLeast(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(1934,c,1815,a)].
% 20.90/21.02 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(1934,c,1817,b)].
% 20.90/21.02 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(1934,c,1818,b)].
% 20.90/21.02 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(1934,c,1819,b)].
% 20.90/21.02 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(1934,c,1820,b)].
% 20.90/21.02 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(1934,c,1821,b)].
% 20.90/21.02 1935 -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(1723,a,1687,b)].
% 20.90/21.02 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeast(B,tc_IntDef_Oint),c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(1935,c,1814,a)].
% 20.90/21.02 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeast(B,tc_nat),c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)). [resolve(1935,c,1815,a)].
% 20.90/21.02 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(1935,c,1817,b)].
% 20.90/21.02 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(1935,c,1818,b)].
% 20.90/21.02 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(1935,c,1819,b)].
% 20.90/21.02 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(1935,c,1820,b)].
% 20.90/21.02 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(1935,c,1821,b)].
% 20.90/21.02 1936 -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(1724,a,1687,b)].
% 20.90/21.02 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(1936,c,1814,a)].
% 20.90/21.02 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(1936,c,1815,a)].
% 20.90/21.02 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(1936,c,1817,b)].
% 20.90/21.02 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(1936,c,1818,b)].
% 20.90/21.02 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(1936,c,1819,b)].
% 20.90/21.02 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(1936,c,1820,b)].
% 20.90/21.02 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(1936,c,1821,b)].
% 20.90/21.02 1937 -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(1725,a,1687,b)].
% 20.90/21.02 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(1937,c,1814,a)].
% 20.90/21.02 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(1937,c,1815,a)].
% 20.90/21.02 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(1937,c,1817,b)].
% 20.90/21.02 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(1937,c,1818,b)].
% 20.90/21.02 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(1937,c,1819,b)].
% 20.90/21.02 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(1937,c,1820,b)].
% 20.90/21.02 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(1937,c,1821,b)].
% 20.90/21.02 1938 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1726,a,1687,b)].
% 20.90/21.02 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(1938,c,1814,a)].
% 20.90/21.02 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(1938,c,1815,a)].
% 20.90/21.02 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1938,c,1817,b)].
% 20.90/21.02 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(1938,c,1818,b)].
% 20.90/21.02 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(1938,c,1819,b)].
% 20.90/21.02 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1938,c,1820,b)].
% 20.90/21.02 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1938,c,1821,b)].
% 20.90/21.02 1939 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1727,a,1687,b)].
% 20.90/21.02 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(1939,b,1814,a)].
% 20.90/21.02 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(1939,b,1815,a)].
% 20.90/21.02 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1939,b,1817,b)].
% 20.90/21.02 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1939,b,1818,b)].
% 20.90/21.02 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1939,b,1819,b)].
% 20.90/21.02 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1939,b,1820,b)].
% 20.90/21.02 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1939,b,1821,b)].
% 20.90/21.02 1940 c_lessequals(A,A,B) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(B). [resolve(1728,a,1687,b)].
% 20.90/21.02 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(1940,b,1814,a)].
% 20.90/21.02 Derived: c_lessequals(A,A,tc_nat). [resolve(1940,b,1815,a)].
% 20.90/21.02 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1940,b,1817,b)].
% 20.90/21.02 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(1940,b,1818,b)].
% 20.90/21.02 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(1940,b,1819,b)].
% 20.90/21.02 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(1940,b,1820,b)].
% 20.90/21.02 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1940,b,1821,b)].
% 20.90/21.02 1941 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1729,a,1687,b)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1941,c,1814,a)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1941,c,1815,a)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1941,c,1817,b)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1941,c,1818,b)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1941,c,1819,b)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1941,c,1820,b)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1941,c,1821,b)].
% 20.90/21.02 1942 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1730,a,1687,b)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1942,c,1814,a)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1942,c,1815,a)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1942,c,1817,b)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1942,c,1818,b)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1942,c,1819,b)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1942,c,1820,b)].
% 20.90/21.02 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1942,c,1821,b)].
% 20.90/21.02 1943 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1731,a,1687,b)].
% 20.90/21.03 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1943,d,1814,a)].
% 20.90/21.03 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(1943,d,1815,a)].
% 20.90/21.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1943,d,1817,b)].
% 20.90/21.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1943,d,1818,b)].
% 20.90/21.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1943,d,1819,b)].
% 20.90/21.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1943,d,1820,b)].
% 20.90/21.03 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1943,d,1821,b)].
% 20.90/21.03 1944 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1732,a,1687,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1944,c,1814,a)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1944,c,1815,a)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1944,c,1817,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1944,c,1818,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1944,c,1819,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1944,c,1820,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1944,c,1821,b)].
% 20.90/21.03 1945 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1733,a,1687,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1945,c,1814,a)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1945,c,1815,a)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1945,c,1817,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1945,c,1818,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1945,c,1819,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1945,c,1820,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1945,c,1821,b)].
% 20.90/21.03 1946 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1734,a,1687,b)].
% 20.90/21.03 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1946,d,1814,a)].
% 20.90/21.03 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(1946,d,1815,a)].
% 20.90/21.03 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1946,d,1817,b)].
% 20.90/21.03 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1946,d,1818,b)].
% 20.90/21.03 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1946,d,1819,b)].
% 20.90/21.03 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1946,d,1820,b)].
% 20.90/21.03 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1946,d,1821,b)].
% 20.90/21.03 1947 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1735,a,1687,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(1947,c,1814,a)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1947,c,1815,a)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1947,c,1817,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1947,c,1818,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1947,c,1819,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1947,c,1820,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1947,c,1821,b)].
% 20.90/21.03 1948 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1736,a,1687,b)].
% 20.90/21.03 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1948,c,1814,a)].
% 20.90/21.03 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(1948,c,1815,a)].
% 20.90/21.03 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1948,c,1817,b)].
% 20.90/21.03 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1948,c,1818,b)].
% 20.90/21.03 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1948,c,1819,b)].
% 20.90/21.03 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1948,c,1820,b)].
% 20.90/21.03 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1948,c,1821,b)].
% 20.90/21.03 1949 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1737,a,1687,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(1949,c,1814,a)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(1949,c,1815,a)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1949,c,1817,b)].
% 20.90/21.03 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1949,c,1818,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1949,c,1819,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1949,c,1820,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1949,c,1821,b)].
% 20.96/21.04 1950 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1738,a,1687,b)].
% 20.96/21.04 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1950,c,1814,a)].
% 20.96/21.04 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(1950,c,1815,a)].
% 20.96/21.04 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1950,c,1817,b)].
% 20.96/21.04 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1950,c,1818,b)].
% 20.96/21.04 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1950,c,1819,b)].
% 20.96/21.04 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1950,c,1820,b)].
% 20.96/21.04 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1950,c,1821,b)].
% 20.96/21.04 1951 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1739,a,1687,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1951,c,1814,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1951,c,1815,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1951,c,1817,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1951,c,1818,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1951,c,1819,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1951,c,1820,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1951,c,1821,b)].
% 20.96/21.04 1952 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1740,a,1687,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(1952,c,1814,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(1952,c,1815,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1952,c,1817,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1952,c,1818,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1952,c,1819,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1952,c,1820,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1952,c,1821,b)].
% 20.96/21.04 1953 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1741,a,1687,b)].
% 20.96/21.04 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1953,d,1814,a)].
% 20.96/21.04 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(1953,d,1815,a)].
% 20.96/21.04 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1953,d,1817,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1953,d,1818,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1953,d,1819,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1953,d,1820,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1953,d,1821,b)].
% 20.96/21.04 1954 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1742,a,1687,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1954,c,1814,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1954,c,1815,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1954,c,1817,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1954,c,1818,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1954,c,1819,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1954,c,1820,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1954,c,1821,b)].
% 20.96/21.04 1955 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(D). [resolve(1743,a,1687,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(1955,c,1814,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(1955,c,1815,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1955,c,1817,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(1955,c,1818,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(1955,c,1819,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(1955,c,1820,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1955,c,1821,b)].
% 20.96/21.04 1956 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1744,a,1687,b)].
% 20.96/21.04 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1956,d,1814,a)].
% 20.96/21.04 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(1956,d,1815,a)].
% 20.96/21.04 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1956,d,1817,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1956,d,1818,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1956,d,1819,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1956,d,1820,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1956,d,1821,b)].
% 20.96/21.04 1957 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1745,a,1687,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(1957,c,1814,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(1957,c,1815,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1957,c,1817,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1957,c,1818,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1957,c,1819,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1957,c,1820,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1957,c,1821,b)].
% 20.96/21.04 1958 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1746,a,1687,b)].
% 20.96/21.04 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1958,c,1814,a)].
% 20.96/21.04 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(1958,c,1815,a)].
% 20.96/21.04 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1958,c,1817,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1958,c,1818,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1958,c,1819,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1958,c,1820,b)].
% 20.96/21.04 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1958,c,1821,b)].
% 20.96/21.04 1959 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1747,a,1687,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(1959,c,1814,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(1959,c,1815,a)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1959,c,1817,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1959,c,1818,b)].
% 20.96/21.04 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1959,c,1819,b)].
% 20.96/21.05 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1959,c,1820,b)].
% 20.96/21.05 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1959,c,1821,b)].
% 20.96/21.05 1960 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1748,a,1687,b)].
% 20.96/21.05 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(1960,c,1814,a)].
% 20.96/21.05 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(1960,c,1815,a)].
% 20.96/21.05 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1960,c,1817,b)].
% 20.96/21.05 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(1960,c,1818,b)].
% 20.96/21.05 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(1960,c,1819,b)].
% 20.96/21.05 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1960,c,1820,b)].
% 20.96/21.05 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1960,c,1821,b)].
% 20.96/21.05 1961 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1773,a,1754,b)].
% 20.96/21.05 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(1961,c,1814,a)].
% 20.96/21.05 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(1961,c,1815,a)].
% 20.96/21.05 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1961,c,1817,b)].
% 20.96/21.05 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1961,c,1818,b)].
% 20.96/21.05 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1961,c,1819,b)].
% 20.96/21.05 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1961,c,1820,b)].
% 20.96/21.05 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1961,c,1821,b)].
% 20.96/21.05 1962 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(C). [resolve(1774,a,1754,b)].
% 20.96/21.05 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(1962,c,1814,a)].
% 20.96/21.05 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(1962,c,1815,a)].
% 20.96/21.05 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1962,c,1817,b)].
% 20.96/21.05 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(1962,c,1818,b)].
% 20.96/21.05 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(1962,c,1819,b)].
% 20.96/21.05 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(1962,c,1820,b)].
% 20.96/21.05 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1962,c,1821,b)].
% 20.96/21.05 1963 class_OrderedGroup_Oab__semigroup__add(A) | -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A). [resolve(1812,a,1754,b)].
% 20.96/21.05 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(1963,b,1814,a)].
% 20.96/21.05 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(1963,b,1815,a)].
% 20.96/21.05 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(1963,b,1818,b)].
% 20.96/21.05 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(1963,b,1819,b)].
% 20.96/21.05 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1963,b,1821,b)].
% 21.90/21.99 1964 -class_Ring__and__Field_Opordered__semiring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__semiring_1) # label(axiom). [assumption].
% 21.90/21.99 1965 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_40) # label(axiom). [assumption].
% 21.90/21.99 1966 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat_37) # label(axiom). [assumption].
% 21.90/21.99 1967 -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].
% 21.90/21.99 1968 -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].
% 21.90/21.99 1969 -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].
% 21.90/21.99 1970 -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].
% 21.90/21.99 1971 -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].
% 21.90/21.99 1972 -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].
% 21.90/21.99 1973 -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].
% 21.90/21.99 1974 -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].
% 21.90/21.99 1975 -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].
% 21.90/21.99 1976 -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].
% 21.90/21.99 1977 -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].
% 21.90/21.99 1978 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__semiring_2) # label(axiom). [assumption].
% 21.90/21.99 1979 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_5) # label(axiom). [assumption].
% 21.90/21.99 1980 -class_Ring__and__Field_Opordered__semiring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__semiring_6) # label(axiom). [assumption].
% 21.90/21.99 1981 class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint). [resolve(372,a,318,a)].
% 21.90/21.99 1982 class_Ring__and__Field_Opordered__semiring(tc_nat). [resolve(372,a,343,a)].
% 21.90/21.99 1983 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(372,a,344,b)].
% 21.90/21.99 1984 class_Ring__and__Field_Opordered__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(372,a,345,b)].
% 21.90/21.99 1985 -class_Ring__and__Field_Opordered__semiring(A) | c_plus(B,c_0,A) = B. [resolve(672,b,642,a)].
% 21.90/21.99 1986 -class_Ring__and__Field_Opordered__semiring(A) | c_plus(c_0,B,A) = B. [resolve(672,b,643,a)].
% 21.90/21.99 1987 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,B,A). [resolve(912,b,880,a)].
% 21.90/21.99 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1987,a,1967,b)].
% 21.90/21.99 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1987,a,1973,b)].
% 21.90/21.99 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1987,a,1974,b)].
% 21.90/22.00 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1987,a,1975,b)].
% 21.90/22.00 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1987,a,1976,b)].
% 21.90/22.00 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1987,a,1977,b)].
% 21.90/22.00 1988 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(912,b,881,a)].
% 21.90/22.00 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1988,a,1967,b)].
% 21.90/22.00 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1988,a,1973,b)].
% 21.90/22.00 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1988,a,1974,b)].
% 21.90/22.00 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1988,a,1975,b)].
% 21.90/22.00 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1988,a,1976,b)].
% 21.90/22.00 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1988,a,1977,b)].
% 21.90/22.00 1989 -class_Ring__and__Field_Opordered__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(912,b,882,a)].
% 21.90/22.00 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1989,a,1967,b)].
% 21.90/22.00 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1989,a,1973,b)].
% 21.90/22.00 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1989,a,1974,b)].
% 21.90/22.00 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1989,a,1975,b)].
% 21.90/22.00 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1989,a,1976,b)].
% 21.90/22.00 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1989,a,1977,b)].
% 21.90/22.00 1990 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(912,b,883,a)].
% 21.90/22.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1990,a,1967,b)].
% 21.90/22.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1990,a,1973,b)].
% 21.90/22.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1990,a,1974,b)].
% 21.90/22.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1990,a,1975,b)].
% 21.90/22.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1990,a,1976,b)].
% 21.90/22.00 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1990,a,1977,b)].
% 21.90/22.00 1991 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(912,b,884,a)].
% 21.90/22.00 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(1991,a,1967,b)].
% 21.90/22.00 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(1991,a,1973,b)].
% 21.92/22.01 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1991,a,1974,b)].
% 21.92/22.01 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1991,a,1975,b)].
% 21.92/22.01 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1991,a,1976,b)].
% 21.92/22.01 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1991,a,1977,b)].
% 21.92/22.01 1992 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(912,b,885,a)].
% 21.92/22.01 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1992,a,1967,b)].
% 21.92/22.01 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1992,a,1973,b)].
% 21.92/22.01 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1992,a,1974,b)].
% 21.92/22.01 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1992,a,1975,b)].
% 21.92/22.01 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1992,a,1976,b)].
% 21.92/22.01 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__ring(C). [resolve(1992,a,1977,b)].
% 21.92/22.01 1993 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(912,b,886,a)].
% 21.92/22.01 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1993,a,1967,b)].
% 21.92/22.01 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1993,a,1973,b)].
% 21.92/22.01 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1993,a,1974,b)].
% 21.92/22.01 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1993,a,1975,b)].
% 21.92/22.01 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1993,a,1976,b)].
% 21.92/22.01 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1993,a,1977,b)].
% 21.92/22.01 1994 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(912,b,887,a)].
% 21.92/22.01 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Olordered__ring(C). [resolve(1994,a,1967,b)].
% 21.92/22.01 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1994,a,1973,b)].
% 21.95/22.10 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_Opordered__cancel__semiring(C). [resolve(1994,a,1974,b)].
% 21.95/22.10 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_Opordered__comm__ring(C). [resolve(1994,a,1975,b)].
% 21.95/22.10 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_Opordered__comm__semiring(C). [resolve(1994,a,1976,b)].
% 21.95/22.10 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_Opordered__ring(C). [resolve(1994,a,1977,b)].
% 21.95/22.10 1995 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(912,b,888,a)].
% 21.95/22.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1995,a,1967,b)].
% 21.95/22.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1995,a,1973,b)].
% 21.95/22.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1995,a,1974,b)].
% 21.95/22.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(1995,a,1975,b)].
% 21.95/22.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1995,a,1976,b)].
% 21.95/22.10 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1995,a,1977,b)].
% 21.95/22.10 1996 -class_Ring__and__Field_Opordered__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(912,b,889,a)].
% 21.95/22.10 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1996,a,1967,b)].
% 21.95/22.10 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1996,a,1973,b)].
% 21.95/22.10 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1996,a,1974,b)].
% 21.95/22.10 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1996,a,1975,b)].
% 21.95/22.10 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1996,a,1976,b)].
% 21.95/22.10 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1996,a,1977,b)].
% 21.95/22.10 1997 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(B,B,A). [resolve(912,b,890,a)].
% 21.95/22.10 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1997,a,1967,b)].
% 21.95/22.10 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1997,a,1973,b)].
% 21.95/22.10 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1997,a,1974,b)].
% 21.95/22.10 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(1997,a,1975,b)].
% 21.95/22.10 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1997,a,1976,b)].
% 21.95/22.10 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1997,a,1977,b)].
% 21.95/22.10 1998 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1051,b,1010,a)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(1998,a,1967,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(1998,a,1973,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(1998,a,1974,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(1998,a,1975,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(1998,a,1976,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(1998,a,1977,b)].
% 21.95/22.11 1999 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1051,b,1011,a)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(1999,a,1967,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(1999,a,1973,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(1999,a,1974,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(1999,a,1975,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(1999,a,1976,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(1999,a,1977,b)].
% 21.95/22.11 2000 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1051,b,1012,a)].
% 21.95/22.11 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2000,a,1967,b)].
% 21.95/22.11 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2000,a,1973,b)].
% 21.95/22.11 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2000,a,1974,b)].
% 21.95/22.11 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2000,a,1975,b)].
% 21.95/22.11 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2000,a,1976,b)].
% 21.95/22.11 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2000,a,1977,b)].
% 21.95/22.11 2001 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1051,b,1013,a)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2001,a,1967,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2001,a,1973,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2001,a,1974,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2001,a,1975,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2001,a,1976,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2001,a,1977,b)].
% 21.95/22.11 2002 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1051,b,1014,a)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2002,a,1967,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2002,a,1973,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2002,a,1974,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2002,a,1975,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2002,a,1976,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2002,a,1977,b)].
% 21.95/22.11 2003 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1051,b,1015,a)].
% 21.95/22.11 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2003,a,1967,b)].
% 21.95/22.11 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2003,a,1973,b)].
% 21.95/22.11 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2003,a,1974,b)].
% 21.95/22.11 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2003,a,1975,b)].
% 21.95/22.11 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2003,a,1976,b)].
% 21.95/22.11 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2003,a,1977,b)].
% 21.95/22.11 2004 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1051,b,1016,a)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2004,a,1967,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2004,a,1973,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2004,a,1974,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2004,a,1975,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2004,a,1976,b)].
% 21.95/22.11 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2004,a,1977,b)].
% 21.95/22.11 2005 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1051,b,1017,a)].
% 21.95/22.11 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2005,a,1967,b)].
% 21.95/22.11 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2005,a,1973,b)].
% 22.04/22.12 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2005,a,1974,b)].
% 22.04/22.12 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2005,a,1975,b)].
% 22.04/22.12 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2005,a,1976,b)].
% 22.04/22.12 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2005,a,1977,b)].
% 22.04/22.12 2006 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1051,b,1018,a)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2006,a,1967,b)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2006,a,1973,b)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2006,a,1974,b)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2006,a,1975,b)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2006,a,1976,b)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2006,a,1977,b)].
% 22.04/22.12 2007 -class_Ring__and__Field_Opordered__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1051,b,1019,a)].
% 22.04/22.12 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2007,a,1967,b)].
% 22.04/22.12 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2007,a,1973,b)].
% 22.04/22.12 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2007,a,1974,b)].
% 22.04/22.12 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2007,a,1975,b)].
% 22.04/22.12 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2007,a,1976,b)].
% 22.04/22.12 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2007,a,1977,b)].
% 22.04/22.12 2008 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1051,b,1020,a)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2008,a,1967,b)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2008,a,1973,b)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2008,a,1974,b)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2008,a,1975,b)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2008,a,1976,b)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2008,a,1977,b)].
% 22.04/22.12 2009 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1051,b,1021,a)].
% 22.04/22.12 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2009,a,1967,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2009,a,1973,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2009,a,1974,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2009,a,1975,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2009,a,1976,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2009,a,1977,b)].
% 22.04/22.13 2010 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1051,b,1022,a)].
% 22.04/22.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2010,a,1967,b)].
% 22.04/22.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2010,a,1973,b)].
% 22.04/22.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2010,a,1974,b)].
% 22.04/22.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2010,a,1975,b)].
% 22.04/22.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2010,a,1976,b)].
% 22.04/22.13 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2010,a,1977,b)].
% 22.04/22.13 2011 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1051,b,1023,a)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2011,a,1967,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2011,a,1973,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2011,a,1974,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2011,a,1975,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2011,a,1976,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2011,a,1977,b)].
% 22.04/22.13 2012 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1051,b,1024,a)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2012,a,1967,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2012,a,1973,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2012,a,1974,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2012,a,1975,b)].
% 22.04/22.13 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2012,a,1976,b)].
% 22.04/22.14 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2012,a,1977,b)].
% 22.04/22.14 2013 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1051,b,1025,a)].
% 22.04/22.14 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2013,a,1967,b)].
% 22.04/22.14 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2013,a,1973,b)].
% 22.04/22.14 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2013,a,1974,b)].
% 22.04/22.14 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2013,a,1975,b)].
% 22.04/22.14 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2013,a,1976,b)].
% 22.04/22.14 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2013,a,1977,b)].
% 22.04/22.14 2014 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1051,b,1026,a)].
% 22.04/22.14 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2014,a,1967,b)].
% 22.04/22.14 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2014,a,1973,b)].
% 22.04/22.14 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2014,a,1974,b)].
% 22.04/22.14 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2014,a,1975,b)].
% 22.04/22.14 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2014,a,1976,b)].
% 22.04/22.14 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2014,a,1977,b)].
% 22.04/22.14 2015 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1051,b,1027,a)].
% 22.04/22.14 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2015,a,1967,b)].
% 22.04/22.14 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2015,a,1973,b)].
% 22.04/22.14 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2015,a,1974,b)].
% 22.04/22.14 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2015,a,1975,b)].
% 22.04/22.14 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2015,a,1976,b)].
% 22.04/22.14 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2015,a,1977,b)].
% 22.04/22.14 2016 -class_Ring__and__Field_Opordered__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1051,b,1028,a)].
% 22.04/22.14 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2016,a,1967,b)].
% 22.04/22.14 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2016,a,1973,b)].
% 22.04/22.14 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2016,a,1974,b)].
% 22.04/22.15 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2016,a,1975,b)].
% 22.04/22.15 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2016,a,1976,b)].
% 22.04/22.15 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2016,a,1977,b)].
% 22.04/22.15 2017 -class_Ring__and__Field_Opordered__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1051,b,1029,a)].
% 22.04/22.15 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2017,a,1967,b)].
% 22.04/22.15 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2017,a,1973,b)].
% 22.04/22.15 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2017,a,1974,b)].
% 22.04/22.15 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2017,a,1975,b)].
% 22.04/22.15 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2017,a,1976,b)].
% 22.04/22.15 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2017,a,1977,b)].
% 22.04/22.15 2018 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1108,a,1129,b)].
% 22.04/22.15 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2018,b,1967,b)].
% 22.04/22.15 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2018,b,1971,b)].
% 22.04/22.15 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2018,b,1972,b)].
% 22.04/22.15 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2018,b,1974,b)].
% 22.04/22.15 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2018,b,1976,b)].
% 22.04/22.15 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2018,b,1977,b)].
% 22.04/22.15 2019 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1132,a,1129,b)].
% 22.04/22.15 2020 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1133,a,1129,b)].
% 22.04/22.15 2021 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__semiring(A). [resolve(1135,a,1129,b)].
% 22.04/22.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2021,b,1967,b)].
% 22.04/22.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2021,b,1971,b)].
% 22.04/22.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2021,b,1972,b)].
% 22.04/22.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2021,b,1974,b)].
% 22.04/22.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2021,b,1976,b)].
% 22.04/22.15 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2021,b,1977,b)].
% 22.04/22.15 2022 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(1148,a,1129,b)].
% 22.04/22.15 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2022,b,1967,b)].
% 22.04/22.15 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2022,b,1971,b)].
% 22.04/22.15 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2022,b,1972,b)].
% 22.04/22.15 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2022,b,1974,b)].
% 22.04/22.15 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2022,b,1976,b)].
% 22.50/22.62 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(2022,b,1977,b)].
% 22.50/22.62 2023 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__semiring(B). [resolve(1149,a,1129,b)].
% 22.50/22.62 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2023,b,1967,b)].
% 22.50/22.62 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2023,b,1971,b)].
% 22.50/22.62 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2023,b,1972,b)].
% 22.50/22.62 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2023,b,1974,b)].
% 22.50/22.62 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2023,b,1976,b)].
% 22.50/22.62 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(2023,b,1977,b)].
% 22.50/22.62 2024 -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].
% 22.50/22.62 2025 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_41) # label(axiom). [assumption].
% 22.50/22.62 2026 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat_38) # label(axiom). [assumption].
% 22.50/22.62 2027 -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].
% 22.50/22.62 2028 -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].
% 22.50/22.62 2029 -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].
% 22.50/22.62 2030 -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].
% 22.50/22.62 2031 -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].
% 22.50/22.62 2032 -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].
% 22.50/22.62 2033 -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].
% 22.50/22.62 2034 -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].
% 22.50/22.62 2035 -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].
% 22.50/22.62 2036 -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].
% 22.50/22.62 2037 -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].
% 22.50/22.62 2038 class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint). [resolve(370,a,318,a)].
% 22.50/22.62 2039 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat). [resolve(370,a,343,a)].
% 22.50/22.62 2040 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(370,a,344,b)].
% 22.50/22.62 2041 class_Ring__and__Field_Opordered__cancel__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(370,a,345,b)].
% 22.50/22.62 2042 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,c_0,A) = B. [resolve(668,b,642,a)].
% 22.50/22.62 2043 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(c_0,B,A) = B. [resolve(668,b,643,a)].
% 22.67/22.73 2044 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(751,b,726,a)].
% 22.67/22.73 2045 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(751,b,727,a)].
% 22.67/22.73 2046 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,B,A). [resolve(908,b,880,a)].
% 22.67/22.73 2047 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(908,b,881,a)].
% 22.67/22.73 2048 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(908,b,882,a)].
% 22.67/22.73 2049 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(908,b,883,a)].
% 22.67/22.73 2050 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(908,b,884,a)].
% 22.67/22.73 2051 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(908,b,885,a)].
% 22.67/22.73 2052 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(908,b,886,a)].
% 22.67/22.73 2053 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(908,b,887,a)].
% 22.67/22.73 2054 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(908,b,888,a)].
% 22.67/22.73 2055 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(908,b,889,a)].
% 22.67/22.73 2056 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(B,B,A). [resolve(908,b,890,a)].
% 22.67/22.73 2057 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(982,b,967,a)].
% 22.67/22.73 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2057,a,2027,b)].
% 22.67/22.73 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2057,a,2028,b)].
% 22.67/22.73 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2057,a,2031,b)].
% 22.67/22.73 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2057,a,2032,b)].
% 22.67/22.73 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2057,a,2033,b)].
% 22.67/22.73 2058 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(982,b,968,a)].
% 22.67/22.73 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2058,a,2027,b)].
% 22.67/22.73 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2058,a,2028,b)].
% 22.67/22.73 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2058,a,2031,b)].
% 22.67/22.73 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2058,a,2032,b)].
% 22.67/22.73 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2058,a,2033,b)].
% 22.67/22.73 2059 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(988,a,982,b)].
% 22.67/22.73 2060 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(989,a,982,b)].
% 22.67/22.73 2061 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(991,a,982,b)].
% 22.67/22.73 2062 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(992,a,982,b)].
% 22.67/22.73 2063 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1005,a,982,b)].
% 22.74/22.82 2064 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1006,a,982,b)].
% 22.74/22.82 2065 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1007,a,982,b)].
% 22.74/22.82 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(2065,c,2027,b)].
% 22.74/22.82 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2065,c,2033,b)].
% 22.74/22.82 2066 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1008,a,982,b)].
% 22.74/22.82 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(2066,c,2027,b)].
% 22.74/22.82 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2066,c,2033,b)].
% 22.74/22.82 2067 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1047,b,1010,a)].
% 22.74/22.82 2068 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1047,b,1011,a)].
% 22.74/22.82 2069 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1047,b,1012,a)].
% 22.74/22.82 2070 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1047,b,1013,a)].
% 22.74/22.82 2071 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1047,b,1014,a)].
% 22.74/22.82 2072 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1047,b,1015,a)].
% 22.74/22.82 2073 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1047,b,1016,a)].
% 22.74/22.82 2074 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1047,b,1017,a)].
% 22.74/22.82 2075 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1047,b,1018,a)].
% 22.74/22.82 2076 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1047,b,1019,a)].
% 22.74/22.82 2077 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1047,b,1020,a)].
% 22.74/22.82 2078 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1047,b,1021,a)].
% 22.74/22.82 2079 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1047,b,1022,a)].
% 22.74/22.82 2080 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1047,b,1023,a)].
% 22.74/22.82 2081 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1047,b,1024,a)].
% 22.74/22.82 2082 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1047,b,1025,a)].
% 22.74/22.82 2083 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1047,b,1026,a)].
% 22.74/22.82 2084 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1047,b,1027,a)].
% 22.74/22.82 2085 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1047,b,1028,a)].
% 22.74/22.82 2086 -class_Ring__and__Field_Opordered__cancel__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1047,b,1029,a)].
% 22.89/22.97 2087 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1267,a,1209,a)].
% 22.89/22.97 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2087,a,2033,b)].
% 22.89/22.97 2088 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1267,a,1213,a)].
% 22.89/22.97 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2088,a,2027,b)].
% 22.89/22.97 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2088,a,2032,b)].
% 22.89/22.97 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2088,a,2033,b)].
% 22.89/22.97 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2088,a,2037,b)].
% 22.89/22.97 2089 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1987,a,1974,b)].
% 22.89/22.97 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2089,b,2025,a)].
% 22.89/22.97 Derived: -c_less(A,A,tc_nat). [resolve(2089,b,2026,a)].
% 22.89/22.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2089,b,2027,b)].
% 22.89/22.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2089,b,2028,b)].
% 22.89/22.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2089,b,2029,b)].
% 22.89/22.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2089,b,2030,b)].
% 22.89/22.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2089,b,2031,b)].
% 22.89/22.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2089,b,2032,b)].
% 22.89/22.97 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2089,b,2033,b)].
% 22.89/22.97 2090 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1988,a,1974,b)].
% 22.89/22.97 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2090,c,2025,a)].
% 22.89/22.97 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2090,c,2026,a)].
% 22.89/22.97 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2090,c,2027,b)].
% 22.89/22.97 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2090,c,2028,b)].
% 22.89/22.97 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2090,c,2029,b)].
% 22.89/22.97 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2090,c,2030,b)].
% 22.89/22.97 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2090,c,2031,b)].
% 22.89/22.97 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2090,c,2032,b)].
% 22.89/22.97 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2090,c,2033,b)].
% 22.89/22.97 2091 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1989,a,1974,b)].
% 22.89/22.97 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2091,b,2025,a)].
% 22.89/22.97 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2091,b,2026,a)].
% 22.89/22.97 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2091,b,2027,b)].
% 22.89/22.97 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2091,b,2028,b)].
% 22.89/22.97 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2091,b,2029,b)].
% 22.89/22.97 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2091,b,2030,b)].
% 22.89/22.97 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2091,b,2031,b)].
% 22.89/22.97 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2091,b,2032,b)].
% 22.89/22.97 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2091,b,2033,b)].
