TSTP Solution File: LCL752-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL752-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 13:49:49 EDT 2022
% Result : Unknown 278.55s 278.76s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL752-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 2 13:16:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.18/1.59 ============================== Prover9 ===============================
% 1.18/1.59 Prover9 (32) version 2009-11A, November 2009.
% 1.18/1.59 Process 29972 was started by sandbox on n013.cluster.edu,
% 1.18/1.59 Sat Jul 2 13:16:45 2022
% 1.18/1.59 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29818_n013.cluster.edu".
% 1.18/1.59 ============================== end of head ===========================
% 1.18/1.59
% 1.18/1.59 ============================== INPUT =================================
% 1.18/1.59
% 1.18/1.59 % Reading from file /tmp/Prover9_29818_n013.cluster.edu
% 1.18/1.59
% 1.18/1.59 set(prolog_style_variables).
% 1.18/1.59 set(auto2).
% 1.18/1.59 % set(auto2) -> set(auto).
% 1.18/1.59 % set(auto) -> set(auto_inference).
% 1.18/1.59 % set(auto) -> set(auto_setup).
% 1.18/1.59 % set(auto_setup) -> set(predicate_elim).
% 1.18/1.59 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.18/1.59 % set(auto) -> set(auto_limits).
% 1.18/1.59 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.18/1.59 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.18/1.59 % set(auto) -> set(auto_denials).
% 1.18/1.59 % set(auto) -> set(auto_process).
% 1.18/1.59 % set(auto2) -> assign(new_constants, 1).
% 1.18/1.59 % set(auto2) -> assign(fold_denial_max, 3).
% 1.18/1.59 % set(auto2) -> assign(max_weight, "200.000").
% 1.18/1.59 % set(auto2) -> assign(max_hours, 1).
% 1.18/1.59 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.18/1.59 % set(auto2) -> assign(max_seconds, 0).
% 1.18/1.59 % set(auto2) -> assign(max_minutes, 5).
% 1.18/1.59 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.18/1.59 % set(auto2) -> set(sort_initial_sos).
% 1.18/1.59 % set(auto2) -> assign(sos_limit, -1).
% 1.18/1.59 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.18/1.59 % set(auto2) -> assign(max_megs, 400).
% 1.18/1.59 % set(auto2) -> assign(stats, some).
% 1.18/1.59 % set(auto2) -> clear(echo_input).
% 1.18/1.59 % set(auto2) -> set(quiet).
% 1.18/1.59 % set(auto2) -> clear(print_initial_clauses).
% 1.18/1.59 % set(auto2) -> clear(print_given).
% 1.18/1.59 assign(lrs_ticks,-1).
% 1.18/1.59 assign(sos_limit,10000).
% 1.18/1.59 assign(order,kbo).
% 1.18/1.59 set(lex_order_vars).
% 1.18/1.59 clear(print_given).
% 1.18/1.59
% 1.18/1.59 % formulas(sos). % not echoed (1138 formulas)
% 1.18/1.59
% 1.18/1.59 ============================== end of input ==========================
% 1.18/1.59
% 1.18/1.59 % From the command line: assign(max_seconds, 300).
% 1.18/1.59
% 1.18/1.59 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.18/1.59
% 1.18/1.59 % Formulas that are not ordinary clauses:
% 1.18/1.59
% 1.18/1.59 ============================== end of process non-clausal formulas ===
% 1.18/1.59
% 1.18/1.59 ============================== PROCESS INITIAL CLAUSES ===============
% 1.18/1.59
% 1.18/1.59 ============================== PREDICATE ELIMINATION =================
% 1.18/1.59 1 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.18/1.59 2 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 1.18/1.59 3 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 1.18/1.59 4 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom). [assumption].
% 1.18/1.59 5 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom). [assumption].
% 1.18/1.59 6 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 1.18/1.59 7 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 1.37/1.63 8 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 1.37/1.63 9 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 1.37/1.63 10 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 1.37/1.63 11 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 1.37/1.63 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(1,a,2,a)].
% 1.37/1.63 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))). [resolve(1,a,3,a)].
% 1.37/1.63 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(1,a,4,a)].
% 1.37/1.63 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(1,a,5,a)].
% 1.37/1.63 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1,a,6,a)].
% 1.37/1.63 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1,a,7,a)].
% 1.37/1.63 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(1,a,8,a)].
% 1.37/1.63 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))). [resolve(1,a,9,a)].
% 1.37/1.63 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1,a,10,a)].
% 1.37/1.63 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(1,a,11,a)].
% 1.37/1.63 12 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.37/1.63 13 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 1.37/1.63 14 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 1.37/1.63 15 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mult__cancel__right_2) # label(axiom). [assumption].
% 1.37/1.63 16 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,A) # label(cls_dvd__mult__cancel__left_2) # label(axiom). [assumption].
% 1.37/1.63 17 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 1.37/1.63 18 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 1.37/1.63 19 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 1.37/1.63 20 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_HOL_Ozero__class_Ozero(A)),A) # label(cls_dvd__mult__cancel__right_1) # label(axiom). [assumption].
% 1.37/1.63 21 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),C),A) # label(cls_dvd__mult__cancel__left_1) # label(axiom). [assumption].
% 1.37/1.63 22 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_dvd__mult__cancel__left_0) # label(axiom). [assumption].
% 1.37/1.63 23 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_dvd__mult__cancel__right_0) # label(axiom). [assumption].
% 1.37/1.63 24 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 1.37/1.63 25 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 1.37/1.63 26 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 1.37/1.63 27 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 1.37/1.63 28 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 1.37/1.63 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)). [resolve(12,a,13,a)].
% 1.37/1.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(12,a,15,a)].
% 1.37/1.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Int_Oint). [resolve(12,a,16,a)].
% 1.37/1.63 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(12,a,17,a)].
% 1.37/1.63 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)) | B = D | A = C. [resolve(12,a,18,a)].
% 1.37/1.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),tc_Int_Oint). [resolve(12,a,20,a)].
% 1.37/1.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B),tc_Int_Oint). [resolve(12,a,21,a)].
% 1.37/1.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint). [resolve(12,a,22,a)].
% 1.37/1.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(12,a,23,a)].
% 1.37/1.63 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(12,a,24,a)].
% 1.37/1.63 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)). [resolve(12,a,25,a)].
% 1.37/1.63 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(12,a,26,a)].
% 1.37/1.63 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(12,a,27,a)].
% 1.37/1.68 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(12,a,28,a)].
% 1.37/1.68 29 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.37/1.68 30 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 1.37/1.68 31 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 1.37/1.68 32 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 1.37/1.68 33 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 1.37/1.68 34 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 1.37/1.68 35 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 1.37/1.68 36 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_power__mono_0) # label(axiom). [assumption].
% 1.37/1.68 37 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)),A),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 1.37/1.68 38 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.37/1.68 39 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.37/1.68 40 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 1.37/1.68 41 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)))) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.37/1.68 42 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(B,D,A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.37/1.68 43 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.37/1.68 44 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.37/1.68 45 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(D,B,A),A),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 1.37/1.68 46 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(D,B,A),A),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 1.37/1.68 47 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 1.37/1.68 48 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 1.37/1.68 49 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,D,A),A),c_Power_Opower__class_Opower(C,D,A))) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 1.37/1.68 50 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)))) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 1.37/1.68 51 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 1.37/1.68 52 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),A),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.37/1.68 53 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.37/1.68 54 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),A),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.37/1.68 55 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.37/1.68 56 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(B,c_Suc(D),A),A),c_Power_Opower__class_Opower(C,c_Suc(D),A))) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 1.37/1.68 57 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) != c_Power_Opower__class_Opower(D,c_Suc(C),A) | B = D | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 1.37/1.68 58 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),c_Power_Opower__class_Opower(B,c_Suc(C),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.37/1.68 59 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(D,C,A) | B = D | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 1.37/1.68 60 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 1.37/1.68 61 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.37/1.68 62 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Power_Opower__class_Opower(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.37/1.68 63 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.37/1.68 64 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.37/1.68 65 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.37/1.68 66 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(D,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 1.37/1.68 67 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.37/1.68 68 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.43/1.68 69 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.43/1.68 70 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),A),A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.43/1.68 71 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.43/1.68 72 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(29,a,30,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(29,a,31,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(29,a,32,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(29,a,33,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(29,a,34,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(29,a,35,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(29,a,36,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Power_Opower__class_Opower(A,B,tc_nat)),tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(29,a,37,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(29,a,38,a)].