% 22.89/22.97 2092 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1990,a,1974,b)].
% 22.89/22.97 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2092,c,2025,a)].
% 22.89/22.97 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2092,c,2026,a)].
% 22.89/22.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2092,c,2027,b)].
% 22.89/22.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2092,c,2028,b)].
% 22.89/22.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2092,c,2029,b)].
% 22.89/22.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2092,c,2030,b)].
% 22.89/22.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2092,c,2031,b)].
% 22.89/22.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2092,c,2032,b)].
% 22.89/22.97 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2092,c,2033,b)].
% 22.89/22.97 2093 -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(1991,a,1974,b)].
% 22.89/22.97 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(2093,c,2025,a)].
% 22.89/22.97 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(2093,c,2026,a)].
% 22.89/22.97 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_Olordered__ring(B). [resolve(2093,c,2027,b)].
% 22.89/22.97 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_Oordered__comm__semiring__strict(B). [resolve(2093,c,2028,b)].
% 22.89/22.97 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_Oordered__field(B). [resolve(2093,c,2029,b)].
% 22.89/22.97 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_Oordered__idom(B). [resolve(2093,c,2030,b)].
% 22.89/22.97 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_Oordered__ring__strict(B). [resolve(2093,c,2031,b)].
% 22.89/22.97 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_Oordered__semiring__strict(B). [resolve(2093,c,2032,b)].
% 22.89/22.97 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(2093,c,2033,b)].
% 22.89/22.98 2094 -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(1992,a,1974,b)].
% 22.89/22.98 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(2094,c,2025,a)].
% 22.89/22.98 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(2094,c,2026,a)].
% 22.89/22.98 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(2094,c,2027,b)].
% 22.89/22.98 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(2094,c,2028,b)].
% 22.89/22.98 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(2094,c,2029,b)].
% 22.89/22.98 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(2094,c,2030,b)].
% 22.89/22.98 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(2094,c,2031,b)].
% 22.89/22.98 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(2094,c,2032,b)].
% 22.89/22.98 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(2094,c,2033,b)].
% 22.89/22.98 2095 -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(1993,a,1974,b)].
% 22.89/22.98 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(2095,c,2025,a)].
% 22.89/22.98 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(2095,c,2026,a)].
% 22.89/22.98 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(2095,c,2027,b)].
% 22.89/22.98 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(2095,c,2028,b)].
% 22.89/22.98 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(2095,c,2029,b)].
% 22.89/22.98 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(2095,c,2030,b)].
% 22.89/22.98 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(2095,c,2031,b)].
% 22.89/22.98 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(2095,c,2032,b)].
% 22.89/22.98 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(2095,c,2033,b)].
% 22.89/22.98 2096 -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(1994,a,1974,b)].
% 22.89/22.98 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(2096,c,2025,a)].
% 22.89/22.98 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(2096,c,2026,a)].
% 22.89/22.98 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(2096,c,2027,b)].
% 22.89/22.98 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(2096,c,2028,b)].
% 22.89/22.98 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(2096,c,2029,b)].
% 22.89/22.98 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(2096,c,2030,b)].
% 22.89/22.98 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(2096,c,2031,b)].
% 22.89/22.98 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(2096,c,2032,b)].
% 22.89/22.98 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(2096,c,2033,b)].
% 22.89/22.98 2097 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(1995,a,1974,b)].
% 22.89/22.98 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2097,c,2025,a)].
% 22.89/22.98 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2097,c,2026,a)].
% 22.89/22.98 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2097,c,2027,b)].
% 22.89/22.98 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2097,c,2028,b)].
% 22.89/22.98 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2097,c,2029,b)].
% 22.89/22.98 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2097,c,2030,b)].
% 22.89/22.98 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2097,c,2031,b)].
% 22.89/22.98 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2097,c,2032,b)].
% 22.89/22.98 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2097,c,2033,b)].
% 22.89/22.98 2098 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1996,a,1974,b)].
% 22.89/22.98 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2098,b,2025,a)].
% 22.89/22.98 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(2098,b,2026,a)].
% 22.89/22.98 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2098,b,2027,b)].
% 22.89/22.98 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2098,b,2028,b)].
% 22.89/22.99 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2098,b,2029,b)].
% 22.89/22.99 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2098,b,2030,b)].
% 22.89/22.99 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2098,b,2031,b)].
% 22.89/22.99 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2098,b,2032,b)].
% 22.89/22.99 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2098,b,2033,b)].
% 22.89/22.99 2099 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(1997,a,1974,b)].
% 22.89/22.99 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2099,b,2025,a)].
% 22.89/22.99 Derived: c_lessequals(A,A,tc_nat). [resolve(2099,b,2026,a)].
% 22.89/22.99 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2099,b,2027,b)].
% 22.89/22.99 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2099,b,2028,b)].
% 22.89/22.99 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2099,b,2029,b)].
% 22.89/22.99 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2099,b,2030,b)].
% 22.89/22.99 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2099,b,2031,b)].
% 22.89/22.99 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2099,b,2032,b)].
% 22.89/22.99 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2099,b,2033,b)].
% 22.89/22.99 2100 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(1998,a,1974,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2100,c,2025,a)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2100,c,2026,a)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2100,c,2027,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2100,c,2028,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2100,c,2029,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2100,c,2030,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2100,c,2031,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2100,c,2032,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2100,c,2033,b)].
% 22.89/22.99 2101 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(1999,a,1974,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2101,c,2025,a)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2101,c,2026,a)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2101,c,2027,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2101,c,2028,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2101,c,2029,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2101,c,2030,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2101,c,2031,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2101,c,2032,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2101,c,2033,b)].
% 22.89/22.99 2102 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2000,a,1974,b)].
% 22.89/22.99 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2102,d,2025,a)].
% 22.89/22.99 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(2102,d,2026,a)].
% 22.89/22.99 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2102,d,2027,b)].
% 22.89/22.99 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2102,d,2028,b)].
% 22.89/22.99 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2102,d,2029,b)].
% 22.89/22.99 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2102,d,2030,b)].
% 22.89/22.99 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2102,d,2031,b)].
% 22.89/22.99 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2102,d,2032,b)].
% 22.89/22.99 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2102,d,2033,b)].
% 22.89/22.99 2103 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2001,a,1974,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2103,c,2025,a)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2103,c,2026,a)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2103,c,2027,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2103,c,2028,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2103,c,2029,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2103,c,2030,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2103,c,2031,b)].
% 22.89/22.99 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2103,c,2032,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2103,c,2033,b)].
% 22.89/23.00 2104 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2002,a,1974,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2104,c,2025,a)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2104,c,2026,a)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2104,c,2027,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2104,c,2028,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2104,c,2029,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2104,c,2030,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2104,c,2031,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2104,c,2032,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2104,c,2033,b)].
% 22.89/23.00 2105 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2003,a,1974,b)].
% 22.89/23.00 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2105,d,2025,a)].
% 22.89/23.00 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(2105,d,2026,a)].
% 22.89/23.00 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2105,d,2027,b)].
% 22.89/23.00 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2105,d,2028,b)].
% 22.89/23.00 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2105,d,2029,b)].
% 22.89/23.00 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2105,d,2030,b)].
% 22.89/23.00 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2105,d,2031,b)].
% 22.89/23.00 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2105,d,2032,b)].
% 22.89/23.00 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2105,d,2033,b)].
% 22.89/23.00 2106 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2004,a,1974,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2106,c,2025,a)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2106,c,2026,a)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2106,c,2027,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2106,c,2028,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2106,c,2029,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2106,c,2030,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2106,c,2031,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2106,c,2032,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2106,c,2033,b)].
% 22.89/23.00 2107 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2005,a,1974,b)].
% 22.89/23.00 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2107,c,2025,a)].
% 22.89/23.00 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2107,c,2026,a)].
% 22.89/23.00 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2107,c,2027,b)].
% 22.89/23.00 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2107,c,2028,b)].
% 22.89/23.00 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2107,c,2029,b)].
% 22.89/23.00 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2107,c,2030,b)].
% 22.89/23.00 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2107,c,2031,b)].
% 22.89/23.00 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2107,c,2032,b)].
% 22.89/23.00 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2107,c,2033,b)].
% 22.89/23.00 2108 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2006,a,1974,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2108,c,2025,a)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2108,c,2026,a)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2108,c,2027,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2108,c,2028,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2108,c,2029,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2108,c,2030,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2108,c,2031,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2108,c,2032,b)].
% 22.89/23.00 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2108,c,2033,b)].
% 22.89/23.00 2109 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2007,a,1974,b)].
% 22.89/23.00 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2109,c,2025,a)].
% 22.89/23.00 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2109,c,2026,a)].
% 22.89/23.00 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2109,c,2027,b)].
% 22.93/23.01 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2109,c,2028,b)].
% 22.93/23.01 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2109,c,2029,b)].
% 22.93/23.01 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2109,c,2030,b)].
% 22.93/23.01 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2109,c,2031,b)].
% 22.93/23.01 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2109,c,2032,b)].
% 22.93/23.01 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2109,c,2033,b)].
% 22.93/23.01 2110 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2008,a,1974,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2110,c,2025,a)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2110,c,2026,a)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2110,c,2027,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2110,c,2028,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2110,c,2029,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2110,c,2030,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2110,c,2031,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2110,c,2032,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2110,c,2033,b)].
% 22.93/23.01 2111 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2009,a,1974,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2111,c,2025,a)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2111,c,2026,a)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2111,c,2027,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2111,c,2028,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2111,c,2029,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2111,c,2030,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2111,c,2031,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2111,c,2032,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2111,c,2033,b)].
% 22.93/23.01 2112 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2010,a,1974,b)].
% 22.93/23.01 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2112,d,2025,a)].
% 22.93/23.01 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(2112,d,2026,a)].
% 22.93/23.01 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2112,d,2027,b)].
% 22.93/23.01 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2112,d,2028,b)].
% 22.93/23.01 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2112,d,2029,b)].
% 22.93/23.01 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2112,d,2030,b)].
% 22.93/23.01 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2112,d,2031,b)].
% 22.93/23.01 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2112,d,2032,b)].
% 22.93/23.01 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2112,d,2033,b)].
% 22.93/23.01 2113 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2011,a,1974,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2113,c,2025,a)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2113,c,2026,a)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2113,c,2027,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2113,c,2028,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2113,c,2029,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2113,c,2030,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2113,c,2031,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2113,c,2032,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2113,c,2033,b)].
% 22.93/23.01 2114 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__semiring(D). [resolve(2012,a,1974,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2114,c,2025,a)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2114,c,2026,a)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2114,c,2027,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2114,c,2028,b)].
% 22.93/23.01 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2114,c,2029,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2114,c,2030,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2114,c,2031,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2114,c,2032,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2114,c,2033,b)].
% 22.93/23.02 2115 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2013,a,1974,b)].
% 22.93/23.02 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2115,d,2025,a)].
% 22.93/23.02 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(2115,d,2026,a)].
% 22.93/23.02 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2115,d,2027,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2115,d,2028,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2115,d,2029,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2115,d,2030,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2115,d,2031,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2115,d,2032,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2115,d,2033,b)].
% 22.93/23.02 2116 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2014,a,1974,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2116,c,2025,a)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2116,c,2026,a)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2116,c,2027,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2116,c,2028,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2116,c,2029,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2116,c,2030,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2116,c,2031,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2116,c,2032,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2116,c,2033,b)].
% 22.93/23.02 2117 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2015,a,1974,b)].
% 22.93/23.02 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2117,c,2025,a)].
% 22.93/23.02 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2117,c,2026,a)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2117,c,2027,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2117,c,2028,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2117,c,2029,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2117,c,2030,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2117,c,2031,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2117,c,2032,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2117,c,2033,b)].
% 22.93/23.02 2118 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2016,a,1974,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2118,c,2025,a)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2118,c,2026,a)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2118,c,2027,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2118,c,2028,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2118,c,2029,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2118,c,2030,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2118,c,2031,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2118,c,2032,b)].
% 22.93/23.02 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2118,c,2033,b)].
% 22.93/23.02 2119 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__semiring(C). [resolve(2017,a,1974,b)].
% 22.93/23.02 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2119,c,2025,a)].
% 22.93/23.02 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2119,c,2026,a)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2119,c,2027,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2119,c,2028,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2119,c,2029,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2119,c,2030,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2119,c,2031,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2119,c,2032,b)].
% 22.93/23.02 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2119,c,2033,b)].
% 22.93/23.02 2120 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2018,b,1974,b)].
% 22.93/23.03 Derived: class_Ring__and__Field_Osemiring(tc_IntDef_Oint). [resolve(2120,b,2025,a)].
% 22.93/23.03 Derived: class_Ring__and__Field_Osemiring(tc_nat). [resolve(2120,b,2026,a)].
% 22.93/23.03 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2120,b,2027,b)].
% 22.93/23.03 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2120,b,2028,b)].
% 22.93/23.03 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2120,b,2029,b)].
% 22.93/23.03 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2120,b,2030,b)].
% 22.93/23.03 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2120,b,2031,b)].
% 22.93/23.03 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2120,b,2032,b)].
% 22.93/23.03 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2120,b,2033,b)].
% 22.93/23.03 2121 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__semiring(A). [resolve(2021,b,1974,b)].
% 22.93/23.03 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2121,b,2025,a)].
% 22.93/23.03 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2121,b,2026,a)].
% 22.93/23.03 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2121,b,2027,b)].
% 22.93/23.03 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2121,b,2028,b)].
% 22.93/23.03 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2121,b,2029,b)].
% 22.93/23.03 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2121,b,2030,b)].
% 22.93/23.03 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2121,b,2031,b)].
% 22.93/23.03 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2121,b,2032,b)].
% 22.93/23.03 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2121,b,2033,b)].
% 22.93/23.03 2122 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2022,b,1974,b)].
% 22.93/23.03 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(2122,b,2025,a)].
% 22.93/23.03 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(2122,b,2026,a)].
% 22.93/23.03 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2122,b,2027,b)].
% 22.93/23.03 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2122,b,2028,b)].
% 22.93/23.03 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2122,b,2029,b)].
% 22.93/23.03 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2122,b,2030,b)].
% 22.93/23.03 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2122,b,2031,b)].
% 22.93/23.03 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2122,b,2032,b)].
% 22.93/23.03 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2122,b,2033,b)].
% 22.93/23.03 2123 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__semiring(B). [resolve(2023,b,1974,b)].
% 22.93/23.03 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(2123,b,2025,a)].
% 22.93/23.03 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(2123,b,2026,a)].
% 22.93/23.03 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2123,b,2027,b)].
% 22.93/23.03 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2123,b,2028,b)].
% 22.93/23.03 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2123,b,2029,b)].
% 22.93/23.03 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2123,b,2030,b)].
% 22.93/23.03 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2123,b,2031,b)].
% 23.18/23.28 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2123,b,2032,b)].
% 23.18/23.28 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2123,b,2033,b)].
% 23.18/23.28 2124 -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].
% 23.18/23.28 2125 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_42) # label(axiom). [assumption].
% 23.18/23.28 2126 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat_39) # label(axiom). [assumption].
% 23.18/23.28 2127 -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].
% 23.18/23.28 2128 -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].
% 23.18/23.28 2129 -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].
% 23.18/23.28 2130 -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].
% 23.18/23.28 2131 -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].
% 23.18/23.28 2132 -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].
% 23.18/23.28 2133 -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].
% 23.18/23.28 2134 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(72,b,2,a)].
% 23.18/23.28 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2134,a,2127,b)].
% 23.18/23.28 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2134,a,2130,b)].
% 23.18/23.28 2135 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(72,b,3,a)].
% 23.18/23.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2135,a,2127,b)].
% 23.18/23.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2135,a,2130,b)].
% 23.18/23.28 2136 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(72,b,4,a)].
% 23.18/23.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2136,a,2127,b)].
% 23.18/23.28 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2136,a,2130,b)].
% 23.18/23.28 2137 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(72,b,5,a)].
% 23.18/23.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2137,a,2127,b)].
% 23.18/23.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2137,a,2130,b)].
% 23.18/23.29 2138 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(72,b,6,a)].
% 23.18/23.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2138,a,2127,b)].
% 23.18/23.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2138,a,2130,b)].
% 23.18/23.29 2139 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(72,b,7,a)].
% 23.18/23.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2139,a,2127,b)].
% 23.18/23.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2139,a,2130,b)].
% 23.18/23.29 2140 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(72,b,8,a)].
% 23.18/23.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2140,a,2127,b)].
% 23.18/23.29 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2140,a,2130,b)].
% 23.18/23.29 2141 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(72,b,9,a)].
% 23.18/23.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2141,a,2127,b)].
% 23.18/23.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2141,a,2130,b)].
% 23.18/23.29 2142 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(72,b,10,a)].
% 23.18/23.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2142,a,2127,b)].
% 23.18/23.29 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2142,a,2130,b)].
% 23.18/23.29 2143 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(72,b,11,a)].
% 23.23/23.30 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2143,a,2127,b)].
% 23.23/23.30 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2143,a,2130,b)].
% 23.23/23.30 2144 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(72,b,12,a)].
% 23.23/23.30 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2144,a,2127,b)].
% 23.23/23.30 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2144,a,2130,b)].
% 23.23/23.30 2145 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(72,b,13,a)].
% 23.23/23.30 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2145,a,2127,b)].
% 23.23/23.30 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2145,a,2130,b)].
% 23.23/23.30 2146 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(72,b,14,a)].
% 23.23/23.30 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2146,a,2127,b)].
% 23.23/23.30 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2146,a,2130,b)].
% 23.23/23.30 2147 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(72,b,15,a)].
% 23.23/23.30 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2147,a,2127,b)].
% 23.23/23.30 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2147,a,2130,b)].
% 23.23/23.30 2148 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(72,b,16,a)].
% 23.23/23.30 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2148,a,2127,b)].
% 23.23/23.30 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2148,a,2130,b)].
% 23.23/23.30 2149 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(72,b,17,a)].
% 23.23/23.31 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2149,a,2127,b)].
% 23.23/23.31 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2149,a,2130,b)].
% 23.23/23.31 2150 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(72,b,18,a)].
% 23.23/23.31 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2150,a,2127,b)].
% 23.23/23.31 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2150,a,2130,b)].
% 23.23/23.31 2151 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(72,b,19,a)].
% 23.23/23.31 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2151,a,2127,b)].
% 23.23/23.31 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2151,a,2130,b)].
% 23.23/23.31 2152 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(72,b,20,a)].
% 23.23/23.31 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2152,a,2127,b)].
% 23.23/23.31 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2152,a,2130,b)].
% 23.23/23.31 2153 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(72,b,21,a)].
% 23.23/23.31 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2153,a,2127,b)].
% 23.23/23.31 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2153,a,2130,b)].
% 23.23/23.31 2154 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(72,b,22,a)].
% 23.23/23.31 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2154,a,2127,b)].
% 23.23/23.31 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2154,a,2130,b)].
% 23.23/23.31 2155 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(72,b,23,a)].
% 23.23/23.31 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2155,a,2127,b)].
% 23.23/23.31 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2155,a,2130,b)].
% 23.23/23.32 2156 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(72,b,24,a)].
% 23.23/23.32 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2156,a,2127,b)].
% 23.23/23.32 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2156,a,2130,b)].
% 23.23/23.32 2157 -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(72,b,25,b)].
% 23.23/23.32 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2157,a,2127,b)].
% 23.23/23.32 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2157,a,2130,b)].
% 23.23/23.32 2158 -class_Ring__and__Field_Oordered__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(72,b,26,b)].
% 23.23/23.32 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2158,a,2127,b)].
% 23.23/23.32 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2158,a,2130,b)].
% 23.23/23.32 2159 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(72,b,27,a)].
% 23.23/23.32 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2159,a,2127,b)].
% 23.23/23.32 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2159,a,2130,b)].
% 23.23/23.32 2160 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(72,b,28,a)].
% 23.23/23.32 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2160,a,2127,b)].
% 23.23/23.32 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2160,a,2130,b)].
% 23.23/23.32 2161 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(72,b,29,a)].
% 23.23/23.32 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2161,a,2127,b)].
% 23.23/23.32 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2161,a,2130,b)].
% 23.23/23.32 2162 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(72,b,30,a)].
% 23.23/23.32 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2162,a,2127,b)].
% 23.23/23.32 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2162,a,2130,b)].
% 23.23/23.32 2163 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(72,b,31,a)].
% 23.23/23.32 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2163,a,2127,b)].
% 23.23/23.32 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2163,a,2130,b)].
% 23.23/23.32 2164 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(72,b,32,a)].
% 23.23/23.34 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2164,a,2127,b)].
% 23.23/23.34 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2164,a,2130,b)].
% 23.23/23.34 2165 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(72,b,33,a)].
% 23.23/23.34 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2165,a,2127,b)].
% 23.23/23.34 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2165,a,2130,b)].
% 23.23/23.34 2166 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(72,b,34,a)].
% 23.23/23.34 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2166,a,2127,b)].
% 23.23/23.34 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2166,a,2130,b)].
% 23.23/23.34 2167 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(72,b,35,a)].
% 23.23/23.34 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2167,a,2127,b)].
% 23.23/23.34 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2167,a,2130,b)].
% 23.23/23.34 2168 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(72,b,36,a)].
% 23.23/23.34 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2168,a,2127,b)].
% 23.23/23.34 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2168,a,2130,b)].
% 23.23/23.34 2169 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(72,b,37,a)].
% 23.23/23.34 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2169,a,2127,b)].
% 23.23/23.34 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2169,a,2130,b)].
% 23.23/23.34 2170 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(72,b,38,a)].
% 23.23/23.34 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2170,a,2127,b)].
% 23.23/23.34 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2170,a,2130,b)].
% 23.23/23.34 2171 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(72,b,39,a)].
% 23.23/23.34 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2171,a,2127,b)].
% 23.23/23.34 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2171,a,2130,b)].
% 23.23/23.34 2172 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(72,b,40,a)].
% 23.23/23.34 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2172,a,2127,b)].
% 23.23/23.34 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2172,a,2130,b)].
% 23.29/23.35 2173 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(72,b,41,a)].
% 23.29/23.35 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2173,a,2127,b)].
% 23.29/23.35 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2173,a,2130,b)].
% 23.29/23.35 2174 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(72,b,42,a)].
% 23.29/23.35 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2174,a,2127,b)].
% 23.29/23.35 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2174,a,2130,b)].
% 23.29/23.35 2175 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(72,b,43,a)].
% 23.29/23.35 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2175,a,2127,b)].
% 23.29/23.35 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2175,a,2130,b)].
% 23.29/23.35 2176 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(72,b,44,a)].
% 23.29/23.35 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2176,a,2127,b)].
% 23.29/23.35 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2176,a,2130,b)].
% 23.29/23.35 2177 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(72,b,45,a)].
% 23.29/23.35 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2177,a,2127,b)].
% 23.29/23.35 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2177,a,2130,b)].
% 23.29/23.35 2178 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(72,b,46,a)].
% 23.29/23.35 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2178,a,2127,b)].
% 23.29/23.35 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2178,a,2130,b)].
% 23.29/23.35 2179 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(72,b,47,a)].
% 23.29/23.35 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2179,a,2127,b)].
% 23.29/23.35 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2179,a,2130,b)].
% 23.29/23.35 2180 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(72,b,48,a)].
% 23.29/23.35 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2180,a,2127,b)].
% 23.29/23.35 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2180,a,2130,b)].
% 23.29/23.35 2181 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(72,b,49,a)].
% 23.29/23.36 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2181,a,2127,b)].
% 23.29/23.36 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2181,a,2130,b)].
% 23.29/23.36 2182 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(72,b,50,a)].
% 23.29/23.36 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(2182,a,2127,b)].
% 23.29/23.36 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(2182,a,2130,b)].
% 23.29/23.36 2183 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(72,b,51,a)].
% 23.29/23.36 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(2183,a,2127,b)].
% 23.29/23.36 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(2183,a,2130,b)].
% 23.29/23.36 2184 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(72,b,52,a)].
% 23.29/23.36 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2184,a,2127,b)].
% 23.29/23.36 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2184,a,2130,b)].
% 23.29/23.36 2185 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(72,b,53,a)].
% 23.29/23.36 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2185,a,2127,b)].
% 23.29/23.36 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2185,a,2130,b)].
% 23.29/23.36 2186 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(72,b,54,a)].
% 23.29/23.36 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2186,a,2127,b)].
% 23.29/23.36 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2186,a,2130,b)].
% 23.29/23.36 2187 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(72,b,55,a)].
% 23.29/23.36 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2187,a,2127,b)].
% 23.39/23.51 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2187,a,2130,b)].
% 23.39/23.51 2188 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(72,b,56,a)].
% 23.39/23.51 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2188,a,2127,b)].
% 23.39/23.51 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2188,a,2130,b)].
% 23.39/23.51 2189 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(72,b,57,a)].
% 23.39/23.51 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2189,a,2127,b)].
% 23.39/23.51 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2189,a,2130,b)].
% 23.39/23.51 2190 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(72,b,58,a)].
% 23.39/23.51 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2190,a,2127,b)].
% 23.39/23.51 Derived: -c_lessequals(c_SetInterval_OlessThan(A,B),c_SetInterval_OlessThan(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2190,a,2130,b)].
% 23.39/23.51 2191 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(72,b,59,a)].
% 23.39/23.51 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(2191,a,2127,b)].
% 23.39/23.51 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(2191,a,2130,b)].
% 23.39/23.51 2192 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(289,b,273,a)].
% 23.39/23.51 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2192,a,2127,b)].
% 23.39/23.51 2193 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(312,b,296,a)].
% 23.39/23.51 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2193,a,2127,b)].
% 23.39/23.51 2194 class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint). [resolve(363,a,318,a)].
% 23.39/23.51 2195 class_Ring__and__Field_Oordered__semiring__strict(tc_nat). [resolve(363,a,343,a)].
% 23.39/23.51 2196 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(363,a,344,b)].
% 23.39/23.51 2197 class_Ring__and__Field_Oordered__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(363,a,345,b)].
% 23.39/23.51 2198 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,c_0,A) = B. [resolve(666,b,642,a)].
% 23.39/23.51 2199 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(c_0,B,A) = B. [resolve(666,b,643,a)].
% 23.39/23.51 2200 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(718,b,690,a)].
% 23.39/23.51 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2200,a,2127,b)].
% 23.39/23.52 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2200,a,2128,b)].
% 23.39/23.52 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2200,a,2129,b)].
% 23.39/23.52 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2200,a,2130,b)].
% 23.39/23.52 2201 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(718,b,691,a)].
% 23.39/23.52 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2201,a,2127,b)].
% 23.39/23.52 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2201,a,2128,b)].
% 23.39/23.52 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2201,a,2129,b)].
% 23.39/23.52 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2201,a,2130,b)].
% 23.39/23.52 2202 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(718,b,692,a)].
% 23.39/23.52 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2202,a,2127,b)].
% 23.39/23.52 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2202,a,2128,b)].
% 23.39/23.52 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2202,a,2129,b)].
% 23.39/23.52 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2202,a,2130,b)].
% 23.39/23.52 2203 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(718,b,693,a)].
% 23.39/23.52 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2203,a,2127,b)].
% 23.39/23.52 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2203,a,2128,b)].
% 23.39/23.52 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2203,a,2129,b)].
% 23.39/23.52 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2203,a,2130,b)].
% 23.39/23.52 2204 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(718,b,694,a)].
% 23.39/23.52 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2204,a,2127,b)].
% 23.39/23.52 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2204,a,2128,b)].
% 23.39/23.52 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2204,a,2129,b)].
% 23.39/23.52 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2204,a,2130,b)].
% 23.39/23.52 2205 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(718,b,695,a)].
% 23.39/23.52 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2205,a,2127,b)].
% 23.39/23.52 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2205,a,2128,b)].
% 23.39/23.52 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2205,a,2129,b)].
% 23.39/23.52 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2205,a,2130,b)].
% 23.54/23.61 2206 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(718,b,696,a)].
% 23.54/23.61 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2206,a,2127,b)].
% 23.54/23.61 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2206,a,2128,b)].
% 23.54/23.61 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2206,a,2129,b)].
% 23.54/23.61 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2206,a,2130,b)].
% 23.54/23.61 2207 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(718,b,697,a)].
% 23.54/23.61 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2207,a,2127,b)].
% 23.54/23.61 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2207,a,2128,b)].
% 23.54/23.61 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2207,a,2129,b)].
% 23.54/23.61 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2207,a,2130,b)].
% 23.54/23.61 2208 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(749,b,726,a)].
% 23.54/23.61 2209 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(749,b,727,a)].
% 23.54/23.61 2210 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,B,A). [resolve(906,b,880,a)].
% 23.54/23.61 2211 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(906,b,881,a)].
% 23.54/23.61 2212 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(906,b,882,a)].
% 23.54/23.61 2213 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(906,b,883,a)].
% 23.54/23.61 2214 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(906,b,884,a)].
% 23.54/23.61 2215 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(906,b,885,a)].
% 23.54/23.61 2216 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(906,b,886,a)].
% 23.54/23.61 2217 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(906,b,887,a)].
% 23.54/23.61 2218 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(906,b,888,a)].
% 23.54/23.61 2219 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(906,b,889,a)].
% 23.54/23.61 2220 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,B,A). [resolve(906,b,890,a)].
% 23.54/23.61 2221 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(980,b,967,a)].
% 23.54/23.61 2222 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(980,b,968,a)].
% 23.54/23.61 2223 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(988,a,980,b)].
% 23.54/23.61 2224 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(989,a,980,b)].
% 23.54/23.61 2225 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(991,a,980,b)].
% 23.70/23.79 2226 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(992,a,980,b)].
% 23.70/23.79 2227 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1005,a,980,b)].
% 23.70/23.79 2228 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1006,a,980,b)].
% 23.70/23.79 2229 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1007,a,980,b)].
% 23.70/23.79 2230 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1008,a,980,b)].
% 23.70/23.79 2231 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1045,b,1010,a)].
% 23.70/23.79 2232 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1045,b,1011,a)].
% 23.70/23.79 2233 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1045,b,1012,a)].
% 23.70/23.79 2234 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1045,b,1013,a)].
% 23.70/23.79 2235 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1045,b,1014,a)].
% 23.70/23.79 2236 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1045,b,1015,a)].
% 23.70/23.79 2237 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1045,b,1016,a)].
% 23.70/23.79 2238 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1045,b,1017,a)].
% 23.70/23.79 2239 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1045,b,1018,a)].
% 23.70/23.79 2240 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1045,b,1019,a)].
% 23.70/23.79 2241 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1045,b,1020,a)].
% 23.70/23.79 2242 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1045,b,1021,a)].
% 23.70/23.79 2243 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1045,b,1022,a)].
% 23.70/23.79 2244 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1045,b,1023,a)].
% 23.70/23.79 2245 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1045,b,1024,a)].
% 23.70/23.79 2246 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1045,b,1025,a)].
% 23.70/23.79 2247 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1045,b,1026,a)].
% 23.70/23.79 2248 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1045,b,1027,a)].
% 23.70/23.79 2249 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1045,b,1028,a)].
% 23.70/23.79 2250 -class_Ring__and__Field_Oordered__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1045,b,1029,a)].
% 23.70/23.79 2251 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1265,a,1209,a)].
% 23.70/23.79 2252 -class_Ring__and__Field_Oordered__semiring__strict(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1265,a,1213,a)].
% 23.70/23.79 2253 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1930,b,1821,b)].
% 23.79/23.84 2254 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1931,c,1821,b)].
% 23.79/23.84 2255 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1932,b,1821,b)].
% 23.79/23.84 2256 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1933,c,1821,b)].
% 23.79/23.84 2257 -c_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(1934,c,1821,b)].
% 23.79/23.84 2258 -c_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(1935,c,1821,b)].
% 23.79/23.84 2259 -c_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(1936,c,1821,b)].
% 23.79/23.84 2260 -c_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(1937,c,1821,b)].
% 23.79/23.84 2261 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1938,c,1821,b)].
% 23.79/23.84 2262 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1939,b,1821,b)].
% 23.79/23.84 2263 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(1940,b,1821,b)].
% 23.79/23.84 2264 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1941,c,1821,b)].