% 1.43/1.68 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(29,a,39,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Power_Opower__class_Opower(A,B,tc_nat)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(29,a,40,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))). [resolve(29,a,41,a)].
% 1.43/1.68 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(A,C,tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | B = C. [resolve(29,a,42,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(29,a,43,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(C,A,tc_nat),tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)). [resolve(29,a,45,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(29,a,47,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(29,a,48,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat))). [resolve(29,a,49,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)))). [resolve(29,a,50,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Power_Opower__class_Opower(A,B,tc_nat)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(29,a,51,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_nat),tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)). [resolve(29,a,52,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(29,a,53,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_nat),tc_nat),c_Power_Opower__class_Opower(B,c_Suc(C),tc_nat))). [resolve(29,a,56,a)].
% 1.43/1.68 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_nat) | A = C | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(29,a,57,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(29,a,58,a)].
% 1.43/1.68 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(C,B,tc_nat) | A = C | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(29,a,59,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(29,a,60,a)].
% 1.43/1.68 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(29,a,61,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(29,a,62,a)].
% 1.43/1.68 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(29,a,63,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(29,a,64,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(29,a,65,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(29,a,66,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(29,a,67,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(29,a,68,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(29,a,69,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(29,a,70,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(29,a,71,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(29,a,72,a)].
% 1.43/1.68 73 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(73,a,30,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))). [resolve(73,a,31,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,32,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,33,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(73,a,34,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(73,a,35,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(73,a,36,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Power_Opower__class_Opower(A,B,tc_Int_Oint)),tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,37,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(73,a,38,a)].
% 1.43/1.68 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(73,a,39,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Power_Opower__class_Opower(A,B,tc_Int_Oint)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,40,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)))). [resolve(73,a,41,a)].
% 1.43/1.68 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_Power_Opower__class_Opower(A,C,tc_Int_Oint) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | B = C. [resolve(73,a,42,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint))). [resolve(73,a,43,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(C,A,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),C)). [resolve(73,a,45,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,47,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,48,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint))). [resolve(73,a,49,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint)))). [resolve(73,a,50,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Power_Opower__class_Opower(A,B,tc_Int_Oint)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,51,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),C)). [resolve(73,a,52,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(73,a,53,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(B,c_Suc(C),tc_Int_Oint))). [resolve(73,a,56,a)].
% 1.43/1.68 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_Int_Oint) | A = C | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,57,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,58,a)].
% 1.43/1.68 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_Power_Opower__class_Opower(C,B,tc_Int_Oint) | A = C | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,59,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,60,a)].
% 1.43/1.68 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(73,a,61,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,62,a)].
% 1.43/1.68 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(73,a,63,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(73,a,64,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(73,a,65,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(73,a,66,a)].
% 1.43/1.68 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(73,a,67,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))). [resolve(73,a,68,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(73,a,69,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(73,a,70,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(73,a,71,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint))). [resolve(73,a,72,a)].
% 1.43/1.69 74 class_Ring__and__Field_Oordered__semidom(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(74,a,30,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,31,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,32,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,33,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(74,a,34,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(74,a,35,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(C,B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(74,a,36,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral)),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,37,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,38,a)].
% 1.43/1.69 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,39,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,40,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))). [resolve(74,a,41,a)].
% 1.43/1.69 Derived: c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral) != c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | B = C. [resolve(74,a,42,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,43,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(C,A,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(C,B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)). [resolve(74,a,45,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,47,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,48,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(B,C,tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,49,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))). [resolve(74,a,50,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,51,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(C,B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)). [resolve(74,a,52,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(74,a,53,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(B,c_Suc(C),tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,56,a)].
% 1.43/1.69 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Code__Numeral_Ocode__numeral) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_Code__Numeral_Ocode__numeral) | A = C | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,57,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,c_Suc(B),tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,58,a)].
% 1.43/1.69 Derived: c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral) != c_Power_Opower__class_Opower(C,B,tc_Code__Numeral_Ocode__numeral) | A = C | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,59,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,60,a)].
% 1.43/1.69 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,61,a)].
% 1.43/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,62,a)].
% 1.43/1.74 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,63,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,64,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)). [resolve(74,a,65,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(C,B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(74,a,66,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(74,a,67,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,68,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(74,a,69,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(74,a,70,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(74,a,71,a)].
% 1.43/1.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral))). [resolve(74,a,72,a)].
% 1.43/1.74 75 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.43/1.74 76 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mod__trivial_0) # label(axiom). [assumption].
% 1.43/1.74 77 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__self_0) # label(axiom). [assumption].
% 1.43/1.74 78 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) # label(cls_zmod__simps_I4_J_0) # label(axiom). [assumption].
% 1.43/1.74 79 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,D,A)),c_Divides_Odiv__class_Odiv(C,D,A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,A) # label(cls_div__add_0) # label(axiom). [assumption].
% 1.43/1.74 80 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(C,B,A))),c_Divides_Odiv__class_Omod(C,B,A))),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D) # label(cls_div__mod__equality2_0) # label(axiom). [assumption].
% 1.43/1.74 81 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A))),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) # label(cls_div__mod__equality_0) # label(axiom). [assumption].
% 1.43/1.74 82 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) # label(cls_dvd__mod__imp__dvd_0) # label(axiom). [assumption].
% 1.43/1.74 83 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mod__iff_1) # label(axiom). [assumption].
% 1.43/1.74 84 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mod__iff_0) # label(axiom). [assumption].
% 1.43/1.74 85 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mod_0) # label(axiom). [assumption].
% 1.43/1.74 86 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__div__trivial_0) # label(axiom). [assumption].
% 1.43/1.74 87 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__mult__eq_0) # label(axiom). [assumption].
% 1.43/1.74 88 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(B,C,A)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2_0) # label(axiom). [assumption].
% 1.43/1.74 89 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_Divides_Odiv__class_Odiv(B,D,A)) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1_0) # label(axiom). [assumption].
% 1.43/1.74 90 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__eq_0) # label(axiom). [assumption].
% 1.43/1.74 91 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__add__left__eq_0) # label(axiom). [assumption].
% 1.43/1.74 92 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__right__eq_0) # label(axiom). [assumption].
% 1.43/1.74 93 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__imp__mod__0_0) # label(axiom). [assumption].
% 1.43/1.74 94 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_HOL_Ozero__class_Ozero(A) | c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__eq__mod__eq__0_1) # label(axiom). [assumption].
% 1.43/1.74 95 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),D) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__mult_0) # label(axiom). [assumption].
% 1.43/1.74 96 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__mult__left__eq_0) # label(axiom). [assumption].
% 1.43/1.74 97 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__mult__right__eq_0) # label(axiom). [assumption].
% 1.43/1.74 98 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,D,A),c_Divides_Odiv__class_Odiv(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,A) # label(cls_div__dvd__div_0) # label(axiom). [assumption].
% 1.43/1.74 99 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__dvd__div_1) # label(axiom). [assumption].
% 1.43/1.74 100 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C) = B | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__mult__self_0) # label(axiom). [assumption].
% 1.43/1.74 101 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(C,B,A)) = C | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mult__div__cancel_0) # label(axiom). [assumption].
% 1.43/1.74 102 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),D),C,A) # label(cls_mod__add__cong_0) # label(axiom). [assumption].
% 1.43/1.74 103 -class_Divides_Osemiring__div(A) | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(B,C,A),D,A) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__power_0) # label(axiom). [assumption].
% 1.43/1.74 104 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2__is__id_0) # label(axiom). [assumption].
% 1.43/1.74 105 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A) = C | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1__is__id_0) # label(axiom). [assumption].
% 1.43/1.74 106 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),D),C,A) # label(cls_mod__mult__cong_0) # label(axiom). [assumption].
% 1.43/1.74 107 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__by__1_0) # label(axiom). [assumption].
% 1.43/1.74 108 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_Divides_Odiv__class_Odiv(D,E,A)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E),A) | -c_Ring__and__Field_Odvd__class_Odvd(E,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__mult__div__if__dvd_0) # label(axiom). [assumption].
% 1.43/1.74 109 -class_Int_Onumber(A) | -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_dvd__eq__mod__eq__0__number__of_0) # label(axiom). [assumption].
% 1.43/1.74 110 -class_Int_Onumber(A) | -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) != c_HOL_Ozero__class_Ozero(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_dvd__eq__mod__eq__0__number__of_1) # label(axiom). [assumption].
% 1.43/1.74 111 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),C),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1__if_0) # label(axiom). [assumption].
% 1.43/1.74 112 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = c_Divides_Odiv__class_Odiv(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1_0) # label(axiom). [assumption].
% 1.43/1.74 113 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) = c_Divides_Odiv__class_Odiv(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult2_0) # label(axiom). [assumption].
% 1.43/1.74 114 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),D,A) = c_Divides_Odiv__class_Omod(B,D,A) # label(cls_mod__mult__self1_0) # label(axiom). [assumption].
% 1.43/1.74 115 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mult__self2_0) # label(axiom). [assumption].
% 1.43/1.74 116 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(C,B,A)),c_HOL_Oone__class_Oone(A)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self1_0) # label(axiom). [assumption].
% 1.43/1.74 117 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_HOL_Oone__class_Oone(A)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self2_0) # label(axiom). [assumption].
% 1.43/1.74 118 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_div__by__1_0) # label(axiom). [assumption].
% 1.43/1.74 119 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__by__0_0) # label(axiom). [assumption].
% 1.43/1.74 120 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__0_0) # label(axiom). [assumption].
% 1.43/1.74 121 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__self_0) # label(axiom). [assumption].
% 1.43/1.74 122 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_mod__by__0_0) # label(axiom). [assumption].
% 1.43/1.74 123 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__0_0) # label(axiom). [assumption].
% 1.43/1.74 124 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__add__self2_0) # label(axiom). [assumption].
% 1.43/1.74 125 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A) = c_Divides_Odiv__class_Omod(C,B,A) # label(cls_mod__add__self1_0) # label(axiom). [assumption].
% 1.43/1.74 126 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),D,A) = c_Divides_Odiv__class_Omod(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) # label(cls_mod__mod__cancel_0) # label(axiom). [assumption].
% 1.43/1.74 127 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self2__is__0_0) # label(axiom). [assumption].
% 1.43/1.74 128 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self1__is__0_0) # label(axiom). [assumption].
% 1.43/1.74 129 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)) = B # label(cls_semiring__div__class_Omod__div__equality_H_0) # label(axiom). [assumption].
% 1.43/1.74 130 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A) # label(cls_zmod__simps_I1_J_0) # label(axiom). [assumption].
% 1.43/1.74 131 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) # label(cls_zmod__simps_I2_J_0) # label(axiom). [assumption].
% 1.43/1.74 132 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(C,B,A))),c_Divides_Odiv__class_Omod(C,B,A)) = C # label(cls_mod__div__equality2_0) # label(axiom). [assumption].
% 1.43/1.74 133 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A)) = B # label(cls_mod__div__equality_0) # label(axiom). [assumption].
% 1.43/1.74 134 -class_Divides_Osemiring__div(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A)) # label(cls_mod__div__decomp_0) # label(axiom). [assumption].
% 1.43/1.74 135 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,D,A)),C) # label(cls_mod__mult__mult2_0) # label(axiom). [assumption].
% 1.43/1.74 136 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(C,D,A)) # label(cls_mod__mult__mult1_0) # label(axiom). [assumption].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(75,a,76,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,77,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),B,tc_nat). [resolve(75,a,78,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,C,tc_nat)),c_Divides_Odiv__class_Odiv(B,C,tc_nat)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat). [resolve(75,a,79,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,A,tc_nat))),c_Divides_Odiv__class_Omod(B,A,tc_nat))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C). [resolve(75,a,80,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)),c_Divides_Odiv__class_Omod(A,B,tc_nat))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C). [resolve(75,a,81,a)].
% 1.43/1.74 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat). [resolve(75,a,82,a)].
% 1.43/1.74 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(75,a,83,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,86,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(75,a,87,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),B,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_Divides_Odiv__class_Odiv(A,B,tc_nat)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,88,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),C,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_Divides_Odiv__class_Odiv(A,C,tc_nat)) | C = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,89,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(75,a,90,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B),C,tc_nat). [resolve(75,a,91,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(75,a,92,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(75,a,93,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(75,a,94,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),C) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(75,a,95,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B),C,tc_nat). [resolve(75,a,96,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(75,a,97,a)].
% 1.43/1.74 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,C,tc_nat),c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat). [resolve(75,a,98,a)].
% 1.43/1.74 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_Divides_Odiv__class_Odiv(C,B,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(75,a,99,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B) = A | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(75,a,100,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,A,tc_nat)) = B | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat). [resolve(75,a,101,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),E),C),B,tc_nat). [resolve(75,a,102,a)].
% 1.43/1.74 Derived: c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(75,a,103,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),B,tc_nat) = A | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,104,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),A,tc_nat) = B | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,105,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),E),C),B,tc_nat). [resolve(75,a,106,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,107,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),c_Divides_Odiv__class_Odiv(C,D,tc_nat)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(75,a,108,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,111,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) = c_Divides_Odiv__class_Odiv(B,C,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,112,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) = c_Divides_Odiv__class_Odiv(A,C,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,113,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),C,tc_nat) = c_Divides_Odiv__class_Omod(A,C,tc_nat). [resolve(75,a,114,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(75,a,115,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(B,A,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,116,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,117,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(75,a,118,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,119,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,120,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,121,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(75,a,122,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,123,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(75,a,124,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat) = c_Divides_Odiv__class_Omod(B,A,tc_nat). [resolve(75,a,125,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat). [resolve(75,a,126,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,127,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,128,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)) = A. [resolve(75,a,129,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat). [resolve(75,a,130,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat). [resolve(75,a,131,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,A,tc_nat))),c_Divides_Odiv__class_Omod(B,A,tc_nat)) = B. [resolve(75,a,132,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)),c_Divides_Odiv__class_Omod(A,B,tc_nat)) = A. [resolve(75,a,133,a)].
% 1.43/1.74 Derived: A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)),c_Divides_Odiv__class_Omod(A,B,tc_nat)). [resolve(75,a,134,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B). [resolve(75,a,135,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)). [resolve(75,a,136,a)].
% 1.43/1.74 137 class_Divides_Osemiring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(137,a,76,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,77,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)),C),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),B,tc_Int_Oint). [resolve(137,a,78,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint)),c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Int_Oint). [resolve(137,a,79,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint))),c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C). [resolve(137,a,80,a)].
% 1.43/1.74 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C). [resolve(137,a,81,a)].
% 1.43/1.74 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(137,a,82,a)].
% 1.43/1.74 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(137,a,83,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,86,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(137,a,87,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),B,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,88,a)].