% 23.79/23.84 2265 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1942,c,1821,b)].
% 23.79/23.84 2266 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1943,d,1821,b)].
% 23.79/23.84 2267 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1944,c,1821,b)].
% 23.79/23.84 2268 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1945,c,1821,b)].
% 23.79/23.84 2269 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1946,d,1821,b)].
% 23.79/23.84 2270 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1947,c,1821,b)].
% 23.79/23.84 2271 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1948,c,1821,b)].
% 23.79/23.84 2272 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1949,c,1821,b)].
% 23.79/23.84 2273 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1950,c,1821,b)].
% 23.79/23.84 2274 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1951,c,1821,b)].
% 23.79/23.84 2275 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1952,c,1821,b)].
% 23.79/23.84 2276 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1953,d,1821,b)].
% 23.79/23.84 2277 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1954,c,1821,b)].
% 23.79/23.84 2278 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(1955,c,1821,b)].
% 23.79/23.89 2279 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1956,d,1821,b)].
% 23.79/23.89 2280 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1957,c,1821,b)].
% 23.79/23.89 2281 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1958,c,1821,b)].
% 23.79/23.89 2282 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1959,c,1821,b)].
% 23.79/23.89 2283 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1960,c,1821,b)].
% 23.79/23.89 2284 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1961,c,1821,b)].
% 23.79/23.89 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2284,c,2125,a)].
% 23.79/23.89 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(2284,c,2126,a)].
% 23.79/23.89 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2284,c,2127,b)].
% 23.79/23.89 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2284,c,2128,b)].
% 23.79/23.89 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2284,c,2129,b)].
% 23.79/23.89 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2284,c,2130,b)].
% 23.79/23.89 2285 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(1962,c,1821,b)].
% 23.79/23.89 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2285,c,2125,a)].
% 23.79/23.89 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(2285,c,2126,a)].
% 23.79/23.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2285,c,2127,b)].
% 23.79/23.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__field(C). [resolve(2285,c,2128,b)].
% 23.79/23.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__idom(C). [resolve(2285,c,2129,b)].
% 23.79/23.89 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2285,c,2130,b)].
% 23.79/23.89 2286 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(1963,b,1821,b)].
% 23.79/23.89 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(2286,b,2125,a)].
% 23.79/23.89 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(2286,b,2126,a)].
% 23.79/23.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2286,b,2127,b)].
% 23.79/23.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2286,b,2128,b)].
% 23.79/23.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2286,b,2129,b)].
% 23.79/23.89 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2286,b,2130,b)].
% 23.79/23.89 2287 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2018,b,1972,b)].
% 23.79/23.89 2288 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2021,b,1972,b)].
% 23.79/23.89 2289 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2022,b,1972,b)].
% 23.79/23.89 2290 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2023,b,1972,b)].
% 23.79/23.89 2291 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2057,a,2032,b)].
% 23.79/23.89 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2291,b,2125,a)].
% 23.79/23.89 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2291,b,2126,a)].
% 23.79/23.89 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2291,b,2127,b)].
% 23.79/23.90 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2291,b,2128,b)].
% 23.79/23.90 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2291,b,2129,b)].
% 23.79/23.90 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2291,b,2130,b)].
% 23.79/23.90 2292 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2058,a,2032,b)].
% 23.79/23.90 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2292,b,2125,a)].
% 23.79/23.90 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2292,b,2126,a)].
% 23.79/23.90 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2292,b,2127,b)].
% 23.79/23.90 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__field(B). [resolve(2292,b,2128,b)].
% 23.79/23.90 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__idom(B). [resolve(2292,b,2129,b)].
% 23.79/23.90 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2292,b,2130,b)].
% 23.79/23.90 2293 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2088,a,2032,b)].
% 23.79/23.90 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2293,b,2125,a)].
% 23.79/23.90 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2293,b,2126,a)].
% 23.79/23.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2293,b,2127,b)].
% 23.79/23.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2293,b,2128,b)].
% 23.79/23.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2293,b,2129,b)].
% 23.79/23.90 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2293,b,2130,b)].
% 23.79/23.90 2294 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2089,b,2032,b)].
% 23.79/23.90 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2294,b,2125,a)].
% 23.79/23.90 Derived: -c_less(A,A,tc_nat). [resolve(2294,b,2126,a)].
% 23.79/23.90 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2294,b,2127,b)].
% 23.79/23.90 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2294,b,2128,b)].
% 23.79/23.90 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2294,b,2129,b)].
% 23.79/23.90 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2294,b,2130,b)].
% 23.79/23.90 2295 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2090,c,2032,b)].
% 23.79/23.90 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2295,c,2125,a)].
% 23.79/23.90 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2295,c,2126,a)].
% 23.79/23.90 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2295,c,2127,b)].
% 23.79/23.90 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2295,c,2128,b)].
% 23.79/23.90 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2295,c,2129,b)].
% 23.79/23.90 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2295,c,2130,b)].
% 23.79/23.90 2296 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2091,b,2032,b)].
% 23.79/23.90 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2296,b,2125,a)].
% 23.79/23.90 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2296,b,2126,a)].
% 23.79/23.90 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2296,b,2127,b)].
% 23.79/23.90 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2296,b,2128,b)].
% 23.85/23.91 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2296,b,2129,b)].
% 23.85/23.91 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2296,b,2130,b)].
% 23.85/23.91 2297 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2092,c,2032,b)].
% 23.85/23.91 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2297,c,2125,a)].
% 23.85/23.91 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2297,c,2126,a)].
% 23.85/23.91 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2297,c,2127,b)].
% 23.85/23.91 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2297,c,2128,b)].
% 23.85/23.91 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2297,c,2129,b)].
% 23.85/23.91 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2297,c,2130,b)].
% 23.85/23.91 2298 -c_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(2093,c,2032,b)].
% 23.85/23.91 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(2298,c,2125,a)].
% 23.85/23.91 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(2298,c,2126,a)].
% 23.85/23.91 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(2298,c,2127,b)].
% 23.85/23.91 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(2298,c,2128,b)].
% 23.85/23.91 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(2298,c,2129,b)].
% 23.85/23.91 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(2298,c,2130,b)].
% 23.85/23.91 2299 -c_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(2094,c,2032,b)].
% 23.85/23.91 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(2299,c,2125,a)].
% 23.85/23.91 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(2299,c,2126,a)].
% 23.85/23.91 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(2299,c,2127,b)].
% 23.85/23.91 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(2299,c,2128,b)].
% 23.85/23.91 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(2299,c,2129,b)].
% 23.85/23.91 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(2299,c,2130,b)].
% 23.85/23.92 2300 -c_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(2095,c,2032,b)].
% 23.85/23.92 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(2300,c,2125,a)].
% 23.85/23.92 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(2300,c,2126,a)].
% 23.85/23.92 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(2300,c,2127,b)].
% 23.85/23.92 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(2300,c,2128,b)].
% 23.85/23.92 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(2300,c,2129,b)].
% 23.85/23.92 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(2300,c,2130,b)].
% 23.85/23.92 2301 -c_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(2096,c,2032,b)].
% 23.85/23.92 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(2301,c,2125,a)].
% 23.85/23.92 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(2301,c,2126,a)].
% 23.85/23.92 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(2301,c,2127,b)].
% 23.85/23.92 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(2301,c,2128,b)].
% 23.85/23.92 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(2301,c,2129,b)].
% 23.85/23.92 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(2301,c,2130,b)].
% 23.85/23.92 2302 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2097,c,2032,b)].
% 23.85/23.92 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2302,c,2125,a)].
% 23.85/23.92 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2302,c,2126,a)].
% 23.85/23.92 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2302,c,2127,b)].
% 23.85/23.92 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2302,c,2128,b)].
% 23.85/23.92 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2302,c,2129,b)].
% 23.85/23.92 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2302,c,2130,b)].
% 23.85/23.92 2303 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2098,b,2032,b)].
% 23.85/23.92 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2303,b,2125,a)].
% 23.85/23.92 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(2303,b,2126,a)].
% 23.85/23.93 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2303,b,2127,b)].
% 23.85/23.93 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2303,b,2128,b)].
% 23.85/23.93 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2303,b,2129,b)].
% 23.85/23.93 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2303,b,2130,b)].
% 23.85/23.93 2304 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2099,b,2032,b)].
% 23.85/23.93 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2304,b,2125,a)].
% 23.85/23.93 Derived: c_lessequals(A,A,tc_nat). [resolve(2304,b,2126,a)].
% 23.85/23.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2304,b,2127,b)].
% 23.85/23.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2304,b,2128,b)].
% 23.85/23.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2304,b,2129,b)].
% 23.85/23.93 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2304,b,2130,b)].
% 23.85/23.93 2305 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2100,c,2032,b)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2305,c,2125,a)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2305,c,2126,a)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2305,c,2127,b)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2305,c,2128,b)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2305,c,2129,b)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2305,c,2130,b)].
% 23.85/23.93 2306 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2101,c,2032,b)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2306,c,2125,a)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2306,c,2126,a)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2306,c,2127,b)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2306,c,2128,b)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2306,c,2129,b)].
% 23.85/23.93 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2306,c,2130,b)].
% 23.85/23.93 2307 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2102,d,2032,b)].
% 23.85/23.93 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2307,d,2125,a)].
% 23.85/23.93 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(2307,d,2126,a)].
% 23.85/23.94 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2307,d,2127,b)].
% 23.85/23.94 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2307,d,2128,b)].
% 23.85/23.94 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2307,d,2129,b)].
% 23.85/23.94 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2307,d,2130,b)].
% 23.85/23.94 2308 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2103,c,2032,b)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2308,c,2125,a)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2308,c,2126,a)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2308,c,2127,b)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2308,c,2128,b)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2308,c,2129,b)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2308,c,2130,b)].
% 23.85/23.94 2309 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2104,c,2032,b)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2309,c,2125,a)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2309,c,2126,a)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2309,c,2127,b)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2309,c,2128,b)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2309,c,2129,b)].
% 23.85/23.94 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2309,c,2130,b)].
% 23.85/23.94 2310 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2105,d,2032,b)].
% 23.85/23.94 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2310,d,2125,a)].
% 23.85/23.94 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(2310,d,2126,a)].
% 23.85/23.94 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2310,d,2127,b)].
% 23.85/23.94 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2310,d,2128,b)].
% 23.85/23.94 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2310,d,2129,b)].
% 23.85/23.94 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2310,d,2130,b)].
% 23.85/23.94 2311 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2106,c,2032,b)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2311,c,2125,a)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2311,c,2126,a)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2311,c,2127,b)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2311,c,2128,b)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2311,c,2129,b)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2311,c,2130,b)].
% 23.85/23.95 2312 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2107,c,2032,b)].
% 23.85/23.95 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2312,c,2125,a)].
% 23.85/23.95 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2312,c,2126,a)].
% 23.85/23.95 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2312,c,2127,b)].
% 23.85/23.95 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2312,c,2128,b)].
% 23.85/23.95 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2312,c,2129,b)].
% 23.85/23.95 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2312,c,2130,b)].
% 23.85/23.95 2313 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2108,c,2032,b)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2313,c,2125,a)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2313,c,2126,a)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2313,c,2127,b)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2313,c,2128,b)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2313,c,2129,b)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2313,c,2130,b)].
% 23.85/23.95 2314 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2109,c,2032,b)].
% 23.85/23.95 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2314,c,2125,a)].
% 23.85/23.95 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2314,c,2126,a)].
% 23.85/23.95 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2314,c,2127,b)].
% 23.85/23.95 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2314,c,2128,b)].
% 23.85/23.95 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2314,c,2129,b)].
% 23.85/23.95 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2314,c,2130,b)].
% 23.85/23.95 2315 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2110,c,2032,b)].
% 23.85/23.95 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2315,c,2125,a)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2315,c,2126,a)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2315,c,2127,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2315,c,2128,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2315,c,2129,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2315,c,2130,b)].
% 23.92/23.96 2316 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2111,c,2032,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2316,c,2125,a)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2316,c,2126,a)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2316,c,2127,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2316,c,2128,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2316,c,2129,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2316,c,2130,b)].
% 23.92/23.96 2317 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2112,d,2032,b)].
% 23.92/23.96 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2317,d,2125,a)].
% 23.92/23.96 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(2317,d,2126,a)].
% 23.92/23.96 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2317,d,2127,b)].
% 23.92/23.96 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2317,d,2128,b)].
% 23.92/23.96 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2317,d,2129,b)].
% 23.92/23.96 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2317,d,2130,b)].
% 23.92/23.96 2318 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2113,c,2032,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2318,c,2125,a)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2318,c,2126,a)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2318,c,2127,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2318,c,2128,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2318,c,2129,b)].
% 23.92/23.96 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2318,c,2130,b)].
% 23.92/23.97 2319 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__semiring__strict(D). [resolve(2114,c,2032,b)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2319,c,2125,a)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2319,c,2126,a)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2319,c,2127,b)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2319,c,2128,b)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2319,c,2129,b)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__ring__strict(D). [resolve(2319,c,2130,b)].
% 23.92/23.97 2320 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2115,d,2032,b)].
% 23.92/23.97 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2320,d,2125,a)].
% 23.92/23.97 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(2320,d,2126,a)].
% 23.92/23.97 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2320,d,2127,b)].
% 23.92/23.97 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2320,d,2128,b)].
% 23.92/23.97 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2320,d,2129,b)].
% 23.92/23.97 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2320,d,2130,b)].
% 23.92/23.97 2321 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2116,c,2032,b)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2321,c,2125,a)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2321,c,2126,a)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2321,c,2127,b)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2321,c,2128,b)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2321,c,2129,b)].
% 23.92/23.97 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2321,c,2130,b)].
% 23.92/23.97 2322 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2117,c,2032,b)].
% 23.92/23.97 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2322,c,2125,a)].
% 23.92/23.97 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2322,c,2126,a)].
% 23.92/23.97 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2322,c,2127,b)].
% 23.92/23.97 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2322,c,2128,b)].
% 23.92/23.97 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2322,c,2129,b)].
% 23.92/23.98 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2322,c,2130,b)].
% 23.92/23.98 2323 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2118,c,2032,b)].
% 23.92/23.98 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2323,c,2125,a)].
% 23.92/23.98 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2323,c,2126,a)].
% 23.92/23.98 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2323,c,2127,b)].
% 23.92/23.98 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2323,c,2128,b)].
% 23.92/23.98 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2323,c,2129,b)].
% 23.92/23.98 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2323,c,2130,b)].
% 23.92/23.98 2324 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__semiring__strict(C). [resolve(2119,c,2032,b)].
% 23.92/23.98 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2324,c,2125,a)].
% 23.92/23.98 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2324,c,2126,a)].
% 23.92/23.98 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2324,c,2127,b)].
% 23.92/23.98 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2324,c,2128,b)].
% 23.92/23.98 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2324,c,2129,b)].
% 23.92/23.98 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(2324,c,2130,b)].
% 23.92/23.98 2325 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2120,b,2032,b)].
% 23.92/23.98 Derived: class_Ring__and__Field_Osemiring(tc_IntDef_Oint). [resolve(2325,b,2125,a)].
% 23.92/23.98 Derived: class_Ring__and__Field_Osemiring(tc_nat). [resolve(2325,b,2126,a)].
% 23.92/23.98 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2325,b,2127,b)].
% 23.92/23.98 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2325,b,2128,b)].
% 23.92/23.98 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2325,b,2129,b)].
% 23.92/23.98 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2325,b,2130,b)].
% 23.92/23.98 2326 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__semiring__strict(A). [resolve(2121,b,2032,b)].
% 23.92/23.98 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2326,b,2125,a)].
% 23.92/23.98 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2326,b,2126,a)].
% 23.92/23.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2326,b,2127,b)].
% 23.92/23.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2326,b,2128,b)].
% 23.92/23.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2326,b,2129,b)].
% 23.92/23.98 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2326,b,2130,b)].
% 23.92/23.98 2327 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2122,b,2032,b)].
% 23.92/23.98 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(2327,b,2125,a)].
% 23.92/23.98 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(2327,b,2126,a)].
% 23.92/23.98 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2327,b,2127,b)].
% 24.30/24.37 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2327,b,2128,b)].
% 24.30/24.37 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2327,b,2129,b)].
% 24.30/24.37 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2327,b,2130,b)].
% 24.30/24.37 2328 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__semiring__strict(B). [resolve(2123,b,2032,b)].
% 24.30/24.37 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(2328,b,2125,a)].
% 24.30/24.37 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(2328,b,2126,a)].
% 24.30/24.37 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2328,b,2127,b)].
% 24.30/24.37 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2328,b,2128,b)].
% 24.30/24.37 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2328,b,2129,b)].
% 24.30/24.37 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__ring__strict(B). [resolve(2328,b,2130,b)].
% 24.30/24.37 2329 -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].
% 24.30/24.37 2330 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_43) # label(axiom). [assumption].
% 24.30/24.37 2331 class_Ring__and__Field_Opordered__comm__semiring(tc_nat) # label(clsarity_nat_40) # label(axiom). [assumption].
% 24.30/24.37 2332 -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].
% 24.30/24.37 2333 -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].
% 24.30/24.37 2334 -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].
% 24.30/24.37 2335 -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].
% 24.30/24.37 2336 -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].
% 24.30/24.37 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2329,a,2332,b)].
% 24.30/24.37 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2329,a,2335,b)].
% 24.30/24.37 2337 -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].
% 24.30/24.37 2338 -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].
% 24.30/24.37 2339 -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].
% 24.30/24.37 2340 -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].
% 24.30/24.37 2341 class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint). [resolve(371,a,318,a)].
% 24.30/24.37 2342 class_Ring__and__Field_Opordered__comm__semiring(tc_nat). [resolve(371,a,343,a)].
% 24.30/24.37 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(2342,a,2329,a)].
% 24.30/24.37 2343 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(371,a,344,b)].
% 24.30/24.37 2344 class_Ring__and__Field_Opordered__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(371,a,345,b)].
% 24.30/24.37 2345 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_plus(B,c_0,A) = B. [resolve(670,b,642,a)].
% 24.48/24.52 2346 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_plus(c_0,B,A) = B. [resolve(670,b,643,a)].
% 24.48/24.52 2347 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,B,A). [resolve(910,b,880,a)].
% 24.48/24.52 2348 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(910,b,881,a)].
% 24.48/24.52 2349 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(910,b,882,a)].
% 24.48/24.52 2350 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(910,b,883,a)].
% 24.48/24.52 2351 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(910,b,884,a)].
% 24.48/24.52 2352 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(910,b,885,a)].
% 24.48/24.52 2353 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(910,b,886,a)].
% 24.48/24.52 2354 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(910,b,887,a)].
% 24.48/24.52 2355 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(910,b,888,a)].
% 24.48/24.52 2356 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(910,b,889,a)].
% 24.48/24.52 2357 -class_Ring__and__Field_Opordered__comm__semiring(A) | c_lessequals(B,B,A). [resolve(910,b,890,a)].
% 24.48/24.52 2358 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1049,b,1010,a)].
% 24.48/24.52 2359 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1049,b,1011,a)].
% 24.48/24.52 2360 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1049,b,1012,a)].
% 24.48/24.52 2361 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1049,b,1013,a)].
% 24.48/24.52 2362 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1049,b,1014,a)].
% 24.48/24.52 2363 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1049,b,1015,a)].
% 24.48/24.52 2364 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1049,b,1016,a)].
% 24.48/24.52 2365 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1049,b,1017,a)].
% 24.48/24.52 2366 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1049,b,1018,a)].
% 24.48/24.52 2367 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1049,b,1019,a)].
% 24.48/24.52 2368 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1049,b,1020,a)].
% 24.48/24.52 2369 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1049,b,1021,a)].
% 24.48/24.52 2370 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1049,b,1022,a)].
% 24.48/24.52 2371 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1049,b,1023,a)].
% 24.60/24.66 2372 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1049,b,1024,a)].
% 24.60/24.66 2373 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1049,b,1025,a)].
% 24.60/24.66 2374 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1049,b,1026,a)].
% 24.60/24.66 2375 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1049,b,1027,a)].
% 24.60/24.66 2376 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1049,b,1028,a)].
% 24.60/24.66 2377 -class_Ring__and__Field_Opordered__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1049,b,1029,a)].
% 24.60/24.66 2378 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1108,a,1127,b)].
% 24.60/24.66 2379 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1132,a,1127,b)].
% 24.60/24.66 2380 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1133,a,1127,b)].
% 24.60/24.66 2381 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1135,a,1127,b)].
% 24.60/24.66 2382 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1148,a,1127,b)].
% 24.60/24.66 2383 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1149,a,1127,b)].
% 24.60/24.66 2384 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1206,b,1186,b)].
% 24.60/24.66 2385 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(1207,b,1186,b)].
% 24.60/24.66 2386 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1987,a,1976,b)].
% 24.60/24.66 Derived: -c_less(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2386,b,2336,b)].
% 24.60/24.66 2387 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1988,a,1976,b)].
% 24.60/24.66 Derived: -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2387,c,2336,b)].
% 24.60/24.66 2388 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1989,a,1976,b)].
% 24.60/24.66 Derived: c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2388,b,2336,b)].
% 24.60/24.66 2389 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1990,a,1976,b)].
% 24.60/24.66 Derived: -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2389,c,2336,b)].
% 24.60/24.66 2390 -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1991,a,1976,b)].
% 24.60/24.66 Derived: -c_lessequals(c_SetInterval_OatLeast(A,B),c_SetInterval_OatLeast(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2390,c,2336,b)].
% 24.60/24.66 2391 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1992,a,1976,b)].
% 24.60/24.66 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeast(B,C),c_SetInterval_OatLeast(A,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2391,c,2336,b)].
% 24.60/24.66 2392 -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1993,a,1976,b)].
% 24.60/24.66 Derived: -c_lessequals(c_SetInterval_OatMost(A,B),c_SetInterval_OatMost(C,B),tc_set(B)) | c_lessequals(A,C,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2392,c,2336,b)].
% 24.60/24.68 2393 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatMost(A,C),c_SetInterval_OatMost(B,C),tc_set(C)) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1994,a,1976,b)].
% 24.60/24.68 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_Opordered__comm__ring(C). [resolve(2393,c,2336,b)].
% 24.60/24.68 2394 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(1995,a,1976,b)].
% 24.60/24.68 Derived: -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2394,c,2336,b)].
% 24.60/24.68 2395 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1996,a,1976,b)].
% 24.60/24.68 Derived: c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2395,b,2336,b)].
% 24.60/24.68 2396 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(1997,a,1976,b)].
% 24.60/24.68 Derived: c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2396,b,2336,b)].
% 24.60/24.68 2397 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(1998,a,1976,b)].
% 24.60/24.68 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2397,c,2336,b)].
% 24.60/24.68 2398 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(1999,a,1976,b)].
% 24.60/24.68 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2398,c,2336,b)].
% 24.60/24.68 2399 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2000,a,1976,b)].
% 24.60/24.68 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2399,d,2336,b)].
% 24.60/24.68 2400 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2001,a,1976,b)].
% 24.60/24.68 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2400,c,2336,b)].
% 24.60/24.68 2401 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2002,a,1976,b)].
% 24.60/24.68 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2401,c,2336,b)].
% 24.60/24.68 2402 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2003,a,1976,b)].
% 24.60/24.68 Derived: -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2402,d,2336,b)].
% 24.60/24.68 2403 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2004,a,1976,b)].
% 24.60/24.68 Derived: -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2403,c,2336,b)].
% 24.60/24.68 2404 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2005,a,1976,b)].
% 24.60/24.68 Derived: -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2404,c,2336,b)].
% 24.60/24.68 2405 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2006,a,1976,b)].
% 24.65/24.70 Derived: -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2405,c,2336,b)].
% 24.65/24.70 2406 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2007,a,1976,b)].
% 24.65/24.70 Derived: -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2406,c,2336,b)].
% 24.65/24.70 2407 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2008,a,1976,b)].
% 24.65/24.70 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2407,c,2336,b)].
% 24.65/24.70 2408 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2009,a,1976,b)].
% 24.65/24.70 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2408,c,2336,b)].
% 24.65/24.70 2409 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2010,a,1976,b)].
% 24.65/24.70 Derived: -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2409,d,2336,b)].
% 24.65/24.70 2410 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2011,a,1976,b)].
% 24.65/24.70 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2410,c,2336,b)].
% 24.65/24.70 2411 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__semiring(D). [resolve(2012,a,1976,b)].
% 24.65/24.70 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__comm__ring(D). [resolve(2411,c,2336,b)].
% 24.65/24.70 2412 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2013,a,1976,b)].
% 24.65/24.70 Derived: -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2412,d,2336,b)].
% 24.65/24.70 2413 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2014,a,1976,b)].
% 24.65/24.70 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2413,c,2336,b)].
% 24.65/24.70 2414 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2015,a,1976,b)].
% 24.65/24.70 Derived: -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2414,c,2336,b)].
% 24.65/24.70 2415 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2016,a,1976,b)].
% 24.65/24.70 Derived: -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2415,c,2336,b)].
% 24.65/24.70 2416 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__semiring(C). [resolve(2017,a,1976,b)].
% 24.65/24.70 Derived: -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__comm__ring(C). [resolve(2416,c,2336,b)].
% 24.65/24.70 2417 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2018,b,1976,b)].
% 24.65/24.70 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2417,b,2336,b)].
% 24.65/24.70 2418 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__semiring(A). [resolve(2021,b,1976,b)].
% 24.65/24.70 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__comm__ring(A). [resolve(2418,b,2336,b)].
% 24.65/24.70 2419 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2022,b,1976,b)].
% 25.10/25.21 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2419,b,2336,b)].
% 25.10/25.21 2420 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__semiring(B). [resolve(2023,b,1976,b)].
% 25.10/25.21 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__comm__ring(B). [resolve(2420,b,2336,b)].
% 25.10/25.21 2421 -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].
% 25.10/25.21 2422 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_44) # label(axiom). [assumption].
% 25.10/25.21 2423 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) # label(clsarity_nat_41) # label(axiom). [assumption].
% 25.10/25.21 2424 -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].
% 25.10/25.21 2425 -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].
% 25.10/25.21 2426 -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].
% 25.10/25.21 2427 -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].
% 25.10/25.21 2428 -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].
% 25.10/25.21 2429 -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].
% 25.10/25.21 2430 -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].
% 25.10/25.21 2431 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint). [resolve(369,a,318,a)].
% 25.10/25.21 2432 class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat). [resolve(369,a,343,a)].
% 25.10/25.21 2433 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(369,a,344,b)].
% 25.10/25.21 2434 class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(369,a,345,b)].
% 25.10/25.21 2435 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,c_0,A) = B. [resolve(667,b,642,a)].
% 25.10/25.21 2436 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(c_0,B,A) = B. [resolve(667,b,643,a)].
% 25.10/25.21 2437 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(667,b,647,a)].
% 25.10/25.21 2438 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(667,b,648,a)].
% 25.10/25.21 2439 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(750,b,726,a)].
% 25.10/25.21 2440 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(750,b,727,a)].
% 25.10/25.21 2441 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,B,A). [resolve(907,b,880,a)].
% 25.10/25.21 2442 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(907,b,881,a)].
% 25.10/25.21 2443 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(907,b,882,a)].
% 25.10/25.21 2444 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(907,b,883,a)].
% 25.19/25.29 2445 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(907,b,884,a)].
% 25.19/25.29 2446 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(907,b,885,a)].
% 25.19/25.29 2447 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(907,b,886,a)].
% 25.19/25.29 2448 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(907,b,887,a)].
% 25.19/25.29 2449 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(907,b,888,a)].
% 25.19/25.29 2450 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(907,b,889,a)].
% 25.19/25.29 2451 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_lessequals(B,B,A). [resolve(907,b,890,a)].
% 25.19/25.29 2452 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(c_0,B,A) = c_0. [resolve(981,b,967,a)].
% 25.19/25.29 2453 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | c_times(B,c_0,A) = c_0. [resolve(981,b,968,a)].
% 25.19/25.29 2454 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(988,a,981,b)].
% 25.19/25.29 2455 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(989,a,981,b)].
% 25.19/25.29 2456 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1005,a,981,b)].
% 25.19/25.29 2457 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1006,a,981,b)].
% 25.19/25.29 2458 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1007,a,981,b)].
% 25.19/25.29 2459 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1008,a,981,b)].
% 25.19/25.29 2460 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1046,b,1010,a)].
% 25.19/25.29 2461 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1046,b,1011,a)].
% 25.19/25.29 2462 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1046,b,1012,a)].
% 25.19/25.29 2463 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1046,b,1013,a)].
% 25.19/25.29 2464 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1046,b,1014,a)].
% 25.19/25.29 2465 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1046,b,1015,a)].
% 25.19/25.29 2466 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1046,b,1016,a)].
% 25.19/25.29 2467 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1046,b,1017,a)].
% 25.19/25.29 2468 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1046,b,1018,a)].
% 25.19/25.29 2469 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1046,b,1019,a)].
% 25.19/25.29 2470 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1046,b,1020,a)].
% 25.39/25.43 2471 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1046,b,1021,a)].
% 25.39/25.43 2472 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1046,b,1022,a)].
% 25.39/25.43 2473 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1046,b,1023,a)].
% 25.39/25.43 2474 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1046,b,1024,a)].
% 25.39/25.43 2475 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1046,b,1025,a)].
% 25.39/25.43 2476 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1046,b,1026,a)].
% 25.39/25.43 2477 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1046,b,1027,a)].
% 25.39/25.43 2478 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1046,b,1028,a)].
% 25.39/25.43 2479 -class_Ring__and__Field_Opordered__cancel__comm__semiring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1046,b,1029,a)].
% 25.39/25.43 2480 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1150,a,1124,b)].
% 25.39/25.43 2481 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1151,a,1124,b)].
% 25.39/25.43 2482 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1200,b,1184,b)].
% 25.39/25.43 2483 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(1201,b,1184,b)].
% 25.39/25.43 2484 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1204,b,1184,b)].
% 25.39/25.43 2485 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1205,b,1184,b)].
% 25.39/25.43 2486 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1987,a,1973,b)].
% 25.39/25.43 2487 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1988,a,1973,b)].
% 25.39/25.43 2488 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1989,a,1973,b)].
% 25.39/25.43 2489 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1990,a,1973,b)].
% 25.39/25.43 2490 -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(1991,a,1973,b)].
% 25.39/25.43 2491 -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(1992,a,1973,b)].
% 25.39/25.43 2492 -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(1993,a,1973,b)].
% 25.39/25.43 2493 -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(1994,a,1973,b)].
% 25.39/25.43 2494 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(1995,a,1973,b)].
% 25.39/25.43 2495 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1996,a,1973,b)].
% 25.39/25.43 2496 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(1997,a,1973,b)].
% 25.39/25.46 2497 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(1998,a,1973,b)].
% 25.39/25.46 2498 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(1999,a,1973,b)].
% 25.39/25.46 2499 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2000,a,1973,b)].
% 25.39/25.46 2500 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2001,a,1973,b)].
% 25.39/25.46 2501 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2002,a,1973,b)].
% 25.39/25.46 2502 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2003,a,1973,b)].
% 25.39/25.46 2503 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2004,a,1973,b)].
% 25.39/25.46 2504 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2005,a,1973,b)].
% 25.39/25.46 2505 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2006,a,1973,b)].
% 25.39/25.46 2506 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2007,a,1973,b)].
% 25.39/25.46 2507 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2008,a,1973,b)].
% 25.39/25.46 2508 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2009,a,1973,b)].
% 25.39/25.46 2509 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2010,a,1973,b)].
% 25.39/25.46 2510 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2011,a,1973,b)].
% 25.39/25.46 2511 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2012,a,1973,b)].
% 25.39/25.46 2512 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2013,a,1973,b)].
% 25.39/25.46 2513 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2014,a,1973,b)].
% 25.39/25.46 2514 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2015,a,1973,b)].
% 25.39/25.46 2515 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2016,a,1973,b)].
% 25.39/25.46 2516 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2017,a,1973,b)].
% 25.39/25.46 2517 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2057,a,2033,b)].
% 25.39/25.46 2518 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2058,a,2033,b)].
% 25.39/25.46 2519 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2065,c,2033,b)].
% 25.39/25.46 2520 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2066,c,2033,b)].