% 1.43/1.74 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),C,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint)) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,89,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(137,a,90,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B),C,tc_Int_Oint). [resolve(137,a,91,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(137,a,92,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(137,a,93,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(137,a,94,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),C) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(137,a,95,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B),C,tc_Int_Oint). [resolve(137,a,96,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(137,a,97,a)].
% 1.43/1.75 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint),c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Int_Oint). [resolve(137,a,98,a)].
% 1.43/1.75 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),c_Divides_Odiv__class_Odiv(C,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(137,a,99,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B) = A | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(137,a,100,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint)) = B | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(137,a,101,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),D),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),E),C),B,tc_Int_Oint). [resolve(137,a,102,a)].
% 1.43/1.75 Derived: c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(137,a,103,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),B,tc_Int_Oint) = A | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,104,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),A,tc_Int_Oint) = B | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,105,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),E),C),B,tc_Int_Oint). [resolve(137,a,106,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,107,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),c_Divides_Odiv__class_Odiv(C,D,tc_Int_Oint)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(137,a,108,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,111,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,112,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,113,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint). [resolve(137,a,114,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(137,a,115,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),A,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint)) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,116,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),B,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,117,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(137,a,118,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,119,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,120,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,121,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(137,a,122,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,123,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(137,a,124,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),A,tc_Int_Oint) = c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint). [resolve(137,a,125,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint). [resolve(137,a,126,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,127,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(137,a,128,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)) = A. [resolve(137,a,129,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)),C),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),B,tc_Int_Oint). [resolve(137,a,130,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint). [resolve(137,a,131,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint))),c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint)) = B. [resolve(137,a,132,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)) = A. [resolve(137,a,133,a)].
% 1.43/1.75 Derived: A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)). [resolve(137,a,134,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B). [resolve(137,a,135,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)). [resolve(137,a,136,a)].
% 1.43/1.75 138 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral),B,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,76,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_Code__Numeral_Ocode__numeral) = c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) | A = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,77,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral)),C),B,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C),B,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,78,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),C,tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(A,C,tc_Code__Numeral_Ocode__numeral)),c_Divides_Odiv__class_Odiv(B,C,tc_Code__Numeral_Ocode__numeral)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,79,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Divides_Odiv__class_Odiv(B,A,tc_Code__Numeral_Ocode__numeral))),c_Divides_Odiv__class_Omod(B,A,tc_Code__Numeral_Ocode__numeral))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C). [resolve(138,a,80,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C). [resolve(138,a,81,a)].
% 1.43/1.75 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral). [resolve(138,a,82,a)].
% 1.43/1.75 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,83,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral),B,tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,86,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),C,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(A,C,tc_Code__Numeral_Ocode__numeral)),c_Divides_Odiv__class_Omod(B,C,tc_Code__Numeral_Ocode__numeral)),C,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,87,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)),B,tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral)) | B = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,88,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)),C,tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),c_Divides_Odiv__class_Odiv(A,C,tc_Code__Numeral_Ocode__numeral)) | C = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,89,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),C,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(A,C,tc_Code__Numeral_Ocode__numeral)),c_Divides_Odiv__class_Omod(B,C,tc_Code__Numeral_Ocode__numeral)),C,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,90,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),C,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(A,C,tc_Code__Numeral_Ocode__numeral)),B),C,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,91,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),C,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_Divides_Odiv__class_Omod(B,C,tc_Code__Numeral_Ocode__numeral)),C,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,92,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,93,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral) != c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,94,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral)),C) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C),B,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,95,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),C,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(A,C,tc_Code__Numeral_Ocode__numeral)),B),C,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,96,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),C,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Divides_Odiv__class_Omod(B,C,tc_Code__Numeral_Ocode__numeral)),C,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,97,a)].
% 1.43/1.75 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,C,tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(B,C,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,98,a)].
% 1.43/1.75 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(C,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,99,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral)),B) = A | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,100,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Divides_Odiv__class_Odiv(B,A,tc_Code__Numeral_Ocode__numeral)) = B | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,101,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(C,B,tc_Code__Numeral_Ocode__numeral) | c_Divides_Odiv__class_Omod(D,B,tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(E,B,tc_Code__Numeral_Ocode__numeral) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),D),A),B,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),E),C),B,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,102,a)].
% 1.43/1.75 Derived: c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral),C,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(B,C,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,103,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),B,tc_Code__Numeral_Ocode__numeral) = A | B = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,104,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),A,tc_Code__Numeral_Ocode__numeral) = B | A = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,105,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(C,B,tc_Code__Numeral_Ocode__numeral) | c_Divides_Odiv__class_Omod(D,B,tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(E,B,tc_Code__Numeral_Ocode__numeral) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),D),A),B,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),E),C),B,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,106,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,107,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral)),c_Divides_Odiv__class_Odiv(C,D,tc_Code__Numeral_Ocode__numeral)) = c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,108,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B),tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,111,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C),tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Odiv(B,C,tc_Code__Numeral_Ocode__numeral) | A = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,112,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B),tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Odiv(A,C,tc_Code__Numeral_Ocode__numeral) | B = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,113,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)),C,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(A,C,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,114,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)),B,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,115,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),A,tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(B,A,tc_Code__Numeral_Ocode__numeral)),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) | A = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,116,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),B,tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral)),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) | B = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,117,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) = A. [resolve(138,a,118,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,119,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A,tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,120,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,121,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) = A. [resolve(138,a,122,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A,tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,123,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),B,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,124,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),A,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(B,A,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,125,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral),C,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(A,C,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,126,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),B,tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,127,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),A,tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(138,a,128,a)].
% 1.43/1.75 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral)),B)) = A. [resolve(138,a,129,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral)),C),B,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C),B,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,130,a)].
% 1.43/1.75 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_Divides_Odiv__class_Omod(B,C,tc_Code__Numeral_Ocode__numeral)),C,tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),C,tc_Code__Numeral_Ocode__numeral). [resolve(138,a,131,a)].
% 1.54/1.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Divides_Odiv__class_Odiv(B,A,tc_Code__Numeral_Ocode__numeral))),c_Divides_Odiv__class_Omod(B,A,tc_Code__Numeral_Ocode__numeral)) = B. [resolve(138,a,132,a)].
% 1.54/1.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral)) = A. [resolve(138,a,133,a)].
% 1.54/1.81 Derived: A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Odiv(A,B,tc_Code__Numeral_Ocode__numeral)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Code__Numeral_Ocode__numeral)). [resolve(138,a,134,a)].
% 1.54/1.81 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B),tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(A,C,tc_Code__Numeral_Ocode__numeral)),B). [resolve(138,a,135,a)].
% 1.54/1.81 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C),tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Divides_Odiv__class_Omod(B,C,tc_Code__Numeral_Ocode__numeral)). [resolve(138,a,136,a)].
% 1.54/1.81 139 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.54/1.81 140 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(B,C,tc_nat),A) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(B,A),C,A) # label(cls_of__nat__power_0) # label(axiom). [assumption].
% 1.54/1.81 141 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom). [assumption].
% 1.54/1.81 142 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 1.54/1.81 143 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__mult_0) # label(axiom). [assumption].
% 1.54/1.81 144 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 1.54/1.81 145 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 1.54/1.81 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),B,tc_nat). [resolve(139,a,140,a)].
% 1.54/1.81 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(139,a,141,a)].
% 1.54/1.81 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)). [resolve(139,a,142,a)].
% 1.54/1.81 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(139,a,143,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(139,a,144,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(139,a,145,a)].
% 1.57/1.87 146 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(A,B,tc_nat),tc_Int_Oint) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(146,a,140,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(146,a,141,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)). [resolve(146,a,142,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)). [resolve(146,a,143,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)). [resolve(146,a,144,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(146,a,145,a)].
% 1.57/1.87 147 class_Ring__and__Field_Osemiring__1(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(A,B,tc_nat),tc_Code__Numeral_Ocode__numeral) = c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral),B,tc_Code__Numeral_Ocode__numeral). [resolve(147,a,140,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Code__Numeral_Ocode__numeral) = c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral). [resolve(147,a,141,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral)). [resolve(147,a,142,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Code__Numeral_Ocode__numeral)). [resolve(147,a,143,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Code__Numeral_Ocode__numeral)). [resolve(147,a,144,a)].
% 1.57/1.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(147,a,145,a)].
% 1.57/1.87 148 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.57/1.87 149 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),c_Int_Onumber__class_Onumber__of(D,A)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Int_Onumber__class_Onumber__of(D,A))) # label(cls_left__diff__distrib__number__of_0) # label(axiom). [assumption].
% 1.57/1.87 150 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D)) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 1.57/1.87 151 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B)),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E) # label(cls_eq__add__iff2_1) # label(axiom). [assumption].
% 1.57/1.87 152 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F) | D = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 1.57/1.87 153 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 1.57/1.87 154 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D)) # label(cls_right__diff__distrib__number__of_0) # label(axiom). [assumption].
% 1.57/1.87 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint))). [resolve(148,a,149,a)].
% 1.57/1.87 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)). [resolve(148,a,150,a)].
% 1.57/1.87 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),A)),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)),D). [resolve(148,a,151,a)].
% 1.57/1.87 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | C = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E). [resolve(148,a,152,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C) = E. [resolve(148,a,153,a)].
% 1.65/1.91 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),C)). [resolve(148,a,154,a)].
% 1.65/1.91 155 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.65/1.91 156 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_dvd__triv__right_0) # label(axiom). [assumption].
% 1.65/1.91 157 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_dvd__triv__left_0) # label(axiom). [assumption].
% 1.65/1.91 158 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 1.65/1.91 159 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 1.65/1.91 160 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Omul__1_0) # label(axiom). [assumption].
% 1.65/1.91 161 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_le__imp__power__dvd_0) # label(axiom). [assumption].
% 1.65/1.91 162 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 1.65/1.91 163 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 1.65/1.91 164 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A),A) # label(cls_dvd__power_1) # label(axiom). [assumption].
% 1.65/1.91 165 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A)) = c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),A) # label(cls_class__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 1.65/1.91 166 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 1.65/1.91 167 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A) = c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),A) # label(cls_class__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 1.65/1.91 168 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)) # label(cls_class__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 1.65/1.91 169 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)) # label(cls_class__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 1.65/1.91 170 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.65/1.91 171 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.65/1.91 172 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 1.65/1.91 173 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 1.65/1.91 174 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 1.65/1.91 175 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 1.65/1.91 176 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 1.65/1.91 177 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__power__same_0) # label(axiom). [assumption].
% 1.65/1.91 178 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 1.65/1.91 179 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__add_0) # label(axiom). [assumption].
% 1.65/1.91 180 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_class__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 1.65/1.91 181 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.65/1.91 182 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.65/1.91 183 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.65/1.91 184 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A))),C) # label(cls_class__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 1.65/1.91 185 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 1.65/1.91 186 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__trans_0) # label(axiom). [assumption].
% 1.65/1.91 187 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,B,A) # label(cls_dvd__refl_0) # label(axiom). [assumption].
% 1.65/1.91 188 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__dvd_0) # label(axiom). [assumption].
% 1.65/1.91 189 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 1.65/1.91 190 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 1.65/1.91 191 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 1.65/1.91 192 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 1.65/1.91 193 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 1.65/1.91 194 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_dvd__0__right_0) # label(axiom). [assumption].
% 1.65/1.91 195 -class_Ring__and__Field_Ocomm__semiring__1(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_dvd__0__left_0) # label(axiom). [assumption].
% 1.65/1.91 196 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 1.65/1.91 197 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 1.65/1.91 198 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 1.65/1.91 199 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)) = c_Power_Opower__class_Opower(B,c_Suc(C),A) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 1.65/1.91 200 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),B) = c_Power_Opower__class_Opower(B,c_Suc(C),A) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 1.65/1.91 201 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,E,A),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),E)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__power__le_0) # label(axiom). [assumption].
% 1.65/1.91 202 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),C,A) # label(cls_dvd__mult__right_0) # label(axiom). [assumption].
% 1.65/1.91 203 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) # label(cls_dvd__mult__left_0) # label(axiom). [assumption].
% 1.65/1.91 204 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mult2_0) # label(axiom). [assumption].
% 1.65/1.91 205 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mult_0) # label(axiom). [assumption].
% 1.65/1.91 206 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,E,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_mult__dvd__mono_0) # label(axiom). [assumption].
% 1.65/1.91 207 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),D,A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),E)) | -c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,E,A),D,A) # label(cls_power__le__dvd_0) # label(axiom). [assumption].
% 1.65/1.91 208 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,D,A)),c_Power_Opower__class_Opower(C,D,A)) # label(cls_class__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 1.65/1.91 209 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.65/1.91 210 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.65/1.91 211 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.65/1.91 212 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.65/1.91 213 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.65/1.91 214 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 1.65/1.91 215 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Omul__d_0) # label(axiom). [assumption].
% 1.65/1.91 216 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Power_Opower__class_Opower(B,C,A),A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) # label(cls_dvd__power_0) # label(axiom). [assumption].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A),tc_nat). [resolve(155,a,156,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat). [resolve(155,a,157,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(155,a,158,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(155,a,159,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(155,a,161,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(155,a,162,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),tc_nat). [resolve(155,a,164,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat)) = c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(155,a,165,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(155,a,166,a)].
% 1.65/1.91 Derived: c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_nat),C,tc_nat) = c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat). [resolve(155,a,167,a)].
% 1.65/1.91 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Power_Opower__class_Opower(A,B,tc_nat)). [resolve(155,a,168,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(155,a,170,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(155,a,172,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(155,a,174,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(155,a,175,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(155,a,176,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(155,a,177,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(155,a,178,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat). [resolve(155,a,179,a)].
% 1.65/1.91 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(155,a,180,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)). [resolve(155,a,181,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))). [resolve(155,a,182,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),D)). [resolve(155,a,183,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B). [resolve(155,a,184,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(155,a,185,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(155,a,186,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_nat). [resolve(155,a,187,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(155,a,188,a)].
% 1.65/1.91 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(155,a,189,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(155,a,190,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(155,a,191,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(155,a,192,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(155,a,194,a)].
% 1.65/1.91 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(155,a,195,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(155,a,196,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(155,a,197,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Power_Opower__class_Opower(A,B,tc_nat)) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat). [resolve(155,a,199,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),A) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat). [resolve(155,a,200,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,D,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(155,a,201,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),B,tc_nat). [resolve(155,a,202,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),B,tc_nat). [resolve(155,a,203,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat). [resolve(155,a,204,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(155,a,205,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(155,a,206,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_nat),C,tc_nat) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,D,tc_nat),C,tc_nat). [resolve(155,a,207,a)].
% 1.65/1.91 Derived: c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat)),c_Power_Opower__class_Opower(B,C,tc_nat)). [resolve(155,a,208,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),B). [resolve(155,a,209,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(155,a,210,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C). [resolve(155,a,211,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(155,a,212,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(155,a,214,a)].
% 1.65/1.91 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(155,a,215,a)].
% 1.65/1.91 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(155,a,216,a)].
% 1.65/1.92 217 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint). [resolve(217,a,156,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint). [resolve(217,a,157,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(217,a,158,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(217,a,159,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(217,a,161,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),A). [resolve(217,a,162,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint),tc_Int_Oint). [resolve(217,a,164,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint)),c_Power_Opower__class_Opower(A,C,tc_Int_Oint)) = c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_Int_Oint). [resolve(217,a,165,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint))),A). [resolve(217,a,166,a)].