% 25.39/25.46 2521 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2087,a,2033,b)].
% 25.39/25.46 2522 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2088,a,2033,b)].
% 25.39/25.51 2523 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2089,b,2033,b)].
% 25.39/25.51 2524 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2090,c,2033,b)].
% 25.39/25.51 2525 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2091,b,2033,b)].
% 25.39/25.51 2526 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2092,c,2033,b)].
% 25.39/25.51 2527 -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(2093,c,2033,b)].
% 25.39/25.51 2528 -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(2094,c,2033,b)].
% 25.39/25.51 2529 -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(2095,c,2033,b)].
% 25.39/25.51 2530 -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(2096,c,2033,b)].
% 25.39/25.51 2531 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2097,c,2033,b)].
% 25.39/25.51 2532 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2098,b,2033,b)].
% 25.39/25.51 2533 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2099,b,2033,b)].
% 25.39/25.51 2534 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2100,c,2033,b)].
% 25.39/25.51 2535 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2101,c,2033,b)].
% 25.39/25.51 2536 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2102,d,2033,b)].
% 25.39/25.51 2537 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2103,c,2033,b)].
% 25.39/25.51 2538 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2104,c,2033,b)].
% 25.39/25.51 2539 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2105,d,2033,b)].
% 25.39/25.51 2540 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2106,c,2033,b)].
% 25.39/25.51 2541 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2107,c,2033,b)].
% 25.39/25.51 2542 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2108,c,2033,b)].
% 25.39/25.51 2543 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2109,c,2033,b)].
% 25.39/25.51 2544 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2110,c,2033,b)].
% 25.39/25.51 2545 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2111,c,2033,b)].
% 25.39/25.51 2546 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2112,d,2033,b)].
% 25.70/25.77 2547 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2113,c,2033,b)].
% 25.70/25.77 2548 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(D). [resolve(2114,c,2033,b)].
% 25.70/25.77 2549 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2115,d,2033,b)].
% 25.70/25.77 2550 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2116,c,2033,b)].
% 25.70/25.77 2551 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2117,c,2033,b)].
% 25.70/25.77 2552 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2118,c,2033,b)].
% 25.70/25.77 2553 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(C). [resolve(2119,c,2033,b)].
% 25.70/25.77 2554 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2120,b,2033,b)].
% 25.70/25.77 2555 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2121,b,2033,b)].
% 25.70/25.77 2556 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2122,b,2033,b)].
% 25.70/25.77 2557 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__cancel__comm__semiring(B). [resolve(2123,b,2033,b)].
% 25.70/25.77 2558 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Opordered__cancel__comm__semiring(A). [resolve(2329,a,2335,b)].
% 25.70/25.77 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(2558,b,2422,a)].
% 25.70/25.77 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2558,b,2424,b)].
% 25.70/25.77 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2558,b,2425,b)].
% 25.70/25.77 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2558,b,2426,b)].
% 25.70/25.77 2559 -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].
% 25.70/25.77 2560 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_45) # label(axiom). [assumption].
% 25.70/25.77 2561 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat_42) # label(axiom). [assumption].
% 25.70/25.77 2562 -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].
% 25.70/25.77 2563 -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].
% 25.70/25.77 2564 -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].
% 25.70/25.77 2565 -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].
% 25.70/25.77 2566 -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].
% 25.70/25.77 2567 -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].
% 25.70/25.77 2568 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(67,b,2,a)].
% 25.70/25.78 2569 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(67,b,3,a)].
% 25.70/25.78 2570 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(67,b,4,a)].
% 25.70/25.78 2571 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(67,b,5,a)].
% 25.70/25.78 2572 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(67,b,6,a)].
% 25.70/25.78 2573 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(67,b,7,a)].
% 25.70/25.78 2574 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(67,b,8,a)].
% 25.70/25.78 2575 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(67,b,9,a)].
% 25.70/25.78 2576 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(67,b,10,a)].
% 25.70/25.78 2577 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(67,b,11,a)].
% 25.70/25.78 2578 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(67,b,12,a)].
% 25.70/25.78 2579 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(67,b,13,a)].
% 25.70/25.78 2580 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(67,b,14,a)].
% 25.70/25.78 2581 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(67,b,15,a)].
% 25.70/25.78 2582 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(67,b,16,a)].
% 25.70/25.78 2583 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(67,b,17,a)].
% 25.70/25.78 2584 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(67,b,18,a)].
% 25.70/25.78 2585 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(67,b,19,a)].
% 25.70/25.78 2586 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(67,b,20,a)].
% 25.70/25.78 2587 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(67,b,21,a)].
% 25.70/25.78 2588 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(67,b,22,a)].
% 25.70/25.78 2589 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(67,b,23,a)].
% 25.70/25.78 2590 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(67,b,24,a)].
% 25.70/25.78 2591 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(67,b,25,b)].
% 25.70/25.78 2592 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(67,b,26,b)].
% 25.70/25.79 2593 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(67,b,27,a)].
% 25.70/25.79 2594 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(67,b,28,a)].
% 25.70/25.79 2595 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(67,b,29,a)].
% 25.70/25.79 2596 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(67,b,30,a)].
% 25.70/25.79 2597 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(67,b,31,a)].
% 25.70/25.79 2598 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(67,b,32,a)].
% 25.70/25.79 2599 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(67,b,33,a)].
% 25.70/25.79 2600 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(67,b,34,a)].
% 25.70/25.79 2601 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(67,b,35,a)].
% 25.70/25.79 2602 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,B,A) = B. [resolve(67,b,36,a)].
% 25.70/25.79 2603 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(67,b,37,a)].
% 25.70/25.79 2604 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(67,b,38,a)].
% 25.70/25.79 2605 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(67,b,39,a)].
% 25.70/25.79 2606 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(67,b,40,a)].
% 25.70/25.79 2607 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,B,A) = B. [resolve(67,b,41,a)].
% 25.70/25.79 2608 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(67,b,42,a)].
% 25.70/25.79 2609 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(67,b,43,a)].
% 25.70/25.79 2610 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(67,b,44,a)].
% 25.70/25.79 2611 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(67,b,45,a)].
% 25.70/25.79 2612 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(67,b,46,a)].
% 25.88/25.92 2613 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(67,b,47,a)].
% 25.88/25.92 2614 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(67,b,48,a)].
% 25.88/25.92 2615 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(67,b,49,a)].
% 25.88/25.92 2616 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(67,b,50,a)].
% 25.88/25.92 2617 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(67,b,51,a)].
% 25.88/25.92 2618 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(67,b,52,a)].
% 25.88/25.92 2619 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(67,b,53,a)].
% 25.88/25.92 2620 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(67,b,54,a)].
% 25.88/25.92 2621 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(67,b,55,a)].
% 25.88/25.92 2622 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(67,b,56,a)].
% 25.88/25.92 2623 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(67,b,57,a)].
% 25.88/25.92 2624 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(67,b,58,a)].
% 25.88/25.92 2625 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(67,b,59,a)].
% 25.88/25.92 2626 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(284,b,273,a)].
% 25.88/25.92 2627 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(307,b,296,a)].
% 25.88/25.92 2628 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint). [resolve(362,a,318,a)].
% 25.88/25.92 2629 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). [resolve(362,a,343,a)].
% 25.88/25.92 2630 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(362,a,344,b)].
% 25.88/25.92 2631 class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(362,a,345,b)].
% 25.88/25.92 2632 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,c_0,A) = B. [resolve(662,b,642,a)].
% 25.88/25.92 2633 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(c_0,B,A) = B. [resolve(662,b,643,a)].
% 25.88/25.92 2634 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(714,b,690,a)].
% 25.88/25.92 2635 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(714,b,691,a)].
% 25.88/25.92 2636 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(714,b,692,a)].
% 25.94/26.00 2637 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(714,b,693,a)].
% 25.94/26.00 2638 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(714,b,694,a)].
% 25.94/26.00 2639 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(714,b,695,a)].
% 25.94/26.00 2640 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(714,b,696,a)].
% 25.94/26.00 2641 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(714,b,697,a)].
% 25.94/26.00 2642 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(745,b,726,a)].
% 25.94/26.00 2643 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(745,b,727,a)].
% 25.94/26.00 2644 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,B,A). [resolve(902,b,880,a)].
% 25.94/26.00 2645 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(902,b,881,a)].
% 25.94/26.00 2646 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(902,b,882,a)].
% 25.94/26.00 2647 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(902,b,883,a)].
% 25.94/26.00 2648 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(902,b,884,a)].
% 25.94/26.00 2649 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(902,b,885,a)].
% 25.94/26.00 2650 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(902,b,886,a)].
% 25.94/26.00 2651 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(902,b,887,a)].
% 25.94/26.00 2652 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(902,b,888,a)].
% 25.94/26.00 2653 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(902,b,889,a)].
% 25.94/26.00 2654 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_lessequals(B,B,A). [resolve(902,b,890,a)].
% 25.94/26.00 2655 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(c_0,B,A) = c_0. [resolve(976,b,967,a)].
% 25.94/26.00 2656 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_times(B,c_0,A) = c_0. [resolve(976,b,968,a)].
% 25.94/26.00 2657 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(988,a,976,b)].
% 25.94/26.00 2658 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(989,a,976,b)].
% 25.94/26.00 2659 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(991,a,976,b)].
% 25.94/26.00 2660 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(992,a,976,b)].
% 25.94/26.00 2661 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1005,a,976,b)].
% 25.94/26.00 2662 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1006,a,976,b)].
% 25.94/26.00 2663 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1007,a,976,b)].
% 25.94/26.00 2664 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1008,a,976,b)].
% 25.94/26.05 2665 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1041,b,1010,a)].
% 25.94/26.05 2666 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1041,b,1011,a)].
% 25.94/26.05 2667 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1041,b,1012,a)].
% 25.94/26.05 2668 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1041,b,1013,a)].
% 25.94/26.05 2669 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1041,b,1014,a)].
% 25.94/26.05 2670 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1041,b,1015,a)].
% 25.94/26.05 2671 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1041,b,1016,a)].
% 25.94/26.05 2672 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1041,b,1017,a)].
% 25.94/26.05 2673 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1041,b,1018,a)].
% 25.94/26.05 2674 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1041,b,1019,a)].
% 25.94/26.05 2675 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1041,b,1020,a)].
% 25.94/26.05 2676 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1041,b,1021,a)].
% 25.94/26.05 2677 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1041,b,1022,a)].
% 25.94/26.05 2678 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1041,b,1023,a)].
% 25.94/26.05 2679 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1041,b,1024,a)].
% 25.94/26.05 2680 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1041,b,1025,a)].
% 25.94/26.05 2681 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1041,b,1026,a)].
% 25.94/26.05 2682 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1041,b,1027,a)].
% 25.94/26.05 2683 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1041,b,1028,a)].
% 25.94/26.05 2684 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1041,b,1029,a)].
% 25.94/26.05 2685 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1200,b,1181,b)].
% 25.94/26.05 2686 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1201,b,1181,b)].
% 25.94/26.05 2687 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1204,b,1181,b)].
% 25.94/26.05 2688 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1205,b,1181,b)].
% 25.94/26.05 2689 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1206,b,1181,b)].
% 25.94/26.05 2690 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1207,b,1181,b)].
% 26.11/26.15 2691 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1812,a,1758,b)].
% 26.11/26.15 2692 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(1929,b,1817,b)].
% 26.11/26.15 2693 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1930,b,1817,b)].
% 26.11/26.15 2694 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1931,c,1817,b)].
% 26.11/26.15 2695 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1932,b,1817,b)].
% 26.11/26.15 2696 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1933,c,1817,b)].
% 26.11/26.15 2697 -c_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(1934,c,1817,b)].
% 26.11/26.15 2698 -c_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(1935,c,1817,b)].
% 26.11/26.15 2699 -c_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(1936,c,1817,b)].
% 26.11/26.15 2700 -c_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(1937,c,1817,b)].
% 26.11/26.15 2701 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1938,c,1817,b)].
% 26.11/26.15 2702 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1939,b,1817,b)].
% 26.11/26.15 2703 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(1940,b,1817,b)].
% 26.11/26.15 2704 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1941,c,1817,b)].
% 26.11/26.15 2705 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1942,c,1817,b)].
% 26.11/26.15 2706 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1943,d,1817,b)].
% 26.11/26.15 2707 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1944,c,1817,b)].
% 26.11/26.15 2708 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1945,c,1817,b)].
% 26.11/26.15 2709 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1946,d,1817,b)].
% 26.11/26.15 2710 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1947,c,1817,b)].
% 26.11/26.15 2711 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1948,c,1817,b)].
% 26.11/26.15 2712 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1949,c,1817,b)].
% 26.11/26.15 2713 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1950,c,1817,b)].
% 26.11/26.15 2714 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1951,c,1817,b)].
% 26.11/26.15 2715 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1952,c,1817,b)].
% 26.18/26.21 2716 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1953,d,1817,b)].
% 26.18/26.21 2717 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1954,c,1817,b)].
% 26.18/26.21 2718 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(1955,c,1817,b)].
% 26.18/26.21 2719 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1956,d,1817,b)].
% 26.18/26.21 2720 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1957,c,1817,b)].
% 26.18/26.21 2721 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1958,c,1817,b)].
% 26.18/26.21 2722 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1959,c,1817,b)].
% 26.18/26.21 2723 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1960,c,1817,b)].
% 26.18/26.21 2724 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1961,c,1817,b)].
% 26.18/26.21 2725 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(1962,c,1817,b)].
% 26.18/26.21 2726 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2057,a,2028,b)].
% 26.18/26.21 2727 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2058,a,2028,b)].
% 26.18/26.21 2728 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2089,b,2028,b)].
% 26.18/26.21 2729 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2090,c,2028,b)].
% 26.18/26.21 2730 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2091,b,2028,b)].
% 26.18/26.21 2731 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2092,c,2028,b)].
% 26.18/26.21 2732 -c_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(2093,c,2028,b)].
% 26.18/26.21 2733 -c_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(2094,c,2028,b)].
% 26.18/26.21 2734 -c_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(2095,c,2028,b)].
% 26.18/26.21 2735 -c_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(2096,c,2028,b)].
% 26.18/26.21 2736 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2097,c,2028,b)].
% 26.18/26.21 2737 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2098,b,2028,b)].
% 26.18/26.21 2738 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2099,b,2028,b)].
% 26.18/26.21 2739 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2100,c,2028,b)].
% 26.18/26.21 2740 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2101,c,2028,b)].
% 26.18/26.21 2741 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2102,d,2028,b)].
% 26.18/26.24 2742 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2103,c,2028,b)].
% 26.18/26.24 2743 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2104,c,2028,b)].
% 26.18/26.24 2744 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2105,d,2028,b)].
% 26.18/26.24 2745 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2106,c,2028,b)].
% 26.18/26.24 2746 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2107,c,2028,b)].
% 26.18/26.24 2747 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2108,c,2028,b)].
% 26.18/26.24 2748 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2109,c,2028,b)].
% 26.18/26.24 2749 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2110,c,2028,b)].
% 26.18/26.24 2750 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2111,c,2028,b)].
% 26.18/26.24 2751 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2112,d,2028,b)].
% 26.18/26.24 2752 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2113,c,2028,b)].
% 26.18/26.24 2753 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2114,c,2028,b)].
% 26.18/26.24 2754 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2115,d,2028,b)].
% 26.18/26.24 2755 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2116,c,2028,b)].
% 26.18/26.24 2756 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2117,c,2028,b)].
% 26.18/26.24 2757 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2118,c,2028,b)].
% 26.18/26.24 2758 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2119,c,2028,b)].
% 26.18/26.24 2759 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2120,b,2028,b)].
% 26.18/26.24 2760 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2121,b,2028,b)].
% 26.18/26.24 2761 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2122,b,2028,b)].
% 26.18/26.24 2762 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2123,b,2028,b)].
% 26.18/26.24 2763 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2134,a,2127,b)].
% 26.18/26.24 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) | B = c_emptyset. [resolve(2763,e,2560,a)].
% 26.18/26.24 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) | B = c_emptyset. [resolve(2763,e,2561,a)].
% 26.18/26.24 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2763,e,2566,b)].
% 26.18/26.24 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(A,c_Finite__Set_OMax(B,C),C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2763,e,2567,b)].
% 26.18/26.24 2764 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2135,a,2127,b)].
% 26.18/26.24 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMax(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(2764,d,2560,a)].
% 26.18/26.24 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMax(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(2764,d,2561,a)].
% 26.18/26.24 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2764,d,2566,b)].
% 26.18/26.24 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMax(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2764,d,2567,b)].
% 26.18/26.24 2765 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2136,a,2127,b)].
% 26.18/26.24 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2765,d,2560,a)].
% 26.18/26.24 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omax(B,c_Finite__Set_OMax(A,tc_nat),tc_nat). [resolve(2765,d,2561,a)].
% 26.18/26.24 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2765,d,2566,b)].
% 26.18/26.24 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMax(c_insert(C,A,B),B) = c_Orderings_Omax(C,c_Finite__Set_OMax(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2765,d,2567,b)].
% 26.18/26.24 2766 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2137,a,2127,b)].
% 26.18/26.24 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(2766,f,2560,a)].
% 26.18/26.24 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat) | B = c_emptyset. [resolve(2766,f,2561,a)].
% 26.18/26.24 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2766,f,2566,b)].
% 26.18/26.24 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(c_Finite__Set_OMax(B,C),D,C) | c_lessequals(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2766,f,2567,b)].
% 26.18/26.24 2767 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2138,a,2127,b)].
% 26.18/26.24 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(2767,e,2560,a)].
% 26.18/26.24 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__le__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2767,e,2561,a)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2767,e,2566,b)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__le__iff__1(A,C,B),A,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2767,e,2567,b)].
% 26.18/26.25 2768 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2139,a,2127,b)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_lessequals(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(2768,e,2560,a)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(c_Main_OMax__le__iff__1(A,B,tc_nat),B,tc_nat) | c_lessequals(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2768,e,2561,a)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2768,e,2566,b)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(c_Main_OMax__le__iff__1(A,C,B),C,B) | c_lessequals(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2768,e,2567,b)].
% 26.18/26.25 2769 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2140,a,2127,b)].
% 26.18/26.25 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint) | B = c_emptyset. [resolve(2769,f,2560,a)].
% 26.18/26.25 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Finite__Set_OMax(B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat) | B = c_emptyset. [resolve(2769,f,2561,a)].
% 26.18/26.25 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2769,f,2566,b)].
% 26.18/26.25 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(c_Finite__Set_OMax(B,C),D,C) | c_less(A,D,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2769,f,2567,b)].
% 26.18/26.25 2770 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2141,a,2127,b)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(2770,e,2560,a)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMax__less__iff__1(A,B,tc_nat),A,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2770,e,2561,a)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2770,e,2566,b)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMax__less__iff__1(A,C,B),A,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2770,e,2567,b)].
% 26.18/26.25 2771 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2142,a,2127,b)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) | c_less(c_Finite__Set_OMax(A,tc_IntDef_Oint),B,tc_IntDef_Oint) | A = c_emptyset. [resolve(2771,e,2560,a)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(c_Main_OMax__less__iff__1(A,B,tc_nat),B,tc_nat) | c_less(c_Finite__Set_OMax(A,tc_nat),B,tc_nat) | A = c_emptyset. [resolve(2771,e,2561,a)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2771,e,2566,b)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(c_Main_OMax__less__iff__1(A,C,B),C,B) | c_less(c_Finite__Set_OMax(A,B),C,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2771,e,2567,b)].
% 26.18/26.25 2772 c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2143,a,2127,b)].
% 26.18/26.25 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2772,b,2560,a)].
% 26.18/26.25 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2772,b,2561,a)].
% 26.18/26.25 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2772,b,2566,b)].
% 26.18/26.25 Derived: c_Finite__Set_OMax(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2772,b,2567,b)].
% 26.18/26.25 2773 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2144,a,2127,b)].
% 26.18/26.25 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(2773,f,2560,a)].
% 26.18/26.25 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_lessequals(C,A,tc_nat) | B = c_emptyset. [resolve(2773,f,2561,a)].
% 26.18/26.25 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2773,f,2566,b)].
% 26.18/26.25 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_lessequals(D,c_Finite__Set_OMin(B,C),C) | c_lessequals(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2773,f,2567,b)].
% 26.18/26.25 2774 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2145,a,2127,b)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2774,e,2560,a)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__ge__iff__1(A,B,tc_nat),A,tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2774,e,2561,a)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2774,e,2566,b)].
% 26.18/26.25 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__ge__iff__1(A,C,B),A,B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2774,e,2567,b)].
% 26.18/26.25 2775 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2146,a,2127,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2775,e,2560,a)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_lessequals(B,c_Main_OMin__ge__iff__1(A,B,tc_nat),tc_nat) | c_lessequals(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2775,e,2561,a)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2775,e,2566,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(A,C,B),B) | c_lessequals(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2775,e,2567,b)].
% 26.18/26.26 2776 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2147,a,2127,b)].
% 26.18/26.26 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(C,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(C,A,tc_IntDef_Oint) | B = c_emptyset. [resolve(2776,f,2560,a)].
% 26.18/26.26 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(C,c_Finite__Set_OMin(B,tc_nat),tc_nat) | c_less(C,A,tc_nat) | B = c_emptyset. [resolve(2776,f,2561,a)].
% 26.18/26.26 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2776,f,2566,b)].
% 26.18/26.26 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | -c_less(D,c_Finite__Set_OMin(B,C),C) | c_less(D,A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2776,f,2567,b)].
% 26.18/26.26 2777 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2148,a,2127,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2777,e,2560,a)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Main_OMin__gr__iff__1(A,B,tc_nat),A,tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2777,e,2561,a)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2777,e,2566,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Main_OMin__gr__iff__1(A,C,B),A,B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2777,e,2567,b)].
% 26.18/26.26 2778 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2149,a,2127,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2778,e,2560,a)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | -c_less(B,c_Main_OMin__gr__iff__1(A,B,tc_nat),tc_nat) | c_less(B,c_Finite__Set_OMin(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2778,e,2561,a)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2778,e,2566,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | -c_less(C,c_Main_OMin__gr__iff__1(A,C,B),B) | c_less(C,c_Finite__Set_OMin(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2778,e,2567,b)].
% 26.18/26.26 2779 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2150,a,2127,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_in(c_Finite__Set_OMin(A,tc_IntDef_Oint),A,tc_IntDef_Oint) | A = c_emptyset. [resolve(2779,d,2560,a)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_in(c_Finite__Set_OMin(A,tc_nat),A,tc_nat) | A = c_emptyset. [resolve(2779,d,2561,a)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2779,d,2566,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_Finite__Set_OMin(A,B),A,B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2779,d,2567,b)].
% 26.18/26.26 2780 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2151,a,2127,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2780,d,2560,a)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(B,A,tc_nat),tc_nat) = c_Orderings_Omin(B,c_Finite__Set_OMin(A,tc_nat),tc_nat). [resolve(2780,d,2561,a)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2780,d,2566,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | A = c_emptyset | c_Finite__Set_OMin(c_insert(C,A,B),B) = c_Orderings_Omin(C,c_Finite__Set_OMin(A,B),B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2780,d,2567,b)].
% 26.18/26.26 2781 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2152,a,2127,b)].
% 26.18/26.26 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(B,tc_IntDef_Oint),A,tc_IntDef_Oint) | B = c_emptyset. [resolve(2781,e,2560,a)].
% 26.18/26.26 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(B,tc_nat),A,tc_nat) | B = c_emptyset. [resolve(2781,e,2561,a)].
% 26.18/26.26 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__field(C). [resolve(2781,e,2566,b)].
% 26.18/26.26 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | c_lessequals(c_Finite__Set_OMin(B,C),A,C) | B = c_emptyset | -class_Ring__and__Field_Oordered__idom(C). [resolve(2781,e,2567,b)].
% 26.18/26.26 2782 c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2153,a,2127,b)].
% 26.18/26.26 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2782,b,2560,a)].
% 26.18/26.26 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,tc_nat),tc_nat) = A. [resolve(2782,b,2561,a)].
% 26.18/26.26 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2782,b,2566,b)].
% 26.18/26.26 Derived: c_Finite__Set_OMin(c_insert(A,c_emptyset,B),B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2782,b,2567,b)].
% 26.18/26.26 2783 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2154,a,2127,b)].
% 26.18/26.26 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | c_lessequals(c_Finite__Set_OMin(A,tc_IntDef_Oint),c_Finite__Set_OMax(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_emptyset. [resolve(2783,d,2560,a)].
% 26.25/26.27 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(tc_nat)) | c_lessequals(c_Finite__Set_OMin(A,tc_nat),c_Finite__Set_OMax(A,tc_nat),tc_nat) | A = c_emptyset. [resolve(2783,d,2561,a)].
% 26.25/26.27 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__field(B). [resolve(2783,d,2566,b)].
% 26.25/26.27 Derived: -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_lessequals(c_Finite__Set_OMin(A,B),c_Finite__Set_OMax(A,B),B) | A = c_emptyset | -class_Ring__and__Field_Oordered__idom(B). [resolve(2783,d,2567,b)].
% 26.25/26.27 2784 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2155,a,2127,b)].
% 26.25/26.27 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2784,e,2560,a)].
% 26.25/26.27 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,tc_nat),tc_nat) = A. [resolve(2784,e,2561,a)].
% 26.25/26.27 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C). [resolve(2784,e,2566,b)].
% 26.25/26.27 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omin(A,c_Finite__Set_OMax(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C). [resolve(2784,e,2567,b)].
% 26.25/26.27 2785 -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2156,a,2127,b)].
% 26.25/26.27 Derived: -c_in(A,B,tc_IntDef_Oint) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_IntDef_Oint),tc_IntDef_Oint) = A. [resolve(2785,e,2560,a)].
% 26.25/26.27 Derived: -c_in(A,B,tc_nat) | -c_in(B,c_Finite__Set_OFinites,tc_set(tc_nat)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,tc_nat),tc_nat) = A. [resolve(2785,e,2561,a)].
% 26.25/26.27 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__field(C). [resolve(2785,e,2566,b)].
% 26.25/26.27 Derived: -c_in(A,B,C) | -c_in(B,c_Finite__Set_OFinites,tc_set(C)) | B = c_emptyset | c_Orderings_Omax(A,c_Finite__Set_OMin(B,C),C) = A | -class_Ring__and__Field_Oordered__idom(C). [resolve(2785,e,2567,b)].
% 26.25/26.27 2786 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2157,a,2127,b)].
% 26.25/26.27 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_less(A,c_0,tc_IntDef_Oint). [resolve(2786,d,2560,a)].
% 26.25/26.27 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(c_plus(A,A,tc_nat),c_0,tc_nat) | c_less(A,c_0,tc_nat). [resolve(2786,d,2561,a)].
% 26.25/26.27 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2786,d,2566,b)].
% 26.25/26.27 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2786,d,2567,b)].
% 26.25/26.27 2787 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2158,a,2127,b)].
% 26.25/26.27 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_0,tc_IntDef_Oint) | c_less(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(2787,d,2560,a)].
% 26.25/26.28 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_nat) | -c_less(A,c_0,tc_nat) | c_less(c_plus(A,A,tc_nat),c_0,tc_nat). [resolve(2787,d,2561,a)].
% 26.25/26.28 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2787,d,2566,b)].
% 26.25/26.28 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2787,d,2567,b)].
% 26.25/26.28 2788 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2159,a,2127,b)].
% 26.25/26.28 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2788,c,2560,a)].
% 26.25/26.28 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(A,C,tc_nat). [resolve(2788,c,2561,a)].
% 26.25/26.28 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2788,c,2566,b)].
% 26.25/26.28 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2788,c,2567,b)].
% 26.25/26.28 2789 -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2160,a,2127,b)].
% 26.25/26.28 Derived: -c_less(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(2789,c,2560,a)].
% 26.25/26.28 Derived: -c_less(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_less(B,C,tc_nat). [resolve(2789,c,2561,a)].
% 26.25/26.28 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2789,c,2566,b)].
% 26.25/26.28 Derived: -c_less(c_Orderings_Omax(A,B,C),D,C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2789,c,2567,b)].
% 26.25/26.28 2790 -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2161,a,2127,b)].
% 26.25/26.28 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,B,tc_IntDef_Oint) | c_less(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(2790,d,2560,a)].
% 26.25/26.28 Derived: -c_less(A,B,tc_nat) | -c_less(C,B,tc_nat) | c_less(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(2790,d,2561,a)].
% 26.25/26.28 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2790,d,2566,b)].
% 26.25/26.28 Derived: -c_less(A,B,C) | -c_less(D,B,C) | c_less(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2790,d,2567,b)].
% 26.25/26.28 2791 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2162,a,2127,b)].
% 26.25/26.28 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2791,c,2560,a)].
% 26.25/26.28 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2791,c,2561,a)].
% 26.25/26.28 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2791,c,2566,b)].
% 26.25/26.28 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2791,c,2567,b)].
% 26.25/26.28 2792 -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2163,a,2127,b)].
% 26.25/26.28 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2792,c,2560,a)].
% 26.25/26.28 Derived: -c_less(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2792,c,2561,a)].
% 26.25/26.28 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2792,c,2566,b)].
% 26.25/26.28 Derived: -c_less(A,c_Orderings_Omin(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2792,c,2567,b)].
% 26.25/26.28 2793 -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2164,a,2127,b)].
% 26.25/26.28 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(A,C,tc_IntDef_Oint) | c_less(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2793,d,2560,a)].
% 26.25/26.28 Derived: -c_less(A,B,tc_nat) | -c_less(A,C,tc_nat) | c_less(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(2793,d,2561,a)].
% 26.25/26.28 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2793,d,2566,b)].
% 26.25/26.28 Derived: -c_less(A,B,C) | -c_less(A,D,C) | c_less(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2793,d,2567,b)].
% 26.25/26.28 2794 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2165,a,2127,b)].
% 26.25/26.28 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2794,c,2560,a)].
% 26.25/26.28 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2794,c,2561,a)].
% 26.25/26.28 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2794,c,2566,b)].
% 26.25/26.28 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,B,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2794,c,2567,b)].
% 26.25/26.28 2795 -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2166,a,2127,b)].
% 26.25/26.28 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2795,c,2560,a)].
% 26.25/26.28 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2795,c,2561,a)].
% 26.25/26.28 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__field(D). [resolve(2795,c,2566,b)].
% 26.25/26.28 Derived: -c_lessequals(A,c_Orderings_Omin(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__idom(D). [resolve(2795,c,2567,b)].
% 26.25/26.28 2796 -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2167,a,2127,b)].
% 26.25/26.28 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(A,C,tc_IntDef_Oint) | c_lessequals(A,c_Orderings_Omin(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2796,d,2560,a)].
% 26.25/26.28 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | c_lessequals(A,c_Orderings_Omin(C,B,tc_nat),tc_nat). [resolve(2796,d,2561,a)].
% 26.25/26.28 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2796,d,2566,b)].
% 26.25/26.28 Derived: -c_lessequals(A,B,C) | -c_lessequals(A,D,C) | c_lessequals(A,c_Orderings_Omin(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2796,d,2567,b)].
% 26.25/26.28 2797 c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2168,a,2127,b)].
% 26.25/26.28 Derived: c_Orderings_Omin(A,A,tc_IntDef_Oint) = A. [resolve(2797,b,2560,a)].
% 26.25/26.28 Derived: c_Orderings_Omin(A,A,tc_nat) = A. [resolve(2797,b,2561,a)].
% 26.25/26.28 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2797,b,2566,b)].
% 26.25/26.28 Derived: c_Orderings_Omin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2797,b,2567,b)].
% 26.25/26.28 2798 c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2169,a,2127,b)].
% 26.25/26.28 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omin(A,B,tc_IntDef_Oint). [resolve(2798,b,2560,a)].
% 26.25/26.28 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Omin(A,B,tc_nat). [resolve(2798,b,2561,a)].
% 26.25/26.28 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2798,b,2566,b)].
% 26.25/26.28 Derived: c_Orderings_Omin(A,c_Orderings_Omin(A,B,C),C) = c_Orderings_Omin(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2798,b,2567,b)].
% 26.25/26.28 2799 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2170,a,2127,b)].
% 26.25/26.29 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2799,c,2560,a)].
% 26.25/26.29 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2799,c,2561,a)].
% 26.25/26.29 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2799,c,2566,b)].
% 26.25/26.29 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2799,c,2567,b)].
% 26.25/26.29 2800 -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2171,a,2127,b)].
% 26.25/26.29 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_IntDef_Oint),C,tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(2800,c,2560,a)].
% 26.25/26.29 Derived: -c_lessequals(c_Orderings_Omax(A,B,tc_nat),C,tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2800,c,2561,a)].
% 26.25/26.29 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2800,c,2566,b)].
% 26.25/26.29 Derived: -c_lessequals(c_Orderings_Omax(A,B,C),D,C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2800,c,2567,b)].
% 26.25/26.29 2801 -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2172,a,2127,b)].
% 26.25/26.29 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,B,tc_IntDef_Oint) | c_lessequals(c_Orderings_Omax(C,A,tc_IntDef_Oint),B,tc_IntDef_Oint). [resolve(2801,d,2560,a)].
% 26.25/26.29 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | c_lessequals(c_Orderings_Omax(C,A,tc_nat),B,tc_nat). [resolve(2801,d,2561,a)].
% 26.25/26.29 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2801,d,2566,b)].
% 26.25/26.29 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,B,C) | c_lessequals(c_Orderings_Omax(D,A,C),B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2801,d,2567,b)].
% 26.25/26.29 2802 c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2173,a,2127,b)].
% 26.25/26.29 Derived: c_Orderings_Omax(A,A,tc_IntDef_Oint) = A. [resolve(2802,b,2560,a)].
% 26.25/26.29 Derived: c_Orderings_Omax(A,A,tc_nat) = A. [resolve(2802,b,2561,a)].
% 26.25/26.29 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2802,b,2566,b)].
% 26.25/26.29 Derived: c_Orderings_Omax(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2802,b,2567,b)].
% 26.25/26.29 2803 c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2174,a,2127,b)].
% 26.25/26.29 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_Orderings_Omax(A,B,tc_IntDef_Oint). [resolve(2803,b,2560,a)].
% 26.25/26.29 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Omax(A,B,tc_nat). [resolve(2803,b,2561,a)].
% 26.25/26.29 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2803,b,2566,b)].
% 26.25/26.29 Derived: c_Orderings_Omax(A,c_Orderings_Omax(A,B,C),C) = c_Orderings_Omax(A,B,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2803,b,2567,b)].
% 26.25/26.29 2804 c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2175,a,2127,b)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OlessThan(A,tc_IntDef_Oint). [resolve(2804,b,2560,a)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OatLeast(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OlessThan(A,tc_nat). [resolve(2804,b,2561,a)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2804,b,2566,b)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OatLeast(A,B),tc_set(B)) = c_SetInterval_OlessThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2804,b,2567,b)].
% 26.25/26.29 2805 c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2176,a,2127,b)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OatMost(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OgreaterThan(A,tc_IntDef_Oint). [resolve(2805,b,2560,a)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OatMost(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OgreaterThan(A,tc_nat). [resolve(2805,b,2561,a)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2805,b,2566,b)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OatMost(A,B),tc_set(B)) = c_SetInterval_OgreaterThan(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2805,b,2567,b)].
% 26.25/26.29 2806 c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2177,a,2127,b)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatMost(A,tc_IntDef_Oint). [resolve(2806,b,2560,a)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatMost(A,tc_nat). [resolve(2806,b,2561,a)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2806,b,2566,b)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OgreaterThan(A,B),tc_set(B)) = c_SetInterval_OatMost(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2806,b,2567,b)].
% 26.25/26.29 2807 c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2178,a,2127,b)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeast(A,tc_IntDef_Oint). [resolve(2807,b,2560,a)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeast(A,tc_nat). [resolve(2807,b,2561,a)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2807,b,2566,b)].
% 26.25/26.29 Derived: c_uminus(c_SetInterval_OlessThan(A,B),tc_set(B)) = c_SetInterval_OatLeast(A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2807,b,2567,b)].
% 26.25/26.29 2808 c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2179,a,2127,b)].
% 26.25/26.29 Derived: c_SetInterval_OatLeast(A,tc_IntDef_Oint) != c_SetInterval_OatLeast(B,tc_IntDef_Oint) | A = B. [resolve(2808,c,2560,a)].
% 26.25/26.29 Derived: c_SetInterval_OatLeast(A,tc_nat) != c_SetInterval_OatLeast(B,tc_nat) | A = B. [resolve(2808,c,2561,a)].
% 26.25/26.29 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2808,c,2566,b)].
% 26.25/26.29 Derived: c_SetInterval_OatLeast(A,B) != c_SetInterval_OatLeast(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2808,c,2567,b)].
% 26.25/26.29 2809 c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2180,a,2127,b)].
% 26.25/26.29 Derived: c_SetInterval_OatMost(A,tc_IntDef_Oint) != c_SetInterval_OatMost(B,tc_IntDef_Oint) | A = B. [resolve(2809,c,2560,a)].
% 26.25/26.29 Derived: c_SetInterval_OatMost(A,tc_nat) != c_SetInterval_OatMost(B,tc_nat) | A = B. [resolve(2809,c,2561,a)].
% 26.25/26.29 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2809,c,2566,b)].
% 26.25/26.29 Derived: c_SetInterval_OatMost(A,B) != c_SetInterval_OatMost(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2809,c,2567,b)].
% 26.25/26.29 2810 c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2181,a,2127,b)].
% 26.25/26.29 Derived: c_SetInterval_OgreaterThan(A,tc_IntDef_Oint) != c_SetInterval_OgreaterThan(B,tc_IntDef_Oint) | A = B. [resolve(2810,c,2560,a)].
% 26.25/26.30 Derived: c_SetInterval_OgreaterThan(A,tc_nat) != c_SetInterval_OgreaterThan(B,tc_nat) | A = B. [resolve(2810,c,2561,a)].
% 26.25/26.30 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2810,c,2566,b)].
% 26.25/26.30 Derived: c_SetInterval_OgreaterThan(A,B) != c_SetInterval_OgreaterThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2810,c,2567,b)].
% 26.25/26.30 2811 -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(2182,a,2127,b)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2811,c,2560,a)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,tc_nat),c_SetInterval_OgreaterThan(B,tc_nat),tc_set(tc_nat)) | c_lessequals(B,A,tc_nat). [resolve(2811,c,2561,a)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__field(B). [resolve(2811,c,2566,b)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OgreaterThan(A,B),c_SetInterval_OgreaterThan(C,B),tc_set(B)) | c_lessequals(C,A,B) | -class_Ring__and__Field_Oordered__idom(B). [resolve(2811,c,2567,b)].
% 26.25/26.30 2812 -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(2183,a,2127,b)].
% 26.25/26.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2812,c,2560,a)].
% 26.25/26.30 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OgreaterThan(B,tc_nat),c_SetInterval_OgreaterThan(A,tc_nat),tc_set(tc_nat)). [resolve(2812,c,2561,a)].
% 26.25/26.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2812,c,2566,b)].
% 26.25/26.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OgreaterThan(B,C),c_SetInterval_OgreaterThan(A,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2812,c,2567,b)].
% 26.25/26.30 2813 -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2184,a,2127,b)].
% 26.25/26.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint). [resolve(2813,c,2560,a)].
% 26.25/26.30 Derived: -c_lessequals(A,B,tc_nat) | c_minus(c_SetInterval_OatLeastLessThan(A,C,tc_nat),c_SetInterval_OatLeastLessThan(A,B,tc_nat),tc_set(tc_nat)) = c_SetInterval_OatLeastLessThan(B,C,tc_nat). [resolve(2813,c,2561,a)].
% 26.25/26.30 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2813,c,2566,b)].
% 26.25/26.30 Derived: -c_lessequals(A,B,C) | c_minus(c_SetInterval_OatLeastLessThan(A,D,C),c_SetInterval_OatLeastLessThan(A,B,C),tc_set(C)) = c_SetInterval_OatLeastLessThan(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2813,c,2567,b)].
% 26.25/26.30 2814 -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2185,a,2127,b)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(C,A,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2814,d,2560,a)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(C,A,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2814,d,2561,a)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2814,d,2566,b)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(D,A,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2814,d,2567,b)].
% 26.25/26.30 2815 -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2186,a,2127,b)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) | c_lessequals(B,D,tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2815,d,2560,a)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)) | c_lessequals(B,D,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2815,d,2561,a)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(2815,d,2566,b)].
% 26.25/26.30 Derived: -c_lessequals(c_SetInterval_OatLeastLessThan(A,B,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | c_lessequals(B,E,C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2815,d,2567,b)].
% 26.25/26.30 2816 -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2187,a,2127,b)].
% 26.25/26.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,D,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2816,c,2560,a)].
% 26.25/26.30 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,tc_nat),c_SetInterval_OatLeastLessThan(C,D,tc_nat),tc_set(tc_nat)). [resolve(2816,c,2561,a)].
% 26.25/26.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2816,c,2566,b)].
% 26.25/26.30 Derived: -c_lessequals(A,B,C) | c_lessequals(c_SetInterval_OatLeastLessThan(B,A,C),c_SetInterval_OatLeastLessThan(D,E,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2816,c,2567,b)].
% 26.25/26.30 2817 -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2188,a,2127,b)].
% 26.25/26.30 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,D,tc_IntDef_Oint) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_IntDef_Oint),c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)). [resolve(2817,d,2560,a)].
% 26.25/26.30 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,D,tc_nat) | c_lessequals(c_SetInterval_OatLeastLessThan(D,A,tc_nat),c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_set(tc_nat)). [resolve(2817,d,2561,a)].
% 26.25/26.30 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__field(C). [resolve(2817,d,2566,b)].
% 26.25/26.30 Derived: -c_lessequals(A,B,C) | -c_lessequals(D,E,C) | c_lessequals(c_SetInterval_OatLeastLessThan(E,A,C),c_SetInterval_OatLeastLessThan(D,B,C),tc_set(C)) | -class_Ring__and__Field_Oordered__idom(C). [resolve(2817,d,2567,b)].
% 26.25/26.30 2818 c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2189,a,2127,b)].
% 26.25/26.31 Derived: c_SetInterval_OlessThan(A,tc_IntDef_Oint) != c_SetInterval_OlessThan(B,tc_IntDef_Oint) | A = B. [resolve(2818,c,2560,a)].
% 26.25/26.31 Derived: c_SetInterval_OlessThan(A,tc_nat) != c_SetInterval_OlessThan(B,tc_nat) | A = B. [resolve(2818,c,2561,a)].
% 26.25/26.31 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__field(B). [resolve(2818,c,2566,b)].
% 26.25/26.31 Derived: c_SetInterval_OlessThan(A,B) != c_SetInterval_OlessThan(C,B) | A = C | -class_Ring__and__Field_Oordered__idom(B). [resolve(2818,c,2567,b)].
% 26.25/26.31 2819 -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(2190,a,2127,b)].
% 26.25/26.31 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(2819,c,2560,a)].
% 26.25/26.31 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(2819,c,2561,a)].
% 26.25/26.31 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(2819,c,2566,b)].
% 26.25/26.31 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(2819,c,2567,b)].
% 26.25/26.31 2820 -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(2191,a,2127,b)].
% 26.25/26.31 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(2820,c,2560,a)].
% 26.25/26.31 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(2820,c,2561,a)].
% 26.25/26.31 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(2820,c,2566,b)].
% 26.25/26.31 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(2820,c,2567,b)].
% 26.25/26.31 2821 c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2192,a,2127,b)].
% 26.25/26.31 Derived: c_LOrder_Ojoin(A,A,tc_IntDef_Oint) = A. [resolve(2821,b,2560,a)].
% 26.25/26.31 Derived: c_LOrder_Ojoin(A,A,tc_nat) = A. [resolve(2821,b,2561,a)].
% 26.25/26.31 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2821,b,2566,b)].
% 26.25/26.31 Derived: c_LOrder_Ojoin(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2821,b,2567,b)].
% 26.25/26.31 2822 c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2193,a,2127,b)].
% 26.25/26.31 Derived: c_LOrder_Omeet(A,A,tc_IntDef_Oint) = A. [resolve(2822,b,2560,a)].
% 26.25/26.31 Derived: c_LOrder_Omeet(A,A,tc_nat) = A. [resolve(2822,b,2561,a)].
% 26.25/26.31 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__field(B). [resolve(2822,b,2566,b)].
% 26.25/26.31 Derived: c_LOrder_Omeet(A,A,B) = A | -class_Ring__and__Field_Oordered__idom(B). [resolve(2822,b,2567,b)].
% 26.25/26.31 2823 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2200,a,2127,b)].
% 26.25/26.31 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(2823,c,2560,a)].
% 26.25/26.31 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_lessequals(B,C,tc_nat). [resolve(2823,c,2561,a)].
% 26.25/26.31 2824 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2201,a,2127,b)].
% 26.25/26.31 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2824,c,2560,a)].
% 26.25/26.32 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(2824,c,2561,a)].
% 26.25/26.32 2825 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2202,a,2127,b)].
% 26.25/26.32 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2825,c,2560,a)].
% 26.25/26.32 Derived: -c_lessequals(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2825,c,2561,a)].
% 26.25/26.32 2826 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2203,a,2127,b)].
% 26.25/26.32 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2826,c,2560,a)].
% 26.25/26.32 Derived: -c_lessequals(A,B,tc_nat) | c_lessequals(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(2826,c,2561,a)].
% 26.25/26.32 2827 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2204,a,2127,b)].
% 26.25/26.32 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(2827,c,2560,a)].
% 26.25/26.32 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) | c_less(B,C,tc_nat). [resolve(2827,c,2561,a)].
% 26.25/26.32 2828 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2205,a,2127,b)].
% 26.25/26.32 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2828,c,2560,a)].
% 26.25/26.32 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(C,A,tc_nat),c_plus(C,B,tc_nat),tc_nat). [resolve(2828,c,2561,a)].
% 26.25/26.32 2829 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2206,a,2127,b)].
% 26.25/26.32 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2829,c,2560,a)].
% 26.25/26.32 Derived: -c_less(c_plus(A,B,tc_nat),c_plus(C,B,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2829,c,2561,a)].
% 26.25/26.32 2830 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2207,a,2127,b)].
% 26.25/26.32 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2830,c,2560,a)].
% 26.25/26.32 Derived: -c_less(A,B,tc_nat) | c_less(c_plus(A,C,tc_nat),c_plus(B,C,tc_nat),tc_nat). [resolve(2830,c,2561,a)].
% 26.25/26.32 2831 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2284,c,2127,b)].
% 26.25/26.32 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(A,C,tc_IntDef_Oint) | B = C. [resolve(2831,c,2560,a)].
% 26.25/26.32 Derived: c_plus(A,B,tc_nat) != c_plus(A,C,tc_nat) | B = C. [resolve(2831,c,2561,a)].
% 26.25/26.32 2832 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2285,c,2127,b)].
% 26.25/26.32 Derived: c_plus(A,B,tc_IntDef_Oint) != c_plus(C,B,tc_IntDef_Oint) | A = C. [resolve(2832,c,2560,a)].
% 26.25/26.32 Derived: c_plus(A,B,tc_nat) != c_plus(C,B,tc_nat) | A = C. [resolve(2832,c,2561,a)].
% 26.25/26.32 2833 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2286,b,2127,b)].
% 26.25/26.32 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(2833,b,2560,a)].
% 26.25/26.32 Derived: class_OrderedGroup_Oab__semigroup__add(tc_nat). [resolve(2833,b,2561,a)].
% 26.25/26.32 2834 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2291,b,2127,b)].
% 26.25/26.32 Derived: c_times(c_0,A,tc_IntDef_Oint) = c_0. [resolve(2834,b,2560,a)].
% 26.25/26.32 Derived: c_times(c_0,A,tc_nat) = c_0. [resolve(2834,b,2561,a)].
% 26.25/26.32 2835 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2292,b,2127,b)].
% 26.25/26.34 Derived: c_times(A,c_0,tc_IntDef_Oint) = c_0. [resolve(2835,b,2560,a)].
% 26.25/26.34 Derived: c_times(A,c_0,tc_nat) = c_0. [resolve(2835,b,2561,a)].
% 26.25/26.34 2836 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2293,b,2127,b)].
% 26.25/26.34 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(2836,b,2560,a)].
% 26.25/26.34 Derived: class_OrderedGroup_Osemigroup__add(tc_nat). [resolve(2836,b,2561,a)].
% 26.25/26.34 2837 -c_less(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2294,b,2127,b)].
% 26.25/26.34 Derived: -c_less(A,A,tc_IntDef_Oint). [resolve(2837,b,2560,a)].
% 26.25/26.34 Derived: -c_less(A,A,tc_nat). [resolve(2837,b,2561,a)].
% 26.25/26.34 2838 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2295,c,2127,b)].
% 26.25/26.34 Derived: -c_less(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2838,c,2560,a)].
% 26.25/26.34 Derived: -c_less(A,B,tc_nat) | c_SetInterval_OatLeastAtMost(B,A,tc_nat) = c_emptyset. [resolve(2838,c,2561,a)].
% 26.25/26.34 2839 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2296,b,2127,b)].
% 26.25/26.34 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_IntDef_Oint) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2839,b,2560,a)].
% 26.25/26.34 Derived: c_SetInterval_OatLeastAtMost(A,A,tc_nat) = c_insert(A,c_emptyset,tc_nat). [resolve(2839,b,2561,a)].
% 26.25/26.34 2840 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2297,c,2127,b)].
% 26.25/26.34 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OatLeastLessThan(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2840,c,2560,a)].
% 26.25/26.34 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset. [resolve(2840,c,2561,a)].
% 26.25/26.34 2841 -c_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(2298,c,2127,b)].
% 26.25/26.34 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(2841,c,2560,a)].
% 26.25/26.34 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(2841,c,2561,a)].
% 26.25/26.34 2842 -c_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(2299,c,2127,b)].
% 26.25/26.34 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(2842,c,2560,a)].
% 26.25/26.34 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(2842,c,2561,a)].
% 26.25/26.34 2843 -c_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(2300,c,2127,b)].
% 26.25/26.34 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(2843,c,2560,a)].
% 26.25/26.34 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(2843,c,2561,a)].
% 26.25/26.34 2844 -c_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(2301,c,2127,b)].
% 26.25/26.34 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(2844,c,2560,a)].
% 26.25/26.34 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(2844,c,2561,a)].
% 26.25/26.35 2845 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2302,c,2127,b)].
% 26.25/26.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_SetInterval_OgreaterThanAtMost(B,A,tc_IntDef_Oint) = c_emptyset. [resolve(2845,c,2560,a)].
% 26.25/26.35 Derived: -c_lessequals(A,B,tc_nat) | c_SetInterval_OgreaterThanAtMost(B,A,tc_nat) = c_emptyset. [resolve(2845,c,2561,a)].
% 26.25/26.35 2846 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2303,b,2127,b)].
% 26.25/26.35 Derived: c_minus(c_insert(A,c_emptyset,tc_IntDef_Oint),c_SetInterval_OlessThan(A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)) = c_insert(A,c_emptyset,tc_IntDef_Oint). [resolve(2846,b,2560,a)].
% 26.25/26.35 Derived: c_minus(c_insert(A,c_emptyset,tc_nat),c_SetInterval_OlessThan(A,tc_nat),tc_set(tc_nat)) = c_insert(A,c_emptyset,tc_nat). [resolve(2846,b,2561,a)].
% 26.25/26.35 2847 c_lessequals(A,A,B) | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2304,b,2127,b)].
% 26.25/26.35 Derived: c_lessequals(A,A,tc_IntDef_Oint). [resolve(2847,b,2560,a)].
% 26.25/26.35 Derived: c_lessequals(A,A,tc_nat). [resolve(2847,b,2561,a)].
% 26.25/26.35 2848 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2305,c,2127,b)].
% 26.25/26.35 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2848,c,2560,a)].
% 26.25/26.35 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2848,c,2561,a)].
% 26.25/26.35 2849 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2306,c,2127,b)].
% 26.25/26.35 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2849,c,2560,a)].
% 26.25/26.35 Derived: -c_in(A,c_SetInterval_OatLeastAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2849,c,2561,a)].
% 26.25/26.35 2850 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2307,d,2127,b)].
% 26.25/26.35 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2850,d,2560,a)].
% 26.25/26.35 Derived: -c_lessequals(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastAtMost(C,B,tc_nat),tc_nat). [resolve(2850,d,2561,a)].
% 26.25/26.35 2851 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2308,c,2127,b)].
% 26.25/26.35 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2851,c,2560,a)].
% 26.25/26.35 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2851,c,2561,a)].
% 26.25/26.35 2852 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2309,c,2127,b)].
% 26.25/26.35 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2852,c,2560,a)].
% 26.25/26.35 Derived: -c_in(A,c_SetInterval_OatLeastLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2852,c,2561,a)].
% 26.25/26.35 2853 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2310,d,2127,b)].
% 26.25/26.35 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2853,d,2560,a)].
% 26.25/26.35 Derived: -c_less(A,B,tc_nat) | -c_lessequals(C,A,tc_nat) | c_in(A,c_SetInterval_OatLeastLessThan(C,B,tc_nat),tc_nat). [resolve(2853,d,2561,a)].
% 26.25/26.35 2854 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2311,c,2127,b)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,A,tc_IntDef_Oint). [resolve(2854,c,2560,a)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OatLeast(B,tc_nat),tc_nat) | c_lessequals(B,A,tc_nat). [resolve(2854,c,2561,a)].
% 26.34/26.37 2855 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2312,c,2127,b)].
% 26.34/26.37 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OatLeast(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2855,c,2560,a)].
% 26.34/26.37 Derived: -c_lessequals(A,B,tc_nat) | c_in(B,c_SetInterval_OatLeast(A,tc_nat),tc_nat). [resolve(2855,c,2561,a)].
% 26.34/26.37 2856 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2313,c,2127,b)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,B,tc_IntDef_Oint). [resolve(2856,c,2560,a)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat) | c_lessequals(A,B,tc_nat). [resolve(2856,c,2561,a)].
% 26.34/26.37 2857 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2314,c,2127,b)].
% 26.34/26.37 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OatMost(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2857,c,2560,a)].
% 26.34/26.37 Derived: -c_lessequals(A,B,tc_nat) | c_in(A,c_SetInterval_OatMost(B,tc_nat),tc_nat). [resolve(2857,c,2561,a)].
% 26.34/26.37 2858 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2315,c,2127,b)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2858,c,2560,a)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2858,c,2561,a)].
% 26.34/26.37 2859 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2316,c,2127,b)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(2859,c,2560,a)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,tc_nat),tc_nat) | c_lessequals(A,C,tc_nat). [resolve(2859,c,2561,a)].
% 26.34/26.37 2860 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2317,d,2127,b)].
% 26.34/26.37 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_lessequals(B,C,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2860,d,2560,a)].
% 26.34/26.37 Derived: -c_less(A,B,tc_nat) | -c_lessequals(B,C,tc_nat) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,C,tc_nat),tc_nat). [resolve(2860,d,2561,a)].
% 26.34/26.37 2861 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2318,c,2127,b)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2861,c,2560,a)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2861,c,2561,a)].
% 26.34/26.37 2862 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Oordered__comm__semiring__strict(D). [resolve(2319,c,2127,b)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(2862,c,2560,a)].
% 26.34/26.37 Derived: -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,tc_nat),tc_nat) | c_less(A,C,tc_nat). [resolve(2862,c,2561,a)].
% 26.34/26.37 2863 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2320,d,2127,b)].
% 26.34/26.37 Derived: -c_less(A,B,tc_IntDef_Oint) | -c_less(C,A,tc_IntDef_Oint) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2863,d,2560,a)].
% 26.34/26.37 Derived: -c_less(A,B,tc_nat) | -c_less(C,A,tc_nat) | c_in(A,c_SetInterval_OgreaterThanLessThan(C,B,tc_nat),tc_nat). [resolve(2863,d,2561,a)].
% 26.73/26.80 2864 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2321,c,2127,b)].
% 26.73/26.80 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,A,tc_IntDef_Oint). [resolve(2864,c,2560,a)].
% 26.73/26.80 Derived: -c_in(A,c_SetInterval_OgreaterThan(B,tc_nat),tc_nat) | c_less(B,A,tc_nat). [resolve(2864,c,2561,a)].
% 26.73/26.80 2865 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2322,c,2127,b)].
% 26.73/26.80 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(B,c_SetInterval_OgreaterThan(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2865,c,2560,a)].
% 26.73/26.80 Derived: -c_less(A,B,tc_nat) | c_in(B,c_SetInterval_OgreaterThan(A,tc_nat),tc_nat). [resolve(2865,c,2561,a)].
% 26.73/26.80 2866 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2323,c,2127,b)].
% 26.73/26.80 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,B,tc_IntDef_Oint). [resolve(2866,c,2560,a)].
% 26.73/26.80 Derived: -c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat) | c_less(A,B,tc_nat). [resolve(2866,c,2561,a)].
% 26.73/26.80 2867 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Oordered__comm__semiring__strict(C). [resolve(2324,c,2127,b)].
% 26.73/26.80 Derived: -c_less(A,B,tc_IntDef_Oint) | c_in(A,c_SetInterval_OlessThan(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(2867,c,2560,a)].
% 26.73/26.80 Derived: -c_less(A,B,tc_nat) | c_in(A,c_SetInterval_OlessThan(B,tc_nat),tc_nat). [resolve(2867,c,2561,a)].
% 26.73/26.80 2868 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2325,b,2127,b)].
% 26.73/26.80 Derived: class_Ring__and__Field_Osemiring(tc_IntDef_Oint). [resolve(2868,b,2560,a)].
% 26.73/26.80 Derived: class_Ring__and__Field_Osemiring(tc_nat). [resolve(2868,b,2561,a)].
% 26.73/26.80 2869 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2326,b,2127,b)].
% 26.73/26.80 Derived: class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint). [resolve(2869,b,2560,a)].
% 26.73/26.80 Derived: class_OrderedGroup_Osemigroup__mult(tc_nat). [resolve(2869,b,2561,a)].
% 26.73/26.80 2870 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2327,b,2127,b)].
% 26.73/26.80 Derived: c_plus(A,c_0,tc_IntDef_Oint) = A. [resolve(2870,b,2560,a)].
% 26.73/26.80 Derived: c_plus(A,c_0,tc_nat) = A. [resolve(2870,b,2561,a)].
% 26.73/26.80 2871 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oordered__comm__semiring__strict(B). [resolve(2328,b,2127,b)].
% 26.73/26.80 Derived: c_plus(c_0,A,tc_IntDef_Oint) = A. [resolve(2871,b,2560,a)].
% 26.73/26.80 Derived: c_plus(c_0,A,tc_nat) = A. [resolve(2871,b,2561,a)].
% 26.73/26.80 2872 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2329,a,2332,b)].
% 26.73/26.80 2873 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oordered__comm__semiring__strict(A). [resolve(2558,b,2424,b)].
% 26.73/26.80 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint). [resolve(2873,b,2560,a)].
% 26.73/26.80 Derived: class_OrderedGroup_Oab__semigroup__mult(tc_nat). [resolve(2873,b,2561,a)].
% 26.73/26.80 2874 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1039,b,1010,a)].
% 26.73/26.80 2875 class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_46) # label(axiom). [assumption].
% 26.73/26.80 2876 -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].
% 26.73/26.80 2877 -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].
% 26.73/26.80 2878 -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].
% 26.73/26.80 2879 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1039,b,1011,a)].
% 27.22/27.24 2880 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1039,b,1012,a)].
% 27.22/27.24 2881 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1039,b,1013,a)].
% 27.22/27.24 2882 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1039,b,1014,a)].
% 27.22/27.24 2883 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1039,b,1015,a)].
% 27.22/27.24 2884 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1039,b,1016,a)].
% 27.22/27.24 2885 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1039,b,1017,a)].
% 27.22/27.24 2886 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1039,b,1018,a)].
% 27.22/27.24 2887 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1039,b,1019,a)].
% 27.22/27.24 2888 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1039,b,1020,a)].
% 27.22/27.24 2889 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1039,b,1021,a)].
% 27.22/27.24 2890 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1039,b,1022,a)].
% 27.22/27.24 2891 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1039,b,1023,a)].
% 27.22/27.24 2892 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1039,b,1024,a)].
% 27.22/27.24 2893 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1039,b,1025,a)].
% 27.22/27.24 2894 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1039,b,1026,a)].
% 27.22/27.24 2895 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1039,b,1027,a)].
% 27.22/27.24 2896 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1039,b,1028,a)].
% 27.22/27.24 2897 -class_Ring__and__Field_Oaxclass__abs__if(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1039,b,1029,a)].
% 27.22/27.24 2898 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Opordered__ring_0) # label(axiom). [assumption].
% 27.22/27.24 2899 class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_49) # label(axiom). [assumption].
% 27.22/27.24 2900 -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].
% 27.22/27.24 2901 -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].
% 27.22/27.24 2902 -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].
% 27.22/27.24 2903 -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].
% 27.22/27.24 Derived: class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2898,a,2900,b)].
% 27.22/27.24 Derived: class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(2898,a,2903,b)].
% 27.22/27.24 2904 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_1) # label(axiom). [assumption].
% 27.33/27.39 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2904,a,2900,b)].
% 27.33/27.39 2905 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_11) # label(axiom). [assumption].
% 27.33/27.39 2906 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Opordered__ring_12) # label(axiom). [assumption].
% 27.33/27.39 2907 -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].
% 27.33/27.39 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(2907,a,2901,b)].
% 27.33/27.39 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(2907,a,2902,b)].
% 27.33/27.39 2908 -class_Ring__and__Field_Opordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Opordered__ring_7) # label(axiom). [assumption].
% 27.33/27.39 2909 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Opordered__ring_8) # label(axiom). [assumption].
% 27.33/27.39 2910 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,c_0,A) = B. [resolve(671,b,642,a)].
% 27.33/27.39 2911 -class_Ring__and__Field_Opordered__ring(A) | c_plus(c_0,B,A) = B. [resolve(671,b,643,a)].
% 27.33/27.39 2912 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(719,b,690,a)].
% 27.33/27.39 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2912,a,2900,b)].
% 27.33/27.39 2913 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(719,b,691,a)].
% 27.33/27.39 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2913,a,2900,b)].
% 27.33/27.39 2914 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(719,b,692,a)].
% 27.33/27.39 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2914,a,2900,b)].
% 27.33/27.39 2915 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(719,b,693,a)].
% 27.33/27.39 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2915,a,2900,b)].
% 27.33/27.39 2916 -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(719,b,694,a)].
% 27.33/27.39 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2916,a,2900,b)].
% 27.33/27.39 2917 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(719,b,695,a)].
% 27.33/27.39 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2917,a,2900,b)].
% 27.33/27.39 2918 -class_Ring__and__Field_Opordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(719,b,696,a)].
% 27.33/27.39 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2918,a,2900,b)].
% 27.33/27.39 2919 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(719,b,697,a)].
% 27.33/27.39 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2919,a,2900,b)].
% 27.33/27.39 2920 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(719,b,709,a)].
% 27.33/27.39 2921 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(719,b,711,a)].
% 27.33/27.39 2922 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(753,b,726,a)].
% 27.43/27.49 2923 -class_Ring__and__Field_Opordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(753,b,727,a)].
% 27.43/27.49 2924 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,B,A). [resolve(911,b,880,a)].
% 27.43/27.49 2925 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(911,b,881,a)].
% 27.43/27.49 2926 -class_Ring__and__Field_Opordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(911,b,882,a)].
% 27.43/27.49 2927 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(911,b,883,a)].
% 27.43/27.49 2928 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(911,b,884,a)].
% 27.43/27.49 2929 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(911,b,885,a)].
% 27.43/27.49 2930 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(911,b,886,a)].
% 27.43/27.49 2931 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(911,b,887,a)].
% 27.43/27.49 2932 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(911,b,888,a)].
% 27.43/27.49 2933 -class_Ring__and__Field_Opordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(911,b,889,a)].
% 27.43/27.49 2934 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,B,A). [resolve(911,b,890,a)].
% 27.43/27.49 2935 -class_Ring__and__Field_Opordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(984,b,967,a)].