% 1.65/1.92 Derived: c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_Int_Oint). [resolve(217,a,167,a)].
% 1.65/1.92 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Power_Opower__class_Opower(A,B,tc_Int_Oint)). [resolve(217,a,168,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A). [resolve(217,a,170,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C). [resolve(217,a,172,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(217,a,174,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)). [resolve(217,a,175,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)). [resolve(217,a,176,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(217,a,177,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D)). [resolve(217,a,178,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(217,a,179,a)].
% 1.65/1.92 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = A. [resolve(217,a,180,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(217,a,181,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))). [resolve(217,a,182,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),D)). [resolve(217,a,183,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint))),B). [resolve(217,a,184,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),c_HOL_Oone__class_Oone(tc_Int_Oint))),A). [resolve(217,a,185,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(217,a,186,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_Int_Oint). [resolve(217,a,187,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(217,a,188,a)].
% 1.65/1.92 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(217,a,189,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(217,a,190,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(217,a,191,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(217,a,192,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(217,a,194,a)].
% 1.65/1.92 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(217,a,195,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(217,a,196,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(217,a,197,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Power_Opower__class_Opower(A,B,tc_Int_Oint)) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint). [resolve(217,a,199,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint)),A) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint). [resolve(217,a,200,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,D,tc_Int_Oint),tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(217,a,201,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),B,tc_Int_Oint). [resolve(217,a,202,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),B,tc_Int_Oint). [resolve(217,a,203,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(217,a,204,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(217,a,205,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(217,a,206,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),C,tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,D,tc_Int_Oint),C,tc_Int_Oint). [resolve(217,a,207,a)].
% 1.65/1.92 Derived: c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint)),c_Power_Opower__class_Opower(B,C,tc_Int_Oint)). [resolve(217,a,208,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),B). [resolve(217,a,209,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(217,a,210,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C). [resolve(217,a,211,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(217,a,212,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(217,a,214,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(217,a,215,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(217,a,216,a)].
% 1.65/1.92 218 class_Ring__and__Field_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),A),tc_Code__Numeral_Ocode__numeral). [resolve(218,a,156,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral). [resolve(218,a,157,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A) = A. [resolve(218,a,158,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(218,a,159,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(218,a,161,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),A). [resolve(218,a,162,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),A,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral). [resolve(218,a,164,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral)),c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral)) = c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_Code__Numeral_Ocode__numeral). [resolve(218,a,165,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),A). [resolve(218,a,166,a)].
% 1.65/1.92 Derived: c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),C,tc_Code__Numeral_Ocode__numeral) = c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_Code__Numeral_Ocode__numeral). [resolve(218,a,167,a)].
% 1.65/1.92 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral)). [resolve(218,a,168,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),A). [resolve(218,a,170,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),C). [resolve(218,a,172,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C)),B). [resolve(218,a,174,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(218,a,175,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(218,a,176,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(C,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,177,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),D)). [resolve(218,a,178,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,179,a)].
% 1.65/1.92 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_Code__Numeral_Ocode__numeral) = A. [resolve(218,a,180,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D)). [resolve(218,a,181,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D))). [resolve(218,a,182,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),D)). [resolve(218,a,183,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),B). [resolve(218,a,184,a)].
% 1.65/1.92 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),A). [resolve(218,a,185,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,186,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,187,a)].
% 1.65/1.92 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),A,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,188,a)].
% 1.65/1.92 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Code__Numeral_Ocode__numeral) = c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral). [resolve(218,a,189,a)].
% 1.65/1.93 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C)),B). [resolve(218,a,190,a)].
% 1.65/1.93 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(218,a,191,a)].
% 1.65/1.93 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(218,a,192,a)].
% 1.65/1.93 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral). [resolve(218,a,194,a)].
% 1.65/1.93 Derived: A = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,195,a)].
% 1.65/1.93 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A) = A. [resolve(218,a,196,a)].
% 1.65/1.93 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(218,a,197,a)].
% 1.65/1.93 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral)) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_Code__Numeral_Ocode__numeral). [resolve(218,a,199,a)].
% 1.65/1.93 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral)),A) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_Code__Numeral_Ocode__numeral). [resolve(218,a,200,a)].
% 1.65/1.93 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(C,D,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,201,a)].
% 1.65/1.93 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),A),B,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,202,a)].
% 1.65/1.93 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C),B,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,203,a)].
% 1.65/1.93 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,204,a)].
% 1.65/1.93 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,205,a)].
% 1.65/1.93 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,206,a)].
% 1.65/1.93 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),C,tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,D,tc_Code__Numeral_Ocode__numeral),C,tc_Code__Numeral_Ocode__numeral). [resolve(218,a,207,a)].
% 1.65/1.97 Derived: c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),C,tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral)),c_Power_Opower__class_Opower(B,C,tc_Code__Numeral_Ocode__numeral)). [resolve(218,a,208,a)].
% 1.65/1.97 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),B). [resolve(218,a,209,a)].
% 1.65/1.97 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(218,a,210,a)].
% 1.65/1.97 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),C). [resolve(218,a,211,a)].
% 1.65/1.97 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(218,a,212,a)].
% 1.65/1.97 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(218,a,214,a)].
% 1.65/1.97 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(218,a,215,a)].
% 1.65/1.97 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(218,a,216,a)].
% 1.65/1.97 219 class_Ring__and__Field_Odvd(tc_nat) # label(clsarity_nat__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 1.65/1.97 220 -class_Ring__and__Field_Odvd(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_dvdI_0) # label(axiom). [assumption].
% 1.65/1.97 221 -class_Ring__and__Field_Odvd(A) | -class_Ring__and__Field_Ocomm__ring(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),F))),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,F,A) # label(cls_inf__period_I4_J_1) # label(axiom). [assumption].
% 1.65/1.97 222 -class_Ring__and__Field_Odvd(A) | -class_Ring__and__Field_Ocomm__ring(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))),F),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),F),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,E,A) # label(cls_inf__period_I4_J_0) # label(axiom). [assumption].
% 1.73/2.02 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),E))),C),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_nat). [resolve(219,a,221,a)].
% 1.73/2.02 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))),E),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),E),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_nat). [resolve(219,a,222,a)].
% 1.73/2.02 223 class_Ring__and__Field_Odvd(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 1.73/2.02 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),E))),C),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_Int_Oint). [resolve(223,a,221,a)].
% 1.73/2.02 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))),E),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),E),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_Int_Oint). [resolve(223,a,222,a)].
% 1.73/2.02 224 class_Ring__and__Field_Odvd(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 1.73/2.02 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Code__Numeral_Ocode__numeral) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),D),E))),C),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_Code__Numeral_Ocode__numeral). [resolve(224,a,221,a)].
% 1.73/2.02 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Code__Numeral_Ocode__numeral) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D))),E),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),E),tc_Code__Numeral_Ocode__numeral) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_Code__Numeral_Ocode__numeral). [resolve(224,a,222,a)].
% 1.73/2.02 225 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.73/2.02 226 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_mult__1__right_0) # label(axiom). [assumption].
% 1.73/2.02 227 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1__left_0) # label(axiom). [assumption].
% 1.73/2.02 228 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)) # label(cls_power__commutes_0) # label(axiom). [assumption].
% 1.73/2.02 229 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),B) # label(cls_power__Suc2_0) # label(axiom). [assumption].
% 1.73/2.02 230 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A)) # label(cls_power__add_0) # label(axiom). [assumption].
% 1.73/2.02 231 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 1.73/2.02 232 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_power__one__right_0) # label(axiom). [assumption].