% 27.43/27.49 2936 -class_Ring__and__Field_Opordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(984,b,968,a)].
% 27.43/27.49 2937 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(988,a,984,b)].
% 27.43/27.49 2938 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(989,a,984,b)].
% 27.43/27.49 2939 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1005,a,984,b)].
% 27.43/27.49 2940 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(1006,a,984,b)].
% 27.43/27.49 2941 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(1007,a,984,b)].
% 27.43/27.49 2942 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Opordered__ring(C). [resolve(1008,a,984,b)].
% 27.43/27.49 2943 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1050,b,1010,a)].
% 27.43/27.49 2944 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1050,b,1011,a)].
% 27.43/27.49 2945 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1050,b,1012,a)].
% 27.43/27.49 2946 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1050,b,1013,a)].
% 27.43/27.49 2947 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1050,b,1014,a)].
% 27.43/27.49 2948 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1050,b,1015,a)].
% 27.43/27.49 2949 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1050,b,1016,a)].
% 27.43/27.49 2950 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1050,b,1017,a)].
% 27.43/27.49 2951 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1050,b,1018,a)].
% 27.43/27.49 2952 -class_Ring__and__Field_Opordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1050,b,1019,a)].
% 27.54/27.60 2953 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1050,b,1020,a)].
% 27.54/27.60 2954 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1050,b,1021,a)].
% 27.54/27.60 2955 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1050,b,1022,a)].
% 27.54/27.60 2956 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1050,b,1023,a)].
% 27.54/27.60 2957 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1050,b,1024,a)].
% 27.54/27.60 2958 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1050,b,1025,a)].
% 27.54/27.60 2959 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1050,b,1026,a)].
% 27.54/27.60 2960 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1050,b,1027,a)].
% 27.54/27.60 2961 -class_Ring__and__Field_Opordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1050,b,1028,a)].
% 27.54/27.60 2962 -class_Ring__and__Field_Opordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1050,b,1029,a)].
% 27.54/27.60 2963 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1162,a,1132,a)].
% 27.54/27.60 2964 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1162,a,1133,a)].
% 27.54/27.60 2965 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(1812,a,1763,b)].
% 27.54/27.60 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2965,b,2900,b)].
% 27.54/27.60 2966 -c_less(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1987,a,1977,b)].
% 27.54/27.60 2967 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1988,a,1977,b)].
% 27.54/27.60 2968 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1989,a,1977,b)].
% 27.54/27.60 2969 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1990,a,1977,b)].
% 27.54/27.60 2970 -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(1991,a,1977,b)].
% 27.54/27.60 2971 -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(1992,a,1977,b)].
% 27.54/27.60 2972 -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(1993,a,1977,b)].
% 27.54/27.60 2973 -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(1994,a,1977,b)].
% 27.54/27.60 2974 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Opordered__ring(C). [resolve(1995,a,1977,b)].
% 27.54/27.60 2975 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1996,a,1977,b)].
% 27.54/27.60 2976 c_lessequals(A,A,B) | -class_Ring__and__Field_Opordered__ring(B). [resolve(1997,a,1977,b)].
% 27.54/27.60 2977 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(1998,a,1977,b)].
% 27.54/27.60 2978 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(1999,a,1977,b)].
% 27.54/27.60 2979 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2000,a,1977,b)].
% 27.85/27.91 2980 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2001,a,1977,b)].
% 27.85/27.91 2981 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2002,a,1977,b)].
% 27.85/27.91 2982 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2003,a,1977,b)].
% 27.85/27.91 2983 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2004,a,1977,b)].
% 27.85/27.91 2984 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2005,a,1977,b)].
% 27.85/27.91 2985 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2006,a,1977,b)].
% 27.85/27.91 2986 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2007,a,1977,b)].
% 27.85/27.91 2987 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2008,a,1977,b)].
% 27.85/27.91 2988 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2009,a,1977,b)].
% 27.85/27.91 2989 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2010,a,1977,b)].
% 27.85/27.91 2990 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2011,a,1977,b)].
% 27.85/27.91 2991 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Opordered__ring(D). [resolve(2012,a,1977,b)].
% 27.85/27.91 2992 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2013,a,1977,b)].
% 27.85/27.91 2993 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2014,a,1977,b)].
% 27.85/27.91 2994 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2015,a,1977,b)].
% 27.85/27.91 2995 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2016,a,1977,b)].
% 27.85/27.91 2996 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Opordered__ring(C). [resolve(2017,a,1977,b)].
% 27.85/27.91 2997 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2018,b,1977,b)].
% 27.85/27.91 2998 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2021,b,1977,b)].
% 27.85/27.91 2999 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(2022,b,1977,b)].
% 27.85/27.91 3000 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Opordered__ring(B). [resolve(2023,b,1977,b)].
% 27.85/27.91 3001 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Opordered__ring(A). [resolve(2088,a,2037,b)].
% 27.85/27.91 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3001,b,2900,b)].
% 27.85/27.91 3002 -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].
% 27.85/27.91 3003 class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_51) # label(axiom). [assumption].
% 27.85/27.91 3004 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_1) # label(axiom). [assumption].
% 27.85/27.91 3005 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_11) # label(axiom). [assumption].
% 27.85/27.91 3006 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__meet_13) # label(axiom). [assumption].
% 27.85/27.91 3007 -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].
% 28.02/28.06 3008 -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].
% 28.02/28.06 3009 -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].
% 28.02/28.06 3010 -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].
% 28.02/28.06 3011 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(281,b,273,a)].
% 28.02/28.06 3012 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(304,b,296,a)].
% 28.02/28.06 3013 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,c_0,A) = B. [resolve(652,b,642,a)].
% 28.02/28.06 3014 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(c_0,B,A) = B. [resolve(652,b,643,a)].
% 28.02/28.06 3015 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(652,b,647,a)].
% 28.02/28.06 3016 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(652,b,648,a)].
% 28.02/28.06 3017 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(701,b,690,a)].
% 28.02/28.06 3018 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(701,b,691,a)].
% 28.02/28.06 3019 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(701,b,692,a)].
% 28.02/28.06 3020 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(701,b,693,a)].
% 28.02/28.06 3021 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(701,b,694,a)].
% 28.02/28.06 3022 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(701,b,695,a)].
% 28.02/28.06 3023 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(701,b,696,a)].
% 28.02/28.06 3024 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(701,b,697,a)].
% 28.02/28.06 3025 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(735,b,726,a)].
% 28.02/28.06 3026 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(735,b,727,a)].
% 28.02/28.06 3027 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(770,a,731,a)].
% 28.02/28.06 3028 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(813,b,779,a)].
% 28.02/28.06 Derived: -c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | c_lessequals(A,c_0,tc_IntDef_Oint). [resolve(3028,a,3003,a)].
% 28.02/28.06 3029 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(813,b,780,a)].
% 28.02/28.06 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_lessequals(c_plus(A,A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3029,a,3003,a)].
% 28.02/28.06 3030 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(813,b,781,a)].
% 28.02/28.06 Derived: c_LOrder_Ojoin(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3030,a,3003,a)].
% 28.02/28.06 3031 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(813,b,782,a)].
% 28.02/28.06 Derived: c_LOrder_Ojoin(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(3031,a,3003,a)].
% 28.02/28.06 3032 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(813,b,783,a)].
% 28.02/28.06 Derived: c_LOrder_Omeet(A,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3032,a,3003,a)].
% 28.02/28.07 3033 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(813,b,784,a)].
% 28.02/28.07 Derived: c_LOrder_Omeet(c_0,c_uminus(c_0,tc_IntDef_Oint),tc_IntDef_Oint) = c_0. [resolve(3033,a,3003,a)].
% 28.02/28.07 3034 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(813,b,785,a)].
% 28.02/28.07 Derived: c_uminus(c_LOrder_Ojoin(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Omeet(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3034,a,3003,a)].
% 28.02/28.07 3035 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(813,b,786,a)].
% 28.02/28.07 Derived: c_uminus(c_LOrder_Omeet(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_LOrder_Ojoin(c_uminus(A,tc_IntDef_Oint),c_uminus(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3035,a,3003,a)].
% 28.02/28.07 3036 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(813,b,787,a)].
% 28.02/28.07 Derived: c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) = c_0. [resolve(3036,a,3003,a)].
% 28.02/28.07 3037 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(813,b,788,a)].
% 28.02/28.07 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = c_0. [resolve(3037,a,3003,a)].
% 28.02/28.07 3038 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(813,b,789,a)].
% 28.02/28.07 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Onprt(A,tc_IntDef_Oint) = A. [resolve(3038,a,3003,a)].
% 28.02/28.07 3039 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(813,b,790,a)].
% 28.02/28.07 Derived: c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3039,a,3003,a)].
% 28.02/28.07 3040 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(813,b,791,a)].
% 28.02/28.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Onprt(A,tc_IntDef_Oint),c_OrderedGroup_Onprt(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3040,a,3003,a)].
% 28.02/28.07 3041 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(813,b,792,a)].
% 28.02/28.07 Derived: c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) = c_0. [resolve(3041,a,3003,a)].
% 28.02/28.07 3042 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(813,b,793,a)].
% 28.02/28.07 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = c_0. [resolve(3042,a,3003,a)].
% 28.02/28.07 3043 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(813,b,794,a)].
% 28.02/28.07 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_OrderedGroup_Opprt(A,tc_IntDef_Oint) = A. [resolve(3043,a,3003,a)].
% 28.02/28.07 3044 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(813,b,795,a)].
% 28.02/28.07 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_OrderedGroup_Opprt(A,tc_IntDef_Oint),c_OrderedGroup_Opprt(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3044,a,3003,a)].
% 28.02/28.07 3045 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(813,b,796,a)].
% 28.02/28.07 Derived: -c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_0,A,tc_IntDef_Oint). [resolve(3045,a,3003,a)].
% 28.02/28.07 3046 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(813,b,797,a)].
% 28.02/28.07 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_lessequals(c_0,c_plus(A,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3046,a,3003,a)].
% 28.02/28.07 3047 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(813,b,798,a)].
% 28.02/28.07 Derived: c_lessequals(c_0,c_OrderedGroup_Opprt(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3047,a,3003,a)].
% 28.08/28.12 3048 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(813,b,799,a)].
% 28.08/28.12 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(3048,a,3003,a)].
% 28.08/28.12 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3048,a,3007,b)].
% 28.08/28.12 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3048,a,3010,b)].
% 28.08/28.12 3049 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__group__add(A). [resolve(813,b,800,a)].
% 28.08/28.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3049,a,3009,b)].
% 28.08/28.12 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3049,a,3010,b)].
% 28.08/28.12 3050 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,B,A). [resolve(895,b,880,a)].
% 28.08/28.12 3051 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(895,b,881,a)].
% 28.08/28.12 3052 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(895,b,882,a)].
% 28.08/28.12 3053 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(895,b,883,a)].
% 28.08/28.12 3054 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(895,b,884,a)].
% 28.08/28.12 3055 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(895,b,885,a)].
% 28.08/28.12 3056 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(895,b,886,a)].
% 28.08/28.12 3057 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(895,b,887,a)].
% 28.08/28.12 3058 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(895,b,888,a)].
% 28.08/28.12 3059 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(895,b,889,a)].
% 28.08/28.12 3060 -class_OrderedGroup_Olordered__ab__group__meet(A) | c_lessequals(B,B,A). [resolve(895,b,890,a)].
% 28.08/28.12 3061 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1034,b,1010,a)].
% 28.08/28.12 3062 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1034,b,1011,a)].
% 28.08/28.12 3063 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1034,b,1012,a)].
% 28.08/28.12 3064 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1034,b,1013,a)].
% 28.08/28.12 3065 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1034,b,1014,a)].
% 28.08/28.12 3066 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1034,b,1015,a)].
% 28.08/28.12 3067 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1034,b,1016,a)].
% 28.08/28.12 3068 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1034,b,1017,a)].
% 28.08/28.12 3069 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1034,b,1018,a)].
% 28.08/28.12 3070 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1034,b,1019,a)].
% 28.16/28.21 3071 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1034,b,1020,a)].
% 28.16/28.21 3072 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1034,b,1021,a)].
% 28.16/28.21 3073 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1034,b,1022,a)].
% 28.16/28.21 3074 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1034,b,1023,a)].
% 28.16/28.21 3075 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1034,b,1024,a)].
% 28.16/28.21 3076 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1034,b,1025,a)].
% 28.16/28.21 3077 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1034,b,1026,a)].
% 28.16/28.21 3078 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1034,b,1027,a)].
% 28.16/28.21 3079 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1034,b,1028,a)].
% 28.16/28.21 3080 -class_OrderedGroup_Olordered__ab__group__meet(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1034,b,1029,a)].
% 28.16/28.21 3081 -class_OrderedGroup_Olordered__ab__group__meet(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1249,a,1209,a)].
% 28.16/28.21 3082 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1718,a,1686,b)].
% 28.16/28.21 3083 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1719,a,1686,b)].
% 28.16/28.21 3084 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1720,a,1686,b)].
% 28.16/28.21 3085 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1721,a,1686,b)].
% 28.16/28.21 3086 -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(1722,a,1686,b)].
% 28.16/28.21 3087 -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(1723,a,1686,b)].
% 28.16/28.21 3088 -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(1724,a,1686,b)].
% 28.16/28.21 3089 -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(1725,a,1686,b)].
% 28.16/28.21 3090 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1726,a,1686,b)].
% 28.16/28.21 3091 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1727,a,1686,b)].
% 28.16/28.21 3092 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__meet(B). [resolve(1728,a,1686,b)].
% 28.16/28.21 3093 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1729,a,1686,b)].
% 28.16/28.21 3094 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1730,a,1686,b)].
% 28.16/28.21 3095 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1731,a,1686,b)].
% 28.16/28.21 3096 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1732,a,1686,b)].
% 28.53/28.55 3097 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1733,a,1686,b)].
% 28.53/28.55 3098 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1734,a,1686,b)].
% 28.53/28.55 3099 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1735,a,1686,b)].
% 28.53/28.55 3100 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1736,a,1686,b)].
% 28.53/28.55 3101 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1737,a,1686,b)].
% 28.53/28.55 3102 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1738,a,1686,b)].
% 28.53/28.55 3103 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1739,a,1686,b)].
% 28.53/28.55 3104 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1740,a,1686,b)].
% 28.53/28.55 3105 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1741,a,1686,b)].
% 28.53/28.55 3106 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1742,a,1686,b)].
% 28.53/28.55 3107 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__meet(D). [resolve(1743,a,1686,b)].
% 28.53/28.55 3108 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1744,a,1686,b)].
% 28.53/28.55 3109 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1745,a,1686,b)].
% 28.53/28.55 3110 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1746,a,1686,b)].
% 28.53/28.55 3111 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1747,a,1686,b)].
% 28.53/28.55 3112 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1748,a,1686,b)].
% 28.53/28.55 3113 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1773,a,1753,b)].
% 28.53/28.55 3114 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__meet(C). [resolve(1774,a,1753,b)].
% 28.53/28.55 3115 -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].
% 28.53/28.55 3116 class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_52) # label(axiom). [assumption].
% 28.53/28.55 3117 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_1) # label(axiom). [assumption].
% 28.53/28.55 3118 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_11) # label(axiom). [assumption].
% 28.53/28.55 3119 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_OrderedGroup_Olordered__ab__group__join_13) # label(axiom). [assumption].
% 28.53/28.55 3120 -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].
% 28.53/28.55 3121 -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].
% 28.53/28.55 3122 -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].
% 28.68/28.70 3123 -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].
% 28.68/28.70 3124 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(280,b,273,a)].
% 28.68/28.70 3125 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(303,b,296,a)].
% 28.68/28.70 3126 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,c_0,A) = B. [resolve(651,b,642,a)].
% 28.68/28.70 3127 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(c_0,B,A) = B. [resolve(651,b,643,a)].
% 28.68/28.70 3128 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(651,b,647,a)].
% 28.68/28.70 3129 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(651,b,648,a)].
% 28.68/28.70 3130 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(700,b,690,a)].
% 28.68/28.70 3131 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(700,b,691,a)].
% 28.68/28.70 3132 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(700,b,692,a)].
% 28.68/28.70 3133 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(700,b,693,a)].
% 28.68/28.70 3134 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(700,b,694,a)].
% 28.68/28.70 3135 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(700,b,695,a)].
% 28.68/28.70 3136 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(700,b,696,a)].
% 28.68/28.70 3137 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(700,b,697,a)].
% 28.68/28.70 3138 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(734,b,726,a)].
% 28.68/28.70 3139 -class_OrderedGroup_Olordered__ab__group__join(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(734,b,727,a)].
% 28.68/28.70 3140 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(769,a,731,a)].
% 28.68/28.70 3141 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(812,b,779,a)].
% 28.68/28.70 3142 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(812,b,780,a)].
% 28.68/28.70 3143 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(812,b,781,a)].
% 28.68/28.70 3144 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(812,b,782,a)].
% 28.68/28.70 3145 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(812,b,783,a)].
% 28.68/28.70 3146 -class_OrderedGroup_Olordered__ab__group__join(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(812,b,784,a)].
% 28.68/28.70 3147 -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(812,b,785,a)].
% 28.68/28.70 3148 -class_OrderedGroup_Olordered__ab__group__join(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(812,b,786,a)].
% 28.68/28.70 3149 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(812,b,787,a)].
% 28.68/28.70 3150 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(812,b,788,a)].
% 28.68/28.70 3151 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(812,b,789,a)].
% 28.68/28.70 3152 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(812,b,790,a)].
% 28.68/28.75 3153 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(812,b,791,a)].
% 28.68/28.75 3154 -class_OrderedGroup_Olordered__ab__group__join(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(812,b,792,a)].
% 28.68/28.75 3155 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(812,b,793,a)].
% 28.68/28.75 3156 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(812,b,794,a)].
% 28.68/28.75 3157 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(812,b,795,a)].
% 28.68/28.75 3158 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(812,b,796,a)].
% 28.68/28.75 3159 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(812,b,797,a)].
% 28.68/28.75 3160 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(812,b,798,a)].
% 28.68/28.75 3161 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(812,b,799,a)].
% 28.68/28.75 3162 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__group__add(A). [resolve(812,b,800,a)].
% 28.68/28.75 3163 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,B,A). [resolve(894,b,880,a)].
% 28.68/28.75 3164 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(894,b,881,a)].
% 28.68/28.75 3165 -class_OrderedGroup_Olordered__ab__group__join(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(894,b,882,a)].
% 28.68/28.75 3166 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(894,b,883,a)].
% 28.68/28.75 3167 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(894,b,884,a)].
% 28.68/28.75 3168 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(894,b,885,a)].
% 28.68/28.75 3169 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(894,b,886,a)].
% 28.68/28.75 3170 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(894,b,887,a)].
% 28.68/28.75 3171 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(894,b,888,a)].
% 28.68/28.75 3172 -class_OrderedGroup_Olordered__ab__group__join(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(894,b,889,a)].
% 28.68/28.75 3173 -class_OrderedGroup_Olordered__ab__group__join(A) | c_lessequals(B,B,A). [resolve(894,b,890,a)].
% 28.68/28.75 3174 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1033,b,1010,a)].
% 28.68/28.75 3175 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1033,b,1011,a)].
% 28.68/28.75 3176 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1033,b,1012,a)].
% 28.68/28.75 3177 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1033,b,1013,a)].
% 28.68/28.75 3178 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1033,b,1014,a)].
% 28.68/28.75 3179 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1033,b,1015,a)].
% 28.82/28.83 3180 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1033,b,1016,a)].
% 28.82/28.83 3181 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1033,b,1017,a)].
% 28.82/28.83 3182 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1033,b,1018,a)].
% 28.82/28.83 3183 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1033,b,1019,a)].
% 28.82/28.83 3184 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1033,b,1020,a)].
% 28.82/28.83 3185 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1033,b,1021,a)].
% 28.82/28.83 3186 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1033,b,1022,a)].
% 28.82/28.83 3187 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1033,b,1023,a)].
% 28.82/28.83 3188 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1033,b,1024,a)].
% 28.82/28.83 3189 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1033,b,1025,a)].
% 28.82/28.83 3190 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1033,b,1026,a)].
% 28.82/28.83 3191 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1033,b,1027,a)].
% 28.82/28.83 3192 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1033,b,1028,a)].
% 28.82/28.83 3193 -class_OrderedGroup_Olordered__ab__group__join(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1033,b,1029,a)].
% 28.82/28.83 3194 -class_OrderedGroup_Olordered__ab__group__join(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1248,a,1209,a)].
% 28.82/28.83 3195 -c_less(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1718,a,1685,b)].
% 28.82/28.83 3196 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1719,a,1685,b)].
% 28.82/28.83 3197 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1720,a,1685,b)].
% 28.82/28.83 3198 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1721,a,1685,b)].
% 28.82/28.83 3199 -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(1722,a,1685,b)].
% 28.82/28.83 3200 -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(1723,a,1685,b)].
% 28.82/28.83 3201 -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(1724,a,1685,b)].
% 28.82/28.83 3202 -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(1725,a,1685,b)].
% 28.82/28.83 3203 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1726,a,1685,b)].
% 28.82/28.83 3204 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1727,a,1685,b)].
% 28.82/28.83 3205 c_lessequals(A,A,B) | -class_OrderedGroup_Olordered__ab__group__join(B). [resolve(1728,a,1685,b)].
% 28.82/28.83 3206 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1729,a,1685,b)].
% 29.13/29.17 3207 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1730,a,1685,b)].
% 29.13/29.17 3208 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1731,a,1685,b)].
% 29.13/29.17 3209 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1732,a,1685,b)].
% 29.13/29.17 3210 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1733,a,1685,b)].
% 29.13/29.17 3211 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1734,a,1685,b)].
% 29.13/29.17 3212 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1735,a,1685,b)].
% 29.13/29.17 3213 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1736,a,1685,b)].
% 29.13/29.17 3214 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1737,a,1685,b)].
% 29.13/29.17 3215 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1738,a,1685,b)].
% 29.13/29.17 3216 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1739,a,1685,b)].
% 29.13/29.17 3217 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1740,a,1685,b)].
% 29.13/29.17 3218 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1741,a,1685,b)].
% 29.13/29.17 3219 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1742,a,1685,b)].
% 29.13/29.17 3220 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_OrderedGroup_Olordered__ab__group__join(D). [resolve(1743,a,1685,b)].
% 29.13/29.17 3221 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1744,a,1685,b)].
% 29.13/29.17 3222 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1745,a,1685,b)].
% 29.13/29.17 3223 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1746,a,1685,b)].
% 29.13/29.17 3224 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1747,a,1685,b)].
% 29.13/29.17 3225 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1748,a,1685,b)].
% 29.13/29.17 3226 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1773,a,1752,b)].
% 29.13/29.17 3227 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_OrderedGroup_Olordered__ab__group__join(C). [resolve(1774,a,1752,b)].
% 29.13/29.17 3228 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Olordered__ring_1) # label(axiom). [assumption].
% 29.13/29.17 3229 class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_53) # label(axiom). [assumption].
% 29.13/29.17 3230 -class_Ring__and__Field_Olordered__ring(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Olordered__ring_14) # label(axiom). [assumption].
% 29.13/29.17 3231 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Olordered__ring_15) # label(axiom). [assumption].
% 29.13/29.17 3232 -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].
% 29.22/29.29 3233 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_20) # label(axiom). [assumption].
% 29.22/29.29 3234 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_22) # label(axiom). [assumption].
% 29.22/29.29 3235 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Olordered__ring_3) # label(axiom). [assumption].
% 29.22/29.29 3236 -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].
% 29.22/29.29 3237 -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].
% 29.22/29.29 3238 -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].
% 29.22/29.29 3239 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(283,b,273,a)].
% 29.22/29.29 3240 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(306,b,296,a)].
% 29.22/29.29 3241 -class_Ring__and__Field_Olordered__ring(A) | c_0 != c_HOL_Oabs(B,A) | B = c_0. [resolve(635,b,603,a)].
% 29.22/29.29 Derived: c_0 != c_HOL_Oabs(A,tc_IntDef_Oint) | A = c_0. [resolve(3241,a,3229,a)].
% 29.22/29.29 3242 -class_Ring__and__Field_Olordered__ring(A) | c_0 = c_HOL_Oabs(c_0,A). [resolve(635,b,604,a)].
% 29.22/29.29 Derived: c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint). [resolve(3242,a,3229,a)].
% 29.22/29.29 3243 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A),A) = c_plus(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A). [resolve(635,b,605,a)].
% 29.22/29.29 Derived: c_HOL_Oabs(c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_HOL_Oabs(A,tc_IntDef_Oint),c_HOL_Oabs(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3243,a,3229,a)].
% 29.22/29.29 3244 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(B,A) != c_0 | B = c_0. [resolve(635,b,606,a)].
% 29.22/29.29 Derived: c_HOL_Oabs(A,tc_IntDef_Oint) != c_0 | A = c_0. [resolve(3244,a,3229,a)].
% 29.22/29.29 3245 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_0,A) = c_0. [resolve(635,b,607,a)].
% 29.22/29.29 Derived: c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0. [resolve(3245,a,3229,a)].
% 29.22/29.29 3246 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_HOL_Oabs(B,A),A). [resolve(635,b,608,a)].
% 29.22/29.29 Derived: c_lessequals(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3246,a,3229,a)].
% 29.22/29.29 3247 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_HOL_Oabs(B,A),A) = c_HOL_Oabs(B,A). [resolve(635,b,609,a)].
% 29.22/29.29 Derived: c_HOL_Oabs(c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3247,a,3229,a)].
% 29.22/29.29 3248 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_HOL_Oabs(B,A),c_0,A) | B = c_0. [resolve(635,b,610,a)].
% 29.22/29.29 Derived: -c_lessequals(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint) | A = c_0. [resolve(3248,a,3229,a)].
% 29.22/29.29 3249 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs(c_0,A),c_0,A). [resolve(635,b,611,a)].
% 29.22/29.29 Derived: c_lessequals(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3249,a,3229,a)].
% 29.22/29.29 3250 -class_Ring__and__Field_Olordered__ring(A) | c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A). [resolve(635,b,612,a)].
% 29.22/29.29 Derived: c_HOL_Oabs(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_HOL_Oabs(A,tc_IntDef_Oint). [resolve(3250,a,3229,a)].
% 29.22/29.29 3251 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_HOL_Oabs(B,A),c_0,A). [resolve(635,b,613,a)].
% 29.22/29.29 Derived: -c_less(c_HOL_Oabs(A,tc_IntDef_Oint),c_0,tc_IntDef_Oint). [resolve(3251,a,3229,a)].
% 29.22/29.29 3252 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_HOL_Oabs(B,A) = B. [resolve(635,b,614,a)].
% 29.22/29.29 Derived: -c_lessequals(c_0,A,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = A. [resolve(3252,a,3229,a)].
% 29.22/29.29 3253 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_HOL_Oabs(B,A) = c_uminus(B,A). [resolve(635,b,615,a)].
% 29.29/29.32 Derived: -c_lessequals(A,c_0,tc_IntDef_Oint) | c_HOL_Oabs(A,tc_IntDef_Oint) = c_uminus(A,tc_IntDef_Oint). [resolve(3253,a,3229,a)].
% 29.29/29.32 3254 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_0,c_HOL_Oabs(c_0,A),A). [resolve(635,b,616,a)].
% 29.29/29.32 Derived: -c_less(c_0,c_HOL_Oabs(c_0,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3254,a,3229,a)].
% 29.29/29.32 3255 -class_Ring__and__Field_Olordered__ring(A) | c_less(c_0,c_HOL_Oabs(B,A),A) | B = c_0. [resolve(635,b,617,a)].
% 29.29/29.32 Derived: c_less(c_0,c_HOL_Oabs(A,tc_IntDef_Oint),tc_IntDef_Oint) | A = c_0. [resolve(3255,a,3229,a)].
% 29.29/29.32 3256 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Opordered__ab__group__add(A). [resolve(635,b,619,a)].
% 29.29/29.32 3257 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(635,b,620,a)].
% 29.29/29.32 3258 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(635,b,622,a)].
% 29.29/29.32 3259 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,c_0,A) = B. [resolve(661,b,642,a)].
% 29.29/29.32 3260 -class_Ring__and__Field_Olordered__ring(A) | c_plus(c_0,B,A) = B. [resolve(661,b,643,a)].
% 29.29/29.32 3261 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(687,b,647,a)].
% 29.29/29.32 3262 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(687,b,648,a)].
% 29.29/29.32 3263 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(B,D,A),A) | c_lessequals(C,D,A). [resolve(713,b,690,a)].
% 29.29/29.32 3264 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(713,b,691,a)].
% 29.29/29.32 3265 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A) | c_lessequals(B,D,A). [resolve(713,b,692,a)].
% 29.29/29.32 3266 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(713,b,693,a)].
% 29.29/29.32 3267 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(B,D,A),A) | c_less(C,D,A). [resolve(713,b,694,a)].
% 29.29/29.32 3268 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(D,B,A),c_plus(D,C,A),A). [resolve(713,b,695,a)].
% 29.29/29.32 3269 -class_Ring__and__Field_Olordered__ring(A) | -c_less(c_plus(B,C,A),c_plus(D,C,A),A) | c_less(B,D,A). [resolve(713,b,696,a)].
% 29.29/29.32 3270 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_less(c_plus(B,D,A),c_plus(C,D,A),A). [resolve(713,b,697,a)].
% 29.29/29.32 3271 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(744,b,726,a)].
% 29.29/29.32 3272 -class_Ring__and__Field_Olordered__ring(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(744,b,727,a)].
% 29.29/29.32 3273 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_plus(B,B,A),c_0,A) | c_lessequals(B,c_0,A). [resolve(814,b,779,a)].
% 29.29/29.32 3274 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_lessequals(c_plus(B,B,A),c_0,A). [resolve(814,b,780,a)].
% 29.29/29.32 3275 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(814,b,781,a)].
% 29.29/29.32 3276 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Ojoin(c_0,c_uminus(c_0,A),A) = c_0. [resolve(814,b,782,a)].
% 29.29/29.32 3277 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(B,c_uminus(B,A),A) != c_0 | B = c_0. [resolve(814,b,783,a)].
% 29.29/29.32 3278 -class_Ring__and__Field_Olordered__ring(A) | c_LOrder_Omeet(c_0,c_uminus(c_0,A),A) = c_0. [resolve(814,b,784,a)].
% 29.29/29.32 3279 -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Ojoin(B,C,A),A) = c_LOrder_Omeet(c_uminus(B,A),c_uminus(C,A),A). [resolve(814,b,785,a)].
% 29.29/29.32 3280 -class_Ring__and__Field_Olordered__ring(A) | c_uminus(c_LOrder_Omeet(B,C,A),A) = c_LOrder_Ojoin(c_uminus(B,A),c_uminus(C,A),A). [resolve(814,b,786,a)].
% 29.29/29.32 3281 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Onprt(c_0,A) = c_0. [resolve(814,b,787,a)].
% 29.29/29.32 3282 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Onprt(B,A) = c_0. [resolve(814,b,788,a)].
% 29.29/29.32 3283 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Onprt(B,A) = B. [resolve(814,b,789,a)].
% 29.35/29.37 3284 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_0,A). [resolve(814,b,790,a)].
% 29.35/29.37 3285 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Onprt(B,A),c_OrderedGroup_Onprt(C,A),A). [resolve(814,b,791,a)].
% 29.35/29.37 3286 -class_Ring__and__Field_Olordered__ring(A) | c_OrderedGroup_Opprt(c_0,A) = c_0. [resolve(814,b,792,a)].
% 29.35/29.37 3287 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,c_0,A) | c_OrderedGroup_Opprt(B,A) = c_0. [resolve(814,b,793,a)].
% 29.35/29.37 3288 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_OrderedGroup_Opprt(B,A) = B. [resolve(814,b,794,a)].
% 29.35/29.37 3289 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_OrderedGroup_Opprt(B,A),c_OrderedGroup_Opprt(C,A),A). [resolve(814,b,795,a)].
% 29.35/29.37 3290 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,c_plus(B,B,A),A) | c_lessequals(c_0,B,A). [resolve(814,b,796,a)].
% 29.35/29.37 3291 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_0,B,A) | c_lessequals(c_0,c_plus(B,B,A),A). [resolve(814,b,797,a)].