% 1.73/2.02 233 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),A) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A) # label(cls_power__mult_0) # label(axiom). [assumption].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),A). [resolve(225,a,229,a)].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat)),c_Power_Opower__class_Opower(A,C,tc_nat)). [resolve(225,a,230,a)].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(225,a,231,a)].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_nat),C,tc_nat). [resolve(225,a,233,a)].
% 1.73/2.02 234 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint)),A). [resolve(234,a,229,a)].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint)),c_Power_Opower__class_Opower(A,C,tc_Int_Oint)). [resolve(234,a,230,a)].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(234,a,231,a)].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_Int_Oint) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),C,tc_Int_Oint). [resolve(234,a,233,a)].
% 1.73/2.02 235 class_OrderedGroup_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral)),A). [resolve(235,a,229,a)].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral)),c_Power_Opower__class_Opower(A,C,tc_Code__Numeral_Ocode__numeral)). [resolve(235,a,230,a)].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),A,tc_Code__Numeral_Ocode__numeral) = c_HOL_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral). [resolve(235,a,231,a)].
% 1.73/2.02 Derived: c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_Code__Numeral_Ocode__numeral) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral),C,tc_Code__Numeral_Ocode__numeral). [resolve(235,a,233,a)].
% 1.84/2.11 236 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.84/2.11 237 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1_0) # label(axiom). [assumption].
% 1.84/2.11 238 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,D,A)),c_Power_Opower__class_Opower(C,D,A)) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 1.84/2.11 239 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.84/2.11 240 class_OrderedGroup_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.84/2.11 241 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.84/2.11 242 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.84/2.11 243 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.84/2.11 244 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.84/2.11 245 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.84/2.11 246 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.84/2.11 247 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.84/2.11 248 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.84/2.11 249 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.84/2.11 250 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.86/2.11 251 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.86/2.11 252 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.86/2.11 253 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.86/2.11 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(241,a,242,a)].
% 1.86/2.11 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)). [resolve(241,a,243,a)].
% 1.86/2.11 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(241,a,244,a)].
% 1.86/2.11 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))). [resolve(241,a,245,a)].
% 1.86/2.11 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(241,a,246,a)].
% 1.86/2.11 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))). [resolve(241,a,247,a)].
% 1.86/2.11 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(241,a,248,a)].
% 1.86/2.11 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(241,a,249,a)].
% 1.86/2.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))). [resolve(241,a,250,a)].
% 1.86/2.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(241,a,251,a)].
% 1.86/2.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))). [resolve(241,a,252,a)].
% 1.86/2.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(241,a,253,a)].
% 1.86/2.11 254 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.86/2.12 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(254,a,242,a)].
% 1.86/2.12 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)). [resolve(254,a,243,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(254,a,244,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))). [resolve(254,a,245,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)). [resolve(254,a,246,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B))). [resolve(254,a,247,a)].
% 1.86/2.12 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(254,a,248,a)].
% 1.86/2.12 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(254,a,249,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B))). [resolve(254,a,250,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)). [resolve(254,a,251,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))). [resolve(254,a,252,a)].
% 1.86/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(254,a,253,a)].
% 1.86/2.12 255 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.86/2.12 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)). [resolve(255,a,242,a)].
% 1.86/2.12 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)). [resolve(255,a,243,a)].
% 1.89/2.16 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(255,a,244,a)].
% 1.89/2.16 Derived: hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(255,a,245,a)].
% 1.89/2.16 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),C)). [resolve(255,a,246,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),A),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(255,a,247,a)].
% 1.89/2.17 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)). [resolve(255,a,248,a)].
% 1.89/2.17 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)). [resolve(255,a,249,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),A),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(255,a,250,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),C)). [resolve(255,a,251,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(255,a,252,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(255,a,253,a)].
% 1.89/2.17 256 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 1.89/2.17 257 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_lessequals(D,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F))) # label(cls_le__add__iff2_1) # label(axiom). [assumption].
% 1.89/2.17 258 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)),E)),F))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F))) # label(cls_le__add__iff2_0) # label(axiom). [assumption].
% 1.89/2.17 259 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D),A),F)) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 1.89/2.17 260 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)),E),A),F)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F))) # label(cls_le__add__iff1_0) # label(axiom). [assumption].
% 1.89/2.17 261 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),B)) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 1.89/2.17 262 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),C)) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 1.89/2.17 263 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.89/2.17 264 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 1.89/2.17 265 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 1.89/2.17 266 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)),E),A),F)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F))) # label(cls_less__add__iff1_0) # label(axiom). [assumption].
% 1.89/2.17 267 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D),A),F)) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 1.89/2.17 268 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)),E)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F))) # label(cls_less__add__iff2_0) # label(axiom). [assumption].
% 1.89/2.17 269 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F))) # label(cls_less__add__iff2_1) # label(axiom). [assumption].
% 1.89/2.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(256,a,257,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C)),D)),E))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)),E))). [resolve(256,a,258,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C),tc_Int_Oint),E)). [resolve(256,a,259,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),C)),D),tc_Int_Oint),E)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),D),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),E))). [resolve(256,a,260,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),A)). [resolve(256,a,261,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),B)). [resolve(256,a,262,a)].
% 1.89/2.17 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(256,a,263,a)].
% 1.89/2.21 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(256,a,265,a)].
% 1.89/2.21 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),C)),D),tc_Int_Oint),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),D),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),E))). [resolve(256,a,266,a)].
% 1.89/2.21 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C),tc_Int_Oint),E)). [resolve(256,a,267,a)].
% 1.89/2.21 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C)),D)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)),E))). [resolve(256,a,268,a)].
% 1.89/2.21 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(256,a,269,a)].
% 1.89/2.21 270 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 1.89/2.21 271 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)))) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 1.89/2.21 272 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 1.89/2.21 273 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 1.89/2.21 274 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 1.89/2.21 275 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 1.89/2.21 276 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 1.89/2.21 277 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 1.89/2.21 278 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 1.89/2.21 279 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 1.89/2.21 280 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 1.89/2.21 281 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 1.89/2.21 282 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 1.89/2.21 283 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 1.89/2.21 284 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 1.89/2.21 285 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 1.89/2.21 286 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)))) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 1.89/2.21 287 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)))) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 1.89/2.21 288 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))))) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 1.89/2.21 289 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 1.89/2.21 290 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 1.89/2.21 291 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 1.89/2.21 292 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 1.89/2.21 293 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_1) # label(axiom). [assumption].
% 1.89/2.21 294 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_0) # label(axiom). [assumption].
% 1.89/2.21 295 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom). [assumption].
% 1.89/2.21 296 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 1.89/2.21 297 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 1.89/2.21 298 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B))) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 1.89/2.21 299 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 1.89/2.21 300 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 1.89/2.21 301 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 1.89/2.21 302 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 1.89/2.21 303 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 1.89/2.21 304 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 1.89/2.21 305 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 1.89/2.21 306 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 1.89/2.21 307 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 1.89/2.21 308 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 1.89/2.21 309 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 1.89/2.21 310 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 1.89/2.21 311 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 1.89/2.21 312 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 1.89/2.21 313 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 1.89/2.21 314 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 1.89/2.21 315 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 1.89/2.21 316 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 1.89/2.21 317 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 1.89/2.21 318 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 1.89/2.21 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)))). [resolve(270,a,271,a)].
% 1.89/2.21 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,272,a)].
% 1.89/2.22 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,273,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(270,a,274,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,275,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,276,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(270,a,277,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A))). [resolve(270,a,278,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(270,a,279,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A))). [resolve(270,a,280,a)].
% 1.89/2.22 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,281,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,282,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,283,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)). [resolve(270,a,284,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(270,a,285,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)))) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(270,a,286,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)))) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(270,a,287,a)].
% 1.89/2.22 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))))). [resolve(270,a,288,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,289,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,290,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,291,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,292,a)].
% 1.89/2.22 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(270,a,293,a)].