% 29.35/29.37 3292 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_0,c_OrderedGroup_Opprt(B,A),A). [resolve(814,b,798,a)].
% 29.35/29.37 3293 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(842,a,814,b)].
% 29.35/29.37 3294 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,B,A). [resolve(901,b,880,a)].
% 29.35/29.37 3295 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(901,b,881,a)].
% 29.35/29.37 3296 -class_Ring__and__Field_Olordered__ring(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(901,b,882,a)].
% 29.35/29.37 3297 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(901,b,883,a)].
% 29.35/29.37 3298 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(901,b,884,a)].
% 29.35/29.37 3299 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(901,b,885,a)].
% 29.35/29.37 3300 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(901,b,886,a)].
% 29.35/29.37 3301 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(901,b,887,a)].
% 29.35/29.37 3302 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(901,b,888,a)].
% 29.35/29.37 3303 -class_Ring__and__Field_Olordered__ring(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(901,b,889,a)].
% 29.35/29.37 3304 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(B,B,A). [resolve(901,b,890,a)].
% 29.35/29.37 3305 -class_Ring__and__Field_Olordered__ring(A) | c_times(c_0,B,A) = c_0. [resolve(975,b,967,a)].
% 29.35/29.37 3306 -class_Ring__and__Field_Olordered__ring(A) | c_times(B,c_0,A) = c_0. [resolve(975,b,968,a)].
% 29.35/29.37 3307 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(988,a,975,b)].
% 29.35/29.37 3308 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(989,a,975,b)].
% 29.35/29.37 3309 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1005,a,975,b)].
% 29.35/29.37 3310 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(1006,a,975,b)].
% 29.35/29.37 3311 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1007,a,975,b)].
% 29.35/29.37 3312 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(1008,a,975,b)].
% 29.35/29.37 3313 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1040,b,1010,a)].
% 29.35/29.37 3314 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1040,b,1011,a)].
% 29.46/29.47 3315 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1040,b,1012,a)].
% 29.46/29.47 3316 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1040,b,1013,a)].
% 29.46/29.47 3317 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1040,b,1014,a)].
% 29.46/29.47 3318 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1040,b,1015,a)].
% 29.46/29.47 3319 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1040,b,1016,a)].
% 29.46/29.47 3320 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1040,b,1017,a)].
% 29.46/29.47 3321 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1040,b,1018,a)].
% 29.46/29.47 3322 -class_Ring__and__Field_Olordered__ring(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1040,b,1019,a)].
% 29.46/29.47 3323 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1040,b,1020,a)].
% 29.46/29.47 3324 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1040,b,1021,a)].
% 29.46/29.47 3325 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1040,b,1022,a)].
% 29.46/29.47 3326 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1040,b,1023,a)].
% 29.46/29.47 3327 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1040,b,1024,a)].
% 29.46/29.47 3328 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1040,b,1025,a)].
% 29.46/29.47 3329 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1040,b,1026,a)].
% 29.46/29.47 3330 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1040,b,1027,a)].
% 29.46/29.47 3331 -class_Ring__and__Field_Olordered__ring(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1040,b,1028,a)].
% 29.46/29.47 3332 -class_Ring__and__Field_Olordered__ring(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1040,b,1029,a)].
% 29.46/29.47 3333 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(1155,a,1132,a)].
% 29.46/29.47 3334 -class_Ring__and__Field_Olordered__ring(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(1155,a,1133,a)].
% 29.46/29.47 3335 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(1812,a,1757,b)].
% 29.46/29.47 3336 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1987,a,1967,b)].
% 29.46/29.47 3337 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1988,a,1967,b)].
% 29.46/29.47 3338 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1989,a,1967,b)].
% 29.46/29.47 3339 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1990,a,1967,b)].
% 29.46/29.47 3340 -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(1991,a,1967,b)].
% 29.46/29.47 3341 -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(1992,a,1967,b)].
% 29.46/29.47 3342 -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(1993,a,1967,b)].
% 29.46/29.49 3343 -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(1994,a,1967,b)].
% 29.46/29.49 3344 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(1995,a,1967,b)].
% 29.46/29.49 3345 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1996,a,1967,b)].
% 29.46/29.49 3346 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(1997,a,1967,b)].
% 29.46/29.49 3347 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(1998,a,1967,b)].
% 29.46/29.49 3348 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(1999,a,1967,b)].
% 29.46/29.49 3349 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2000,a,1967,b)].
% 29.46/29.49 3350 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2001,a,1967,b)].
% 29.46/29.49 3351 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2002,a,1967,b)].
% 29.46/29.49 3352 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2003,a,1967,b)].
% 29.46/29.49 3353 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2004,a,1967,b)].
% 29.46/29.49 3354 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2005,a,1967,b)].
% 29.46/29.49 3355 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2006,a,1967,b)].
% 29.46/29.49 3356 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2007,a,1967,b)].
% 29.46/29.49 3357 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2008,a,1967,b)].
% 29.46/29.49 3358 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2009,a,1967,b)].
% 29.46/29.49 3359 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2010,a,1967,b)].
% 29.46/29.49 3360 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2011,a,1967,b)].
% 29.46/29.49 3361 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2012,a,1967,b)].
% 29.46/29.49 3362 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2013,a,1967,b)].
% 29.46/29.49 3363 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2014,a,1967,b)].
% 29.46/29.49 3364 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2015,a,1967,b)].
% 29.46/29.49 3365 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2016,a,1967,b)].
% 29.46/29.49 3366 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2017,a,1967,b)].
% 29.46/29.49 3367 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2018,b,1967,b)].
% 29.46/29.49 3368 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2021,b,1967,b)].
% 29.46/29.49 3369 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2022,b,1967,b)].
% 29.46/29.49 3370 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2023,b,1967,b)].
% 29.46/29.49 3371 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2057,a,2027,b)].
% 29.49/29.51 3372 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Olordered__ring(B). [resolve(2058,a,2027,b)].
% 29.49/29.51 3373 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(2065,c,2027,b)].
% 29.49/29.51 3374 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Olordered__ring(C). [resolve(2066,c,2027,b)].
% 29.49/29.51 3375 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2088,a,2027,b)].
% 29.49/29.51 3376 -c_less(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2089,b,2027,b)].
% 29.49/29.51 3377 -c_less(A,B,C) | c_SetInterval_OatLeastAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2090,c,2027,b)].
% 29.49/29.51 3378 c_SetInterval_OatLeastAtMost(A,A,B) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2091,b,2027,b)].
% 29.49/29.51 3379 -c_lessequals(A,B,C) | c_SetInterval_OatLeastLessThan(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2092,c,2027,b)].
% 29.49/29.51 3380 -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(2093,c,2027,b)].
% 29.49/29.51 3381 -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(2094,c,2027,b)].
% 29.49/29.51 3382 -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(2095,c,2027,b)].
% 29.49/29.51 3383 -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(2096,c,2027,b)].
% 29.49/29.51 3384 -c_lessequals(A,B,C) | c_SetInterval_OgreaterThanAtMost(B,A,C) = c_emptyset | -class_Ring__and__Field_Olordered__ring(C). [resolve(2097,c,2027,b)].
% 29.49/29.51 3385 c_minus(c_insert(A,c_emptyset,B),c_SetInterval_OlessThan(A,B),tc_set(B)) = c_insert(A,c_emptyset,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2098,b,2027,b)].
% 29.49/29.51 3386 c_lessequals(A,A,B) | -class_Ring__and__Field_Olordered__ring(B). [resolve(2099,b,2027,b)].
% 29.49/29.51 3387 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2100,c,2027,b)].
% 29.49/29.51 3388 -c_in(A,c_SetInterval_OatLeastAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2101,c,2027,b)].
% 29.49/29.51 3389 -c_lessequals(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastAtMost(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2102,d,2027,b)].
% 29.49/29.51 3390 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_lessequals(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2103,c,2027,b)].
% 29.49/29.51 3391 -c_in(A,c_SetInterval_OatLeastLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2104,c,2027,b)].
% 29.49/29.51 3392 -c_less(A,B,C) | -c_lessequals(D,A,C) | c_in(A,c_SetInterval_OatLeastLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2105,d,2027,b)].
% 29.49/29.51 3393 -c_in(A,c_SetInterval_OatLeast(B,C),C) | c_lessequals(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2106,c,2027,b)].
% 29.49/29.51 3394 -c_lessequals(A,B,C) | c_in(B,c_SetInterval_OatLeast(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2107,c,2027,b)].
% 29.49/29.51 3395 -c_in(A,c_SetInterval_OatMost(B,C),C) | c_lessequals(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2108,c,2027,b)].
% 29.49/29.51 3396 -c_lessequals(A,B,C) | c_in(A,c_SetInterval_OatMost(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2109,c,2027,b)].
% 29.49/29.51 3397 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2110,c,2027,b)].
% 29.49/29.51 3398 -c_in(A,c_SetInterval_OgreaterThanAtMost(B,C,D),D) | c_lessequals(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2111,c,2027,b)].
% 29.49/29.51 3399 -c_less(A,B,C) | -c_lessequals(B,D,C) | c_in(B,c_SetInterval_OgreaterThanAtMost(A,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2112,d,2027,b)].
% 29.60/29.65 3400 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(B,A,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2113,c,2027,b)].
% 29.60/29.65 3401 -c_in(A,c_SetInterval_OgreaterThanLessThan(B,C,D),D) | c_less(A,C,D) | -class_Ring__and__Field_Olordered__ring(D). [resolve(2114,c,2027,b)].
% 29.60/29.65 3402 -c_less(A,B,C) | -c_less(D,A,C) | c_in(A,c_SetInterval_OgreaterThanLessThan(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2115,d,2027,b)].
% 29.60/29.65 3403 -c_in(A,c_SetInterval_OgreaterThan(B,C),C) | c_less(B,A,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2116,c,2027,b)].
% 29.60/29.65 3404 -c_less(A,B,C) | c_in(B,c_SetInterval_OgreaterThan(A,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2117,c,2027,b)].
% 29.60/29.65 3405 -c_in(A,c_SetInterval_OlessThan(B,C),C) | c_less(A,B,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2118,c,2027,b)].
% 29.60/29.65 3406 -c_less(A,B,C) | c_in(A,c_SetInterval_OlessThan(B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2119,c,2027,b)].
% 29.60/29.65 3407 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2120,b,2027,b)].
% 29.60/29.65 3408 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2121,b,2027,b)].
% 29.60/29.65 3409 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2122,b,2027,b)].
% 29.60/29.65 3410 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Olordered__ring(B). [resolve(2123,b,2027,b)].
% 29.60/29.65 3411 class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2898,a,2900,b)].
% 29.60/29.65 Derived: class_Ring__and__Field_Oring(tc_IntDef_Oint). [resolve(3411,b,3229,a)].
% 29.60/29.65 Derived: class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3411,b,3236,b)].
% 29.60/29.65 Derived: class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3411,b,3237,b)].
% 29.60/29.65 3412 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2904,a,2900,b)].
% 29.60/29.65 Derived: class_OrderedGroup_Oab__group__add(tc_IntDef_Oint). [resolve(3412,b,3229,a)].
% 29.60/29.65 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3412,b,3236,b)].
% 29.60/29.65 3413 -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2912,a,2900,b)].
% 29.60/29.65 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(B,C,tc_IntDef_Oint). [resolve(3413,c,3229,a)].
% 29.60/29.65 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3413,c,3236,b)].
% 29.60/29.65 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3413,c,3237,b)].
% 29.60/29.65 Derived: -c_lessequals(c_plus(A,B,C),c_plus(A,D,C),C) | c_lessequals(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3413,c,3238,b)].
% 29.60/29.65 3414 -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2913,a,2900,b)].
% 29.60/29.65 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3414,c,3229,a)].
% 29.60/29.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3414,c,3236,b)].
% 29.60/29.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3414,c,3237,b)].
% 29.60/29.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3414,c,3238,b)].
% 29.60/29.65 3415 -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2914,a,2900,b)].
% 29.60/29.65 Derived: -c_lessequals(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,C,tc_IntDef_Oint). [resolve(3415,c,3229,a)].
% 29.60/29.65 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3415,c,3236,b)].
% 29.60/29.65 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3415,c,3237,b)].
% 29.60/29.65 Derived: -c_lessequals(c_plus(A,B,C),c_plus(D,B,C),C) | c_lessequals(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3415,c,3238,b)].
% 29.60/29.65 3416 -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2915,a,2900,b)].
% 29.60/29.65 Derived: -c_lessequals(A,B,tc_IntDef_Oint) | c_lessequals(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3416,c,3229,a)].
% 29.60/29.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3416,c,3236,b)].
% 29.60/29.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3416,c,3237,b)].
% 29.60/29.65 Derived: -c_lessequals(A,B,C) | c_lessequals(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3416,c,3238,b)].
% 29.60/29.65 3417 -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2916,a,2900,b)].
% 29.60/29.65 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(A,C,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(B,C,tc_IntDef_Oint). [resolve(3417,c,3229,a)].
% 29.60/29.65 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3417,c,3236,b)].
% 29.60/29.65 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3417,c,3237,b)].
% 29.60/29.65 Derived: -c_less(c_plus(A,B,C),c_plus(A,D,C),C) | c_less(B,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3417,c,3238,b)].
% 29.60/29.65 3418 -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2917,a,2900,b)].
% 29.60/29.65 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(C,A,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3418,c,3229,a)].
% 29.60/29.65 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3418,c,3236,b)].
% 29.60/29.65 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3418,c,3237,b)].
% 29.60/29.65 Derived: -c_less(A,B,C) | c_less(c_plus(D,A,C),c_plus(D,B,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3418,c,3238,b)].
% 29.60/29.65 3419 -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2918,a,2900,b)].
% 29.60/29.65 Derived: -c_less(c_plus(A,B,tc_IntDef_Oint),c_plus(C,B,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,C,tc_IntDef_Oint). [resolve(3419,c,3229,a)].
% 29.60/29.65 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3419,c,3236,b)].
% 29.60/29.65 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3419,c,3237,b)].
% 29.60/29.65 Derived: -c_less(c_plus(A,B,C),c_plus(D,B,C),C) | c_less(A,D,C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3419,c,3238,b)].
% 29.60/29.65 3420 -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Olordered__ring(C). [resolve(2919,a,2900,b)].
% 29.60/29.65 Derived: -c_less(A,B,tc_IntDef_Oint) | c_less(c_plus(A,C,tc_IntDef_Oint),c_plus(B,C,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3420,c,3229,a)].
% 29.60/29.65 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__field(C). [resolve(3420,c,3236,b)].
% 29.60/29.65 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__idom(C). [resolve(3420,c,3237,b)].
% 29.60/29.65 Derived: -c_less(A,B,C) | c_less(c_plus(A,D,C),c_plus(B,D,C),C) | -class_Ring__and__Field_Oordered__ring__strict(C). [resolve(3420,c,3238,b)].
% 29.60/29.65 3421 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(2965,b,2900,b)].
% 29.60/29.65 Derived: class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint). [resolve(3421,b,3229,a)].
% 30.36/30.36 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3421,b,3236,b)].
% 30.36/30.36 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3421,b,3237,b)].
% 30.36/30.36 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3421,b,3238,b)].
% 30.36/30.36 3422 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3001,b,2900,b)].
% 30.36/30.36 Derived: class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint). [resolve(3422,b,3229,a)].
% 30.36/30.36 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3422,b,3236,b)].
% 30.36/30.36 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3422,b,3237,b)].
% 30.36/30.36 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oordered__ring__strict(A). [resolve(3422,b,3238,b)].
% 30.36/30.36 3423 class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Olordered__ring(A). [resolve(3048,a,3007,b)].
% 30.36/30.36 Derived: class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint). [resolve(3423,b,3229,a)].
% 30.36/30.36 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__field(A). [resolve(3423,b,3236,b)].
% 30.36/30.36 Derived: class_OrderedGroup_Opordered__ab__group__add(A) | -class_Ring__and__Field_Oordered__idom(A). [resolve(3423,b,3237,b)].
% 30.36/30.36 3424 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_17) # label(axiom). [assumption].
% 30.36/30.36 3425 class_Ring__and__Field_Oidom(tc_IntDef_Oint) # label(clsarity_IntDef__Oint_57) # label(axiom). [assumption].
% 30.36/30.36 3426 -class_Ring__and__Field_Ofield(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Ofield_31) # label(axiom). [assumption].
% 30.36/30.36 3427 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A) # label(clsrel_Ring__and__Field_Oidom_20) # label(axiom). [assumption].
% 30.36/30.36 3428 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A) # label(clsrel_Ring__and__Field_Oidom_21) # label(axiom). [assumption].
% 30.36/30.36 3429 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_26) # label(axiom). [assumption].
% 30.36/30.36 3430 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A) # label(clsrel_Ring__and__Field_Oidom_28) # label(axiom). [assumption].
% 30.36/30.36 3431 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Oring(A) # label(clsrel_Ring__and__Field_Oidom_3) # label(axiom). [assumption].
% 30.36/30.36 3432 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__group__add(A) # label(clsrel_Ring__and__Field_Oidom_4) # label(axiom). [assumption].
% 30.36/30.36 3433 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__field_2) # label(axiom). [assumption].
% 30.36/30.36 3434 -class_Ring__and__Field_Oordered__idom(A) | class_Ring__and__Field_Oidom(A) # label(clsrel_Ring__and__Field_Oordered__idom_57) # label(axiom). [assumption].
% 30.36/30.36 3435 -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_OInts,A). [resolve(225,b,176,a)].
% 30.36/30.36 Derived: c_in(c_0,c_IntDef_OInts,tc_IntDef_Oint). [resolve(3435,a,3425,a)].
% 30.36/30.36 Derived: c_in(c_0,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3435,a,3426,b)].
% 30.36/30.36 3436 -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_OInts,A). [resolve(225,b,177,a)].
% 30.36/30.36 Derived: c_in(c_1,c_IntDef_OInts,tc_IntDef_Oint). [resolve(3436,a,3425,a)].
% 30.36/30.36 Derived: c_in(c_1,c_IntDef_OInts,A) | -class_Ring__and__Field_Ofield(A). [resolve(3436,a,3426,b)].
% 30.36/30.36 3437 -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_plus(C,B,A),c_IntDef_OInts,A). [resolve(225,b,178,a)].
% 30.36/30.36 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_plus(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(3437,a,3425,a)].
% 30.36/30.36 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_plus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3437,a,3426,b)].
% 30.36/30.37 3438 -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_minus(C,B,A),c_IntDef_OInts,A). [resolve(225,b,179,a)].
% 30.36/30.37 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_minus(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(3438,a,3425,a)].
% 30.36/30.37 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_minus(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3438,a,3426,b)].
% 30.36/30.37 3439 -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_OInts,A) | c_in(c_uminus(B,A),c_IntDef_OInts,A). [resolve(225,b,180,a)].
% 30.36/30.37 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_uminus(A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(3439,a,3425,a)].
% 30.36/30.37 Derived: -c_in(A,c_IntDef_OInts,B) | c_in(c_uminus(A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3439,a,3426,b)].
% 30.36/30.37 3440 -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_times(C,B,A),c_IntDef_OInts,A). [resolve(225,b,181,a)].
% 30.36/30.37 Derived: -c_in(A,c_IntDef_OInts,tc_IntDef_Oint) | -c_in(B,c_IntDef_OInts,tc_IntDef_Oint) | c_in(c_times(B,A,tc_IntDef_Oint),c_IntDef_OInts,tc_IntDef_Oint). [resolve(3440,a,3425,a)].
% 30.36/30.37 Derived: -c_in(A,c_IntDef_OInts,B) | -c_in(C,c_IntDef_OInts,B) | c_in(c_times(C,A,B),c_IntDef_OInts,B) | -class_Ring__and__Field_Ofield(B). [resolve(3440,a,3426,b)].
% 30.36/30.37 3441 -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_1,A) = c_1. [resolve(225,b,182,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_1,tc_IntDef_Oint) = c_1. [resolve(3441,a,3425,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3441,a,3426,b)].
% 30.36/30.37 3442 -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_plus(B,C,tc_IntDef_Oint),A) = c_plus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(225,b,183,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_plus(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3442,a,3425,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_plus(A,B,tc_IntDef_Oint),C) = c_plus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3442,a,3426,b)].
% 30.36/30.37 3443 -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_minus(B,C,tc_IntDef_Oint),A) = c_minus(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(225,b,184,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3443,a,3425,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_minus(A,B,tc_IntDef_Oint),C) = c_minus(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3443,a,3426,b)].
% 30.36/30.37 3444 -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_IntDef_Oint(B),A) = c_NatArith_Oof__nat(B,A). [resolve(225,b,185,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),tc_IntDef_Oint) = c_NatArith_Oof__nat(A,tc_IntDef_Oint). [resolve(3444,a,3425,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_IntDef_Oint(A),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Ofield(B). [resolve(3444,a,3426,b)].
% 30.36/30.37 3445 -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_uminus(B,tc_IntDef_Oint),A) = c_uminus(c_IntDef_Oof__int(B,A),A). [resolve(225,b,186,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_IntDef_Oof__int(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3445,a,3425,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_uminus(A,tc_IntDef_Oint),B) = c_uminus(c_IntDef_Oof__int(A,B),B) | -class_Ring__and__Field_Ofield(B). [resolve(3445,a,3426,b)].
% 30.36/30.37 3446 -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_times(B,C,tc_IntDef_Oint),A) = c_times(c_IntDef_Oof__int(B,A),c_IntDef_Oof__int(C,A),A). [resolve(225,b,187,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),tc_IntDef_Oint) = c_times(c_IntDef_Oof__int(A,tc_IntDef_Oint),c_IntDef_Oof__int(B,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3446,a,3425,a)].
% 30.36/30.37 Derived: c_IntDef_Oof__int(c_times(A,B,tc_IntDef_Oint),C) = c_times(c_IntDef_Oof__int(A,C),c_IntDef_Oof__int(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3446,a,3426,b)].
% 30.36/30.38 3447 -class_Ring__and__Field_Oidom(A) | c_IntDef_Oof__int(c_NatArith_Oof__nat(B,tc_IntDef_Oint),A) = c_NatArith_Oof__nat(B,A). [resolve(225,b,188,a)].
% 30.36/30.38 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint) = c_NatArith_Oof__nat(A,tc_IntDef_Oint). [resolve(3447,a,3425,a)].
% 30.36/30.38 Derived: c_IntDef_Oof__int(c_NatArith_Oof__nat(A,tc_IntDef_Oint),B) = c_NatArith_Oof__nat(A,B) | -class_Ring__and__Field_Ofield(B). [resolve(3447,a,3426,b)].
% 30.36/30.38 3448 -class_Ring__and__Field_Oidom(A) | -c_lessequals(B,C,tc_nat) | c_NatArith_Oof__nat(c_minus(C,B,tc_nat),A) = c_minus(c_NatArith_Oof__nat(C,A),c_NatArith_Oof__nat(B,A),A). [resolve(225,b,189,a)].
% 30.36/30.38 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),tc_IntDef_Oint) = c_minus(c_NatArith_Oof__nat(B,tc_IntDef_Oint),c_NatArith_Oof__nat(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3448,a,3425,a)].
% 30.36/30.38 Derived: -c_lessequals(A,B,tc_nat) | c_NatArith_Oof__nat(c_minus(B,A,tc_nat),C) = c_minus(c_NatArith_Oof__nat(B,C),c_NatArith_Oof__nat(A,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3448,a,3426,b)].
% 30.36/30.38 3449 -class_Ring__and__Field_Oidom(A) | -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A). [resolve(225,b,190,b)].
% 30.36/30.38 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Nat_Opower(c_uminus(A,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),B,tc_nat),tc_IntDef_Oint) = c_Nat_Opower(A,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),B,tc_nat),tc_IntDef_Oint). [resolve(3449,a,3425,a)].
% 30.36/30.38 Derived: -class_Power_Orecpower(A) | c_Nat_Opower(c_uminus(B,A),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) = c_Nat_Opower(B,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),C,tc_nat),A) | -class_Ring__and__Field_Ofield(A). [resolve(3449,a,3426,b)].
% 30.36/30.38 3450 -class_Ring__and__Field_Oidom(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1. [resolve(225,b,191,b)].
% 30.36/30.38 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_1. [resolve(3450,a,3425,a)].
% 30.36/30.38 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3450,a,3426,b)].
% 30.36/30.38 3451 -class_Ring__and__Field_Oidom(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A). [resolve(225,b,192,b)].
% 30.36/30.38 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint). [resolve(3451,a,3425,a)].
% 30.36/30.38 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(c_1,A),B,A) = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3451,a,3426,b)].
% 30.36/30.38 3452 -class_Ring__and__Field_Oidom(A) | -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A). [resolve(225,b,193,b)].
% 30.36/30.38 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | -c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(B,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_Nat_Opower(B,A,tc_IntDef_Oint). [resolve(3452,a,3425,a)].
% 30.36/30.38 Derived: -class_Power_Orecpower(A) | -c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_Nat_Opower(C,B,A) | -class_Ring__and__Field_Ofield(A). [resolve(3452,a,3426,b)].
% 30.45/30.46 3453 -class_Ring__and__Field_Oidom(A) | -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A). [resolve(225,b,194,b)].
% 30.45/30.46 Derived: -class_Power_Orecpower(tc_IntDef_Oint) | c_Parity_Oeven(A,tc_nat) | c_Nat_Opower(c_uminus(B,tc_IntDef_Oint),A,tc_IntDef_Oint) = c_uminus(c_Nat_Opower(B,A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3453,a,3425,a)].
% 30.45/30.46 Derived: -class_Power_Orecpower(A) | c_Parity_Oeven(B,tc_nat) | c_Nat_Opower(c_uminus(C,A),B,A) = c_uminus(c_Nat_Opower(C,B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3453,a,3426,b)].
% 30.45/30.46 3454 -class_Ring__and__Field_Oidom(A) | c_in(c_0,c_IntDef_ONats,A). [resolve(266,b,230,a)].
% 30.45/30.46 Derived: c_in(c_0,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3454,a,3426,b)].
% 30.45/30.46 3455 -class_Ring__and__Field_Oidom(A) | c_in(c_1,c_IntDef_ONats,A). [resolve(266,b,231,a)].
% 30.45/30.46 Derived: c_in(c_1,c_IntDef_ONats,A) | -class_Ring__and__Field_Ofield(A). [resolve(3455,a,3426,b)].
% 30.45/30.46 3456 -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_plus(C,B,A),c_IntDef_ONats,A). [resolve(266,b,232,a)].
% 30.45/30.46 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_plus(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3456,a,3426,b)].
% 30.45/30.46 3457 -class_Ring__and__Field_Oidom(A) | -c_in(B,c_IntDef_ONats,A) | -c_in(C,c_IntDef_ONats,A) | c_in(c_times(C,B,A),c_IntDef_ONats,A). [resolve(266,b,233,a)].
% 30.45/30.46 Derived: -c_in(A,c_IntDef_ONats,B) | -c_in(C,c_IntDef_ONats,B) | c_in(c_times(C,A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3457,a,3426,b)].
% 30.45/30.46 3458 -class_Ring__and__Field_Oidom(A) | c_in(c_NatArith_Oof__nat(B,A),c_IntDef_ONats,A). [resolve(266,b,234,a)].
% 30.45/30.46 Derived: c_in(c_NatArith_Oof__nat(A,B),c_IntDef_ONats,B) | -class_Ring__and__Field_Ofield(B). [resolve(3458,a,3426,b)].
% 30.45/30.46 3459 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_Suc(B),A) = c_plus(c_NatArith_Oof__nat(B,A),c_1,A). [resolve(266,b,235,a)].
% 30.45/30.46 Derived: c_NatArith_Oof__nat(c_Suc(A),B) = c_plus(c_NatArith_Oof__nat(A,B),c_1,B) | -class_Ring__and__Field_Ofield(B). [resolve(3459,a,3426,b)].
% 30.45/30.46 3460 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_1,A) = c_1. [resolve(266,b,236,a)].
% 30.45/30.46 Derived: c_NatArith_Oof__nat(c_1,A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3460,a,3426,b)].
% 30.45/30.46 3461 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A) = c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(266,b,237,a)].
% 30.45/30.46 Derived: c_NatArith_Oof__nat(c_plus(A,B,tc_nat),C) = c_plus(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3461,a,3426,b)].
% 30.45/30.46 3462 -class_Ring__and__Field_Oidom(A) | c_NatArith_Oof__nat(c_times(B,C,tc_nat),A) = c_times(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A). [resolve(266,b,238,a)].
% 30.45/30.46 Derived: c_NatArith_Oof__nat(c_times(A,B,tc_nat),C) = c_times(c_NatArith_Oof__nat(A,C),c_NatArith_Oof__nat(B,C),C) | -class_Ring__and__Field_Ofield(C). [resolve(3462,a,3426,b)].
% 30.45/30.46 3463 -class_Ring__and__Field_Oidom(A) | -c_IntDef_Oiszero(c_1,A). [resolve(266,b,239,a)].
% 30.45/30.46 Derived: -c_IntDef_Oiszero(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3463,a,3426,b)].
% 30.45/30.46 3464 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(266,b,245,a)].
% 30.45/30.46 3465 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(266,b,246,a)].
% 30.45/30.46 3466 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(266,b,250,a)].
% 30.45/30.46 3467 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__mult(A). [resolve(266,b,259,a)].
% 30.45/30.46 3468 -class_Ring__and__Field_Oidom(A) | class_Ring__and__Field_Osemiring(A). [resolve(266,b,263,a)].
% 30.45/30.46 3469 -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A). [resolve(587,b,570,a)].
% 30.45/30.46 3470 -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1. [resolve(587,b,571,a)].
% 30.55/30.56 3471 -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(587,b,572,a)].
% 30.55/30.56 3472 -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A). [resolve(587,b,573,a)].
% 30.55/30.56 3473 -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A). [resolve(587,b,574,a)].
% 30.55/30.56 3474 -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(587,b,575,a)].
% 30.55/30.56 3475 -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A). [resolve(587,b,576,a)].
% 30.55/30.56 3476 -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(587,b,577,a)].
% 30.55/30.56 3477 -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(587,b,578,a)].
% 30.55/30.56 3478 -class_Ring__and__Field_Oidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(587,b,579,a)].
% 30.55/30.56 3479 -class_Ring__and__Field_Oidom(A) | c_plus(B,c_0,A) = B. [resolve(660,b,642,a)].
% 30.55/30.56 3480 -class_Ring__and__Field_Oidom(A) | c_plus(c_0,B,A) = B. [resolve(660,b,643,a)].
% 30.55/30.56 3481 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Oab__semigroup__add(A). [resolve(684,b,647,a)].
% 30.55/30.56 3482 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__add(A). [resolve(684,b,648,a)].
% 30.55/30.56 3483 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(B,D,A) | C = D. [resolve(743,b,726,a)].
% 30.55/30.56 3484 -class_Ring__and__Field_Oidom(A) | c_plus(B,C,A) != c_plus(D,C,A) | B = D. [resolve(743,b,727,a)].
% 30.55/30.56 3485 -class_Ring__and__Field_Oidom(A) | c_times(c_1,B,A) = B. [resolve(854,b,845,a)].
% 30.55/30.56 3486 -class_Ring__and__Field_Oidom(A) | c_times(B,c_1,A) = B. [resolve(854,b,846,a)].
% 30.55/30.56 3487 -class_Ring__and__Field_Oidom(A) | c_times(c_0,B,A) = c_0. [resolve(974,b,967,a)].
% 30.55/30.56 3488 -class_Ring__and__Field_Oidom(A) | c_times(B,c_0,A) = c_0. [resolve(974,b,968,a)].
% 30.55/30.56 3489 -class_Ring__and__Field_Oidom(A) | class_OrderedGroup_Osemigroup__mult(A). [resolve(1003,b,989,a)].
% 30.55/30.56 3490 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1005,a,974,b)].
% 30.55/30.56 3491 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1006,a,974,b)].
% 30.55/30.56 3492 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(1007,a,974,b)].
% 30.55/30.56 3493 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(1008,a,974,b)].
% 30.55/30.56 3494 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oidom(A). [resolve(1200,b,1180,b)].
% 30.55/30.56 3495 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(1201,b,1180,b)].
% 30.55/30.56 3496 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1204,b,1180,b)].
% 30.55/30.56 3497 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1205,b,1180,b)].
% 30.55/30.56 3498 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1206,b,1180,b)].
% 30.55/30.56 3499 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1207,b,1180,b)].
% 30.55/30.56 3500 class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(1357,b,1335,b)].
% 30.55/30.56 Derived: class_OrderedGroup_Oab__semigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3500,b,3426,b)].
% 30.55/30.56 3501 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(1366,b,1335,b)].
% 30.55/30.56 3502 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(1367,b,1335,b)].
% 30.55/30.56 3503 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(1368,c,1335,b)].
% 30.55/30.56 3504 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(1369,c,1335,b)].
% 30.55/30.58 3505 class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Oidom(A). [resolve(1371,b,1335,b)].
% 30.55/30.58 Derived: class_Ring__and__Field_Osemiring(A) | -class_Ring__and__Field_Ofield(A). [resolve(3505,b,3426,b)].
% 30.55/30.58 3506 class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Oidom(A). [resolve(1372,b,1335,b)].
% 30.55/30.58 Derived: class_OrderedGroup_Osemigroup__mult(A) | -class_Ring__and__Field_Ofield(A). [resolve(3506,b,3426,b)].
% 30.55/30.58 3507 c_plus(A,c_0,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1374,b,1335,b)].
% 30.55/30.58 Derived: c_plus(A,c_0,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3507,b,3426,b)].
% 30.55/30.58 3508 c_plus(c_0,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1375,b,1335,b)].
% 30.55/30.58 Derived: c_plus(c_0,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3508,b,3426,b)].
% 30.55/30.58 3509 class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1376,b,1335,b)].
% 30.55/30.58 Derived: class_OrderedGroup_Oab__semigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3509,b,3426,b)].
% 30.55/30.58 3510 class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1377,b,1335,b)].
% 30.55/30.58 Derived: class_OrderedGroup_Osemigroup__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3510,b,3426,b)].
% 30.55/30.58 3511 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1410,d,1386,b)].
% 30.55/30.58 3512 -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(1411,c,1386,b)].
% 30.55/30.58 3513 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1412,d,1386,b)].
% 30.55/30.58 3514 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1413,d,1386,b)].
% 30.55/30.58 3515 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1414,d,1386,b)].
% 30.55/30.58 3516 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1415,d,1386,b)].
% 30.55/30.58 3517 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(1416,d,1386,b)].
% 30.55/30.58 3518 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1417,d,1386,b)].
% 30.55/30.58 3519 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(1418,d,1386,b)].
% 30.55/30.58 3520 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1419,d,1386,b)].
% 30.55/30.58 3521 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1458,a,1426,b)].
% 30.55/30.58 3522 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1459,a,1426,b)].
% 30.55/30.58 3523 class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Oidom(A). [resolve(1566,a,1569,b)].
% 30.55/30.58 Derived: class_Ring__and__Field_Oring(A) | -class_Ring__and__Field_Ofield(A). [resolve(3523,b,3426,b)].
% 30.55/30.58 3524 class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Oidom(A). [resolve(1572,a,1569,b)].
% 30.55/30.58 Derived: class_OrderedGroup_Oab__group__add(A) | -class_Ring__and__Field_Ofield(A). [resolve(3524,b,3426,b)].
% 30.55/30.58 3525 -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1612,d,1569,b)].
% 30.55/30.58 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(A,tc_IntDef_Oint) != c_1 | A = c_uminus(c_1,tc_IntDef_Oint). [resolve(3525,d,3425,a)].
% 30.55/30.58 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(B,A) != c_1 | B = c_uminus(c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3525,d,3426,b)].
% 30.59/30.59 3526 -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Oidom(A). [resolve(1613,c,1569,b)].
% 30.59/30.59 Derived: -class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) | c_uminus(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) = c_1. [resolve(3526,c,3425,a)].
% 30.59/30.59 Derived: -class_OrderedGroup_Oab__group__add(A) | c_uminus(c_uminus(c_1,A),A) = c_1 | -class_Ring__and__Field_Ofield(A). [resolve(3526,c,3426,b)].
% 30.59/30.59 3527 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1614,d,1569,b)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3527,d,3425,a)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3527,d,3426,b)].
% 30.59/30.59 3528 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1615,d,1569,b)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_lessequals(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3528,d,3425,a)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(B,c_uminus(c_1,A),A) | c_lessequals(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3528,d,3426,b)].
% 30.59/30.59 3529 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1616,d,1569,b)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3529,d,3425,a)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_1,c_uminus(B,A),A) | c_less(B,c_uminus(c_1,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3529,d,3426,b)].
% 30.59/30.59 3530 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Oidom(A). [resolve(1617,d,1569,b)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(A,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) | c_less(c_1,c_uminus(A,tc_IntDef_Oint),tc_IntDef_Oint). [resolve(3530,d,3425,a)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A) | -class_Ring__and__Field_Ofield(A). [resolve(3530,d,3426,b)].
% 30.59/30.59 3531 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(1618,d,1569,b)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(3531,d,3425,a)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(B,A),c_1,A) | c_lessequals(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(3531,d,3426,b)].
% 30.59/30.59 3532 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1619,d,1569,b)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_lessequals(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_lessequals(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(3532,d,3425,a)].
% 30.59/30.59 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3532,d,3426,b)].
% 30.59/30.59 3533 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Oidom(A). [resolve(1620,d,1569,b)].
% 34.57/34.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint) | c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint). [resolve(3533,d,3425,a)].
% 34.57/34.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) | -class_Ring__and__Field_Ofield(A). [resolve(3533,d,3426,b)].
% 34.57/34.58 3534 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Oidom(A). [resolve(1621,d,1569,b)].
% 34.57/34.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) | -c_less(c_uminus(c_1,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_uminus(A,tc_IntDef_Oint),c_1,tc_IntDef_Oint). [resolve(3534,d,3425,a)].
% 34.57/34.58 Derived: -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A) | -class_Ring__and__Field_Ofield(A). [resolve(3534,d,3426,b)].
% 34.57/34.58 3535 c_times(c_1,A,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1622,b,1569,b)].
% 34.57/34.58 Derived: c_times(c_1,A,tc_IntDef_Oint) = A. [resolve(3535,b,3425,a)].
% 34.57/34.58 Derived: c_times(c_1,A,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3535,b,3426,b)].
% 34.57/34.58 3536 c_times(A,c_1,B) = A | -class_Ring__and__Field_Oidom(B). [resolve(1623,b,1569,b)].
% 34.57/34.58 Derived: c_times(A,c_1,tc_IntDef_Oint) = A. [resolve(3536,b,3425,a)].
% 34.57/34.58 Derived: c_times(A,c_1,B) = A | -class_Ring__and__Field_Ofield(B). [resolve(3536,b,3426,b)].
% 34.57/34.58 3537 c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(1624,b,1569,b)].
% 34.57/34.58 Derived: c_times(c_0,A,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3537,b,3426,b)].
% 34.57/34.58 3538 c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Oidom(B). [resolve(1625,b,1569,b)].
% 34.57/34.58 Derived: c_times(A,c_0,B) = c_0 | -class_Ring__and__Field_Ofield(B). [resolve(3538,b,3426,b)].
% 34.57/34.58 3539 c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Oidom(C). [resolve(1626,c,1569,b)].
% 34.57/34.58 Derived: c_plus(A,B,C) != c_plus(A,D,C) | B = D | -class_Ring__and__Field_Ofield(C). [resolve(3539,c,3426,b)].
% 34.57/34.58 3540 c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Oidom(C). [resolve(1627,c,1569,b)].
% 34.57/34.58 Derived: c_plus(A,B,C) != c_plus(D,B,C) | A = D | -class_Ring__and__Field_Ofield(C). [resolve(3540,c,3426,b)].
% 34.57/34.58 3541 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(B,c_Finite__Set_OMax(C,A),A) | C = c_emptyset. [resolve(73,b,2,a)].
% 34.57/34.58 3542 class_Wellfounded__Recursion_Owellorder(tc_nat) # label(clsarity_nat_8) # label(axiom). [assumption].
% 34.57/34.58 3543 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMax(B,A),B,A) | B = c_emptyset. [resolve(73,b,3,a)].
% 34.57/34.58 3544 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMax(c_insert(C,B,A),A) = c_Orderings_Omax(C,c_Finite__Set_OMax(B,A),A). [resolve(73,b,4,a)].
% 34.57/34.58 3545 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Finite__Set_OMax(C,A),D,A) | c_lessequals(B,D,A) | C = c_emptyset. [resolve(73,b,5,a)].
% 34.57/34.58 3546 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__le__iff__1(B,C,A),B,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(73,b,6,a)].
% 34.57/34.58 3547 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(c_Main_OMax__le__iff__1(B,C,A),C,A) | c_lessequals(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(73,b,7,a)].
% 34.57/34.58 3548 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Finite__Set_OMax(C,A),D,A) | c_less(B,D,A) | C = c_emptyset. [resolve(73,b,8,a)].
% 34.57/34.58 3549 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMax__less__iff__1(B,C,A),B,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(73,b,9,a)].
% 34.57/34.59 3550 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(c_Main_OMax__less__iff__1(B,C,A),C,A) | c_less(c_Finite__Set_OMax(B,A),C,A) | B = c_emptyset. [resolve(73,b,10,a)].
% 34.57/34.59 3551 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMax(c_insert(B,c_emptyset,A),A) = B. [resolve(73,b,11,a)].
% 34.57/34.59 3552 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(D,c_Finite__Set_OMin(C,A),A) | c_lessequals(D,B,A) | C = c_emptyset. [resolve(73,b,12,a)].
% 34.57/34.59 3553 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__ge__iff__1(B,C,A),B,A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(73,b,13,a)].
% 34.57/34.59 3554 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_lessequals(C,c_Main_OMin__ge__iff__1(B,C,A),A) | c_lessequals(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(73,b,14,a)].
% 34.57/34.59 3555 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | -c_less(D,c_Finite__Set_OMin(C,A),A) | c_less(D,B,A) | C = c_emptyset. [resolve(73,b,15,a)].
% 34.57/34.59 3556 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Main_OMin__gr__iff__1(B,C,A),B,A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(73,b,16,a)].
% 34.57/34.59 3557 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | -c_less(C,c_Main_OMin__gr__iff__1(B,C,A),A) | c_less(C,c_Finite__Set_OMin(B,A),A) | B = c_emptyset. [resolve(73,b,17,a)].
% 34.57/34.59 3558 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | B = c_emptyset. [resolve(73,b,18,a)].
% 34.57/34.59 3559 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | B = c_emptyset | c_Finite__Set_OMin(c_insert(C,B,A),A) = c_Orderings_Omin(C,c_Finite__Set_OMin(B,A),A). [resolve(73,b,19,a)].
% 34.57/34.59 3560 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(C,A),B,A) | C = c_emptyset. [resolve(73,b,20,a)].
% 34.57/34.59 3561 -class_Wellfounded__Recursion_Owellorder(A) | c_Finite__Set_OMin(c_insert(B,c_emptyset,A),A) = B. [resolve(73,b,21,a)].
% 34.57/34.59 3562 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_lessequals(c_Finite__Set_OMin(B,A),c_Finite__Set_OMax(B,A),A) | B = c_emptyset. [resolve(73,b,22,a)].
% 34.57/34.59 3563 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omin(B,c_Finite__Set_OMax(C,A),A) = B. [resolve(73,b,23,a)].
% 34.57/34.59 3564 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,C,A) | -c_in(C,c_Finite__Set_OFinites,tc_set(A)) | C = c_emptyset | c_Orderings_Omax(B,c_Finite__Set_OMin(C,A),A) = B. [resolve(73,b,24,a)].
% 34.57/34.59 3565 -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_plus(B,B,A),c_0,A) | c_less(B,c_0,A). [resolve(73,b,25,b)].
% 34.57/34.59 3566 -class_Wellfounded__Recursion_Owellorder(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_plus(B,B,A),c_0,A). [resolve(73,b,26,b)].
% 34.57/34.59 3567 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(B,D,A). [resolve(73,b,27,a)].
% 34.57/34.59 3568 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(c_Orderings_Omax(B,C,A),D,A) | c_less(C,D,A). [resolve(73,b,28,a)].
% 34.57/34.59 3569 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,C,A) | c_less(c_Orderings_Omax(D,B,A),C,A). [resolve(73,b,29,a)].
% 34.57/34.59 3570 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,C,A). [resolve(73,b,30,a)].
% 34.57/34.59 3571 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,c_Orderings_Omin(C,D,A),A) | c_less(B,D,A). [resolve(73,b,31,a)].
% 34.57/34.59 3572 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(B,D,A) | c_less(B,c_Orderings_Omin(D,C,A),A). [resolve(73,b,32,a)].
% 34.57/34.59 3573 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,C,A). [resolve(73,b,33,a)].
% 34.57/34.59 3574 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,c_Orderings_Omin(C,D,A),A) | c_lessequals(B,D,A). [resolve(73,b,34,a)].
% 34.57/34.59 3575 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(B,D,A) | c_lessequals(B,c_Orderings_Omin(D,C,A),A). [resolve(73,b,35,a)].
% 34.57/34.59 3576 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,B,A) = B. [resolve(73,b,36,a)].
% 34.57/34.59 3577 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omin(B,c_Orderings_Omin(B,C,A),A) = c_Orderings_Omin(B,C,A). [resolve(73,b,37,a)].
% 34.57/34.59 3578 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(B,D,A). [resolve(73,b,38,a)].
% 34.57/34.59 3579 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_Orderings_Omax(B,C,A),D,A) | c_lessequals(C,D,A). [resolve(73,b,39,a)].
% 34.57/34.59 3580 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,C,A) | c_lessequals(c_Orderings_Omax(D,B,A),C,A). [resolve(73,b,40,a)].
% 34.57/34.59 3581 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,B,A) = B. [resolve(73,b,41,a)].
% 34.57/34.59 3582 -class_Wellfounded__Recursion_Owellorder(A) | c_Orderings_Omax(B,c_Orderings_Omax(B,C,A),A) = c_Orderings_Omax(B,C,A). [resolve(73,b,42,a)].
% 34.57/34.59 3583 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatLeast(B,A),tc_set(A)) = c_SetInterval_OlessThan(B,A). [resolve(73,b,43,a)].
% 34.57/34.59 3584 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OatMost(B,A),tc_set(A)) = c_SetInterval_OgreaterThan(B,A). [resolve(73,b,44,a)].
% 34.57/34.59 3585 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OgreaterThan(B,A),tc_set(A)) = c_SetInterval_OatMost(B,A). [resolve(73,b,45,a)].
% 34.57/34.59 3586 -class_Wellfounded__Recursion_Owellorder(A) | c_uminus(c_SetInterval_OlessThan(B,A),tc_set(A)) = c_SetInterval_OatLeast(B,A). [resolve(73,b,46,a)].
% 34.57/34.59 3587 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeast(B,A) != c_SetInterval_OatLeast(C,A) | B = C. [resolve(73,b,47,a)].
% 34.57/34.59 3588 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatMost(B,A) != c_SetInterval_OatMost(C,A) | B = C. [resolve(73,b,48,a)].
% 34.57/34.59 3589 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OgreaterThan(B,A) != c_SetInterval_OgreaterThan(C,A) | B = C. [resolve(73,b,49,a)].
% 34.57/34.59 3590 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OgreaterThan(B,A),c_SetInterval_OgreaterThan(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(73,b,50,a)].
% 34.57/34.59 3591 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OgreaterThan(C,A),c_SetInterval_OgreaterThan(B,A),tc_set(A)). [resolve(73,b,51,a)].
% 34.57/34.59 3592 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_minus(c_SetInterval_OatLeastLessThan(B,D,A),c_SetInterval_OatLeastLessThan(B,C,A),tc_set(A)) = c_SetInterval_OatLeastLessThan(C,D,A). [resolve(73,b,52,a)].
% 34.57/34.59 3593 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(D,B,A) | c_lessequals(C,B,A). [resolve(73,b,53,a)].
% 34.57/34.59 3594 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeastLessThan(B,C,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)) | c_lessequals(C,E,A) | c_lessequals(C,B,A). [resolve(73,b,54,a)].
% 34.57/34.59 3595 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeastLessThan(C,B,A),c_SetInterval_OatLeastLessThan(D,E,A),tc_set(A)). [resolve(73,b,55,a)].
% 34.57/34.59 3596 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,E,A) | c_lessequals(c_SetInterval_OatLeastLessThan(E,B,A),c_SetInterval_OatLeastLessThan(D,C,A),tc_set(A)). [resolve(73,b,56,a)].
% 34.57/34.59 3597 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OlessThan(B,A) != c_SetInterval_OlessThan(C,A) | B = C. [resolve(73,b,57,a)].
% 34.72/34.73 3598 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(73,b,58,a)].
% 34.72/34.73 3599 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OlessThan(B,A),c_SetInterval_OlessThan(C,A),tc_set(A)). [resolve(73,b,59,a)].
% 34.72/34.73 3600 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Ojoin(B,B,A) = B. [resolve(290,b,273,a)].
% 34.72/34.73 3601 -class_Wellfounded__Recursion_Owellorder(A) | c_LOrder_Omeet(B,B,A) = B. [resolve(313,b,296,a)].
% 34.72/34.73 3602 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,B,A). [resolve(913,b,880,a)].
% 34.72/34.73 3603 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_SetInterval_OatLeastAtMost(C,B,A) = c_emptyset. [resolve(913,b,881,a)].
% 34.72/34.73 3604 -class_Wellfounded__Recursion_Owellorder(A) | c_SetInterval_OatLeastAtMost(B,B,A) = c_insert(B,c_emptyset,A). [resolve(913,b,882,a)].
% 34.72/34.73 3605 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset. [resolve(913,b,883,a)].
% 34.72/34.73 3606 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatLeast(B,A),c_SetInterval_OatLeast(C,A),tc_set(A)) | c_lessequals(C,B,A). [resolve(913,b,884,a)].
% 34.72/34.73 3607 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatLeast(C,A),c_SetInterval_OatLeast(B,A),tc_set(A)). [resolve(913,b,885,a)].
% 34.72/34.73 3608 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)) | c_lessequals(B,C,A). [resolve(913,b,886,a)].
% 34.72/34.73 3609 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_lessequals(c_SetInterval_OatMost(B,A),c_SetInterval_OatMost(C,A),tc_set(A)). [resolve(913,b,887,a)].
% 34.72/34.73 3610 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_SetInterval_OgreaterThanAtMost(C,B,A) = c_emptyset. [resolve(913,b,888,a)].
% 34.72/34.73 3611 -class_Wellfounded__Recursion_Owellorder(A) | c_minus(c_insert(B,c_emptyset,A),c_SetInterval_OlessThan(B,A),tc_set(A)) = c_insert(B,c_emptyset,A). [resolve(913,b,889,a)].
% 34.72/34.73 3612 -class_Wellfounded__Recursion_Owellorder(A) | c_lessequals(B,B,A). [resolve(913,b,890,a)].
% 34.72/34.73 3613 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(C,B,A). [resolve(1052,b,1010,a)].
% 34.72/34.73 3614 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1052,b,1011,a)].
% 34.72/34.73 3615 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastAtMost(D,C,A),A). [resolve(1052,b,1012,a)].
% 34.72/34.73 3616 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_lessequals(C,B,A). [resolve(1052,b,1013,a)].
% 34.72/34.73 3617 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeastLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1052,b,1014,a)].
% 34.72/34.73 3618 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(D,B,A) | c_in(B,c_SetInterval_OatLeastLessThan(D,C,A),A). [resolve(1052,b,1015,a)].
% 34.72/34.73 3619 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatLeast(C,A),A) | c_lessequals(C,B,A). [resolve(1052,b,1016,a)].
% 34.72/34.73 3620 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(C,c_SetInterval_OatLeast(B,A),A). [resolve(1052,b,1017,a)].
% 34.72/34.73 3621 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OatMost(C,A),A) | c_lessequals(B,C,A). [resolve(1052,b,1018,a)].
% 34.72/34.73 3622 -class_Wellfounded__Recursion_Owellorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(1052,b,1019,a)].
% 34.72/34.73 3623 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_less(C,B,A). [resolve(1052,b,1020,a)].
% 34.72/34.73 3624 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanAtMost(C,D,A),A) | c_lessequals(B,D,A). [resolve(1052,b,1021,a)].
% 34.72/34.73 3625 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_lessequals(C,D,A) | c_in(C,c_SetInterval_OgreaterThanAtMost(B,D,A),A). [resolve(1052,b,1022,a)].
% 36.83/36.85 3626 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(C,B,A). [resolve(1052,b,1023,a)].
% 36.83/36.85 3627 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A). [resolve(1052,b,1024,a)].
% 36.83/36.85 3628 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | -c_less(D,B,A) | c_in(B,c_SetInterval_OgreaterThanLessThan(D,C,A),A). [resolve(1052,b,1025,a)].
% 36.83/36.85 3629 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OgreaterThan(C,A),A) | c_less(C,B,A). [resolve(1052,b,1026,a)].
% 36.83/36.85 3630 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(C,c_SetInterval_OgreaterThan(B,A),A). [resolve(1052,b,1027,a)].
% 36.83/36.85 3631 -class_Wellfounded__Recursion_Owellorder(A) | -c_in(B,c_SetInterval_OlessThan(C,A),A) | c_less(B,C,A). [resolve(1052,b,1028,a)].
% 36.83/36.85 3632 -class_Wellfounded__Recursion_Owellorder(A) | -c_less(B,C,A) | c_in(B,c_SetInterval_OlessThan(C,A),A). [resolve(1052,b,1029,a)].
% 36.83/36.85
% 36.83/36.85 ============================== end predicate elimination =============
% 36.83/36.85
% 36.83/36.85 Auto_denials: (non-Horn, no changes).
% 36.83/36.85
% 36.83/36.85 Term ordering decisions:
% 36.83/36.85 Function symbol KB weights: tc_IntDef_Oint=1. tc_nat=1. c_0=1. c_1=1. c_emptyset=1. c_Finite__Set_OFinites=1. c_List_Olist_ONil=1. c_IntDef_ONats=1. c_Numeral_OPls=1. c_IntDef_OInts=1. c_Numeral_Obit_OB1=1. c_Numeral_Obit_OB0=1. c_UNIV=1. c_Numeral_OMin=1. tc_Product__Type_Ounit=1. tc_List_Onibble=1. c_Relation_OId=1. c_IntDef_Ointrel=1. t_a=1. c_Datatype_Ooption_ONone=1. v_cl=1. c_IntDef_OInteg=1. c_Tarski_OCompleteLattice=1. c_Wellfounded__Relations_Oless__than=1. c_Extraction_Osumbool_OLeft=1. c_Extraction_Osumbool_ORight=1. c_List_Onibble_ONibble0=1. c_List_Onibble_ONibble1=1. c_List_Onibble_ONibble2=1. c_List_Onibble_ONibble3=1. c_List_Onibble_ONibble4=1. c_List_Onibble_ONibble5=1. c_List_Onibble_ONibble6=1. c_List_Onibble_ONibble7=1. c_List_Onibble_ONibble8=1. c_List_Onibble_ONibble9=1. c_List_Onibble_ONibbleA=1. c_List_Onibble_ONibbleB=1. c_List_Onibble_ONibbleC=1. c_List_Onibble_ONibbleD=1. c_List_Onibble_ONibbleE=1. c_List_Onibble_ONibbleF=1. c_Product__Type_OUnity=1. c_Tarski_OPartialOrder=1. tc_Extraction_Osumbool=1. tc_Numeral_Obit=1. v_A=1. v_S=1. tc_List_Ochar=1. tc_bool=1. v_r=1. v_x=1. c_Numeral_Onumber__of=1. c_uminus=1. c_NatArith_Oof__nat=1. c_SetInterval_OatMost=1. c_SetInterval_OatLeast=1. c_SetInterval_OlessThan=1. c_Finite__Set_OMax=1. c_Finite__Set_OMin=1. c_SetInterval_OgreaterThan=1. tc_prod=1. c_Numeral_OBit=1. c_HOL_Oabs=1. tc_Datatype__Universe_Onode=1. c_IntDef_Oof__int=1. c_Nat_Osize=1. c_Numeral_Obin__add=1. c_HOL_Oinverse=1. c_List_Oset=1. c_OrderedGroup_Onprt=1. c_OrderedGroup_Opprt=1. c_List_Orev=1. c_Union=1. c_List_Olists=1. c_Transitive__Closure_Ortrancl=1. c_Finite__Set_Ocard=1. c_Inter=1. c_List_Oremdups=1. c_List_Oupt=1. c_List_Olast=1. c_List_Oconcat=1. c_List_Olistrel=1. c_List_Olex=1. c_Pow=1. c_Datatype_Ooption_OSome=1. c_Numeral_Obin__mult=1. c_Relation_Odiag=1. tc_sum=1. c_Binomial_Obinomial=1. c_List_Olexord=1. c_List_Orotate1=1. c_List_Obutlast=1. c_List_Ohd=1. c_List_Otl=1. c_Transitive__Closure_Otrancl=1. c_Tarski_Odual=1. tc_Tarski_Opotype_Opotype__ext__type=1. c_Datatype_Oo2s=1. c_List_Ochar_OChar=1. c_IntDiv_Oadjust=1. c_List_Olistset=1. c_Main_OIdE__1=1. c_Main_OInter__UNIV__conv__1__1=1. c_Main_OInter__UNIV__conv__2__1=1. c_Main_ONil__eq__concat__conv__1=1. c_Main_OUnion__empty__conv__1=1. c_Main_Oconcat__eq__Nil__conv__1=1. c_Main_Oempty__Union__conv__1=1. c_Main_Ofinite__Union__1=1. c_Datatype_Othe=1. c_Fun_Oid=1. c_List_Olenlex=1. c_Main_Oall__not__in__conv__1=1. c_Main_Olexord__Nil__left__1=1. c_Main_Olexord__Nil__left__2=1. c_Main_Omod__eq__0D__dest__1=1. c_Main_Onot__None__eq__1=1. c_Main_Onot__Some__eq__1=1. c_Main_Ozmod__eq__0D__dest__1=1. c_Set_Ocontents=1. tc_fun=1. tc_set=1. tc_List_Olist=1. c_Suc=1. c_IntDef_Oint=1. c_Numeral_Obin__minus=1. c_IntDef_Onat=1. c_GCD_Ogcd=1. c_IntDiv_OnegDivAlg=1. c_IntDiv_OposDivAlg=1. c_Numeral_Obin__pred=1. c_IntDiv_OnegateSnd=1. c_Numeral_Obin__succ=1. c_IntDef_OAbs__Integ=1. tc_Datatype_Ooption=1. c_IntDef_ORep__Integ=1. c_plus=1. c_times=1. c_SetInterval_OatLeastLessThan=1. c_divide=1. c_insert=1. c_minus=1. c_Orderings_Omin=1. c_Orderings_Omax=1. c_Nat_Opower=1. c_SetInterval_OatLeastAtMost=1. c_List_Olist_OCons=1. c_SetInterval_OgreaterThanAtMost=1. c_SetInterval_OgreaterThanLessThan=1. c_Divides_Oop_Amod=1. c_append=1. c_div=1. c_inter=1. c_LOrder_Ojoin=1. c_LOrder_Omeet=1. c_union=1. c_Main_OMax__le__iff__1=1. c_Main_OMax__less__iff__1=1. c_Main_OMin__ge__iff__1=1. c_Main_OMin__gr__iff__1=1. c_List_Onth=1. c_List_Odrop=1. c_List_Otake=1. c_List_Oreplicate=1. c_Datatype__Universe_OIn0=1. c_Datatype__Universe_OIn1=1. c_Relation_ODomain=1. c_Relation_Oconverse=1. c_List_Orotate=1. c_Relation_ORange=1. c_Tarski_Opotype_Oorder=1. c_fst=1. c_snd=1. c_List_Oremove1=1. c_List_Osublist=1. c_Sum__Type_OInl=1. c_Sum__Type_OInr=1. c_List_Olist__inter=1. c_Tarski_Opotype_Opset=1. c_Datatype__Universe_OAtom=1. c_Datatype__Universe_OLeaf=1. c_Datatype__Universe_ONumb=1. c_Equiv__Relations_Oquotient=1. c_List_Oitrev=1. c_Main_OdiagE__1=1. c_Main_OInterI__1=1. c_Main_OInter__iff__1=1. c_Main_OUnionE__1=1. c_Main_OUnion__iff__1=1. c_Main_Oin__listsI__1=1. c_Main_OsubsetI__1=1. c_Tarski_Olub=1. c_Datatype_Ounit_Ounit__case=1. c_Datatype_Ounit_Ounit__rec=1. c_List_Olexn=1. c_List_Oset__Cons=1. c_Main_Osurj__pair__1=1. c_Main_Osurj__pair__2=1. c_Tarski_Oglb=1. c_Tarski_Opotype_Omore=1. c_Pair=1. c_Relation_OImage=1. c_Datatype__Universe_Ontrunc=1. c_Datatype__Universe_OScons=1. c_List_Ozip=1. c_List_Olist__update=1. c_Datatype__Universe_Odsum=1. c_Datatype__Universe_Ousum=1. c_Sum__Type_OPlus=1. c_Datatype__Universe_Odprod=1. c_Datatype__Universe_Ouprod=1. c_Main_OPlusE__1=1. c_Main_OPlusE__2=1. c_Main_OdsumE__1=1. c_Main_OdsumE__2=1. c_Main_OdsumE__3=1. c_Main_OdsumE__4=1. c_Main_OusumE__1=1. c_Main_OusumE__2=1. c_Extraction_Osumbool_Osumbool__case=1. c_Extraction_Osumbool_Osumbool__rec=1. c_Main_OconverseE__1=1. c_Main_OconverseE__2=1. c_Numeral_Obit_Obit__case=1. c_Numeral_Obit_Obit__rec=1. c_Wellfounded__Relations_Olex__prod=1. c_Main_ODomainE__1=1. c_Main_ORangeE__1=1. c_Map_Omap__of=1. c_Tarski_Opotype_Omore__update=1. c_Tarski_Opotype_Oorder__update=1. c_Tarski_Opotype_Opset__update=1. c_Tarski_Opotype_Opotype__ext=1. c_Relation_Orel__comp=1. c_Main_OImageE__1=1. c_Main_OdprodE__1=1. c_Main_OdprodE__2=1. c_Main_OdprodE__3=1. c_Main_OdprodE__4=1. c_Main_Olistrel__Cons1__1=1. c_Main_Olistrel__Cons1__2=1. c_Main_Olistrel__Cons2__1=1. c_Main_Olistrel__Cons2__2=1. c_Main_OuprodE__1=1. c_Main_OuprodE__2=1. c_Main_Orel__compE__1=1. c_Main_Orel__compE__2=1. c_Main_Orel__compE__3=1. c_List_Onibble_Onibble__case=1. c_List_Onibble_Onibble__rec=1.
% 38.26/38.26
% 38.26/38.26 ============================== end of process initial clauses ========
% 38.26/38.26
% 38.26/38.26 ============================== CLAUSES FOR SEARCH ====================
% 38.26/38.26
% 38.26/38.26 ============================== end of clauses for search =============
% 38.26/38.26
% 38.26/38.26 ============================== SEARCH ================================
% 38.26/38.26
% 38.26/38.26 % Starting search at 35.37 seconds.
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=70.000, iters=3704
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=65.000, iters=3692
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=41.000, iters=3456
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=39.000, iters=3374
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=37.000, iters=3339
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=36.000, iters=3348
% 38.26/38.26
% 38.26/38.26 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 111 (0.00 of 35.82 sec).
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=35.000, iters=3354
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=34.000, iters=3354
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=31.000, iters=3377
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=30.000, iters=3338
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=28.000, iters=3346
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=27.000, iters=3380
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=26.000, iters=3337
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=25.000, iters=3355
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=24.000, iters=3353
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=23.000, iters=3344
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=22.000, iters=3363
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=21.000, iters=3345
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=20.000, iters=3358
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=19.000, iters=3366
% 38.26/38.26
% 38.26/38.26 Low Water (keep): wt=18.000, iterCputime limit exceeded (core dumped)
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