% 1.89/2.22 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(270,a,294,a)].
% 1.89/2.22 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(270,a,295,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A))). [resolve(270,a,298,a)].
% 1.89/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(270,a,299,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(270,a,300,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,301,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(270,a,302,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,304,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(270,a,305,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)). [resolve(270,a,308,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,310,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(270,a,311,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(270,a,312,a)].
% 1.97/2.22 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,313,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(270,a,314,a)].
% 1.97/2.22 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(270,a,315,a)].
% 2.04/2.31 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(270,a,316,a)].
% 2.04/2.31 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(270,a,317,a)].
% 2.04/2.31 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(270,a,318,a)].
% 2.04/2.31 319 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 2.04/2.31 320 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 2.04/2.31 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(319,a,320,a)].
% 2.04/2.31 321 class_Nat_Osemiring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 2.04/2.31 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint) | A = B. [resolve(321,a,320,a)].
% 2.04/2.31 322 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 2.04/2.31 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Code__Numeral_Ocode__numeral) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Code__Numeral_Ocode__numeral) | A = B. [resolve(322,a,320,a)].
% 2.04/2.31 323 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.04/2.31 324 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 2.04/2.31 325 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 2.04/2.31 326 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 2.04/2.31 327 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.04/2.31 328 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 2.04/2.31 329 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 2.04/2.31 330 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 2.04/2.31 331 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 2.04/2.31 332 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 2.04/2.31 333 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 2.04/2.31 334 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 2.04/2.31 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(323,a,324,a)].
% 2.04/2.31 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(323,a,325,a)].
% 2.04/2.31 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(323,a,327,a)].
% 2.04/2.31 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(323,a,328,a)].
% 2.04/2.31 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(323,a,329,a)].
% 2.04/2.31 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(323,a,330,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(323,a,331,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(323,a,332,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(323,a,333,a)].
% 2.04/2.32 335 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.04/2.32 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(335,a,324,a)].
% 2.04/2.32 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(335,a,325,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(335,a,327,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(335,a,328,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(335,a,329,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(335,a,330,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(335,a,331,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(335,a,332,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(335,a,333,a)].
% 2.04/2.32 336 class_OrderedGroup_Opordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.04/2.32 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) != c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | B = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(336,a,324,a)].
% 2.04/2.32 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) != c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | A = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(336,a,325,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(336,a,327,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(336,a,328,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(336,a,329,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(336,a,330,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(336,a,331,a)].
% 2.04/2.32 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(336,a,332,a)].
% 2.04/2.36 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(336,a,333,a)].
% 2.04/2.36 337 class_Power_Opower(tc_nat) # label(clsarity_nat__Power_Opower) # label(axiom). [assumption].
% 2.04/2.36 338 -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)) # label(cls_power__Suc_0) # label(axiom). [assumption].
% 2.04/2.36 339 -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0_0) # label(axiom). [assumption].
% 2.04/2.36 340 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 2.04/2.36 341 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 2.04/2.36 342 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 2.04/2.36 343 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 2.04/2.36 344 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 2.04/2.36 345 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 2.04/2.36 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | c_Power_Opower__class_Opower(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(337,a,340,d)].
% 2.04/2.36 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(337,a,342,d)].
% 2.04/2.36 Derived: -class_Ring__and__Field_Osemiring__0(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(337,a,343,b)].
% 2.04/2.36 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(337,a,344,d)].
% 2.15/2.41 Derived: -class_Ring__and__Field_Osemiring__0(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(337,a,345,b)].
% 2.15/2.41 346 class_Power_Opower(tc_Int_Oint) # label(clsarity_Int__Oint__Power_Opower) # label(axiom). [assumption].
% 2.15/2.41 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(346,a,340,d)].
% 2.15/2.41 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(346,a,342,d)].
% 2.15/2.41 Derived: -class_Ring__and__Field_Osemiring__0(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,343,b)].
% 2.15/2.41 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,344,d)].
% 2.15/2.41 Derived: -class_Ring__and__Field_Osemiring__0(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Suc(A),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(346,a,345,b)].
% 2.15/2.41 347 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Power_Opower) # label(axiom). [assumption].
% 2.15/2.41 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | -class_Ring__and__Field_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) | -class_Ring__and__Field_Omult__zero(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(A,B,tc_Code__Numeral_Ocode__numeral) != c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | A = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(347,a,340,d)].
% 2.15/2.41 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | -class_Ring__and__Field_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) | -class_Ring__and__Field_Omult__zero(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Code__Numeral_Ocode__numeral) != c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(347,a,342,d)].
% 2.15/2.41 Derived: -class_Ring__and__Field_Osemiring__0(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A,tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(347,a,343,b)].
% 2.15/2.41 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | -class_Ring__and__Field_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) | -class_Ring__and__Field_Omult__zero(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A,tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(347,a,344,d)].
% 2.15/2.41 Derived: -class_Ring__and__Field_Osemiring__0(tc_Code__Numeral_Ocode__numeral) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),c_Suc(A),tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(347,a,345,b)].
% 2.15/2.41 348 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.17/2.45 349 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 2.17/2.45 350 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 2.17/2.45 351 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 2.17/2.45 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(348,a,349,a)].
% 2.17/2.45 352 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.17/2.45 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(352,a,349,a)].
% 2.17/2.45 353 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.17/2.45 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(353,a,349,a)].
% 2.17/2.45 354 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 2.17/2.45 355 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_add__cancel__21_1) # label(axiom). [assumption].
% 2.17/2.45 356 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 2.17/2.45 357 -class_OrderedGroup_Oab__group__add(A) | c_Finite__Set_Osetsum(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C),D,B,A,A),E,B,A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Finite__Set_Osetsum(C,E,B,A)),c_Finite__Set_Osetsum(D,E,B,A)) # label(cls_setsum__subtractf_0) # label(axiom). [assumption].
% 2.17/2.45 358 -class_OrderedGroup_Oab__group__add(A) | c_List_Olistsum(c_List_Omap(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C),D,B,A,A),E,B,A),A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_List_Olistsum(c_List_Omap(C,E,B,A),A)),c_List_Olistsum(c_List_Omap(D,E,B,A),A)) # label(cls_listsum__subtractf_0) # label(axiom). [assumption].
% 2.17/2.45 359 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__iff__diff__eq__0_0) # label(axiom). [assumption].
% 2.17/2.45 360 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),D) | B = C # label(cls_eq__eqI_1) # label(axiom). [assumption].
% 2.17/2.45 361 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D) | C = D # label(cls_eq__eqI_0) # label(axiom). [assumption].
% 2.27/2.54 362 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_eq__iff__diff__eq__0_1) # label(axiom). [assumption].
% 2.27/2.54 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) = D. [resolve(354,a,356,a)].
% 2.27/2.54 Derived: c_Finite__Set_Osetsum(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_HOL_Ominus__class_Ominus(tc_Int_Oint)),B),C,A,tc_Int_Oint,tc_Int_Oint),D,A,tc_Int_Oint) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Finite__Set_Osetsum(B,D,A,tc_Int_Oint)),c_Finite__Set_Osetsum(C,D,A,tc_Int_Oint)). [resolve(354,a,357,a)].
% 2.27/2.54 Derived: c_List_Olistsum(c_List_Omap(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_HOL_Ominus__class_Ominus(tc_Int_Oint)),B),C,A,tc_Int_Oint,tc_Int_Oint),D,A,tc_Int_Oint),tc_Int_Oint) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_List_Olistsum(c_List_Omap(B,D,A,tc_Int_Oint),tc_Int_Oint)),c_List_Olistsum(c_List_Omap(C,D,A,tc_Int_Oint),tc_Int_Oint)). [resolve(354,a,358,a)].
% 2.27/2.54 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(354,a,359,a)].
% 2.27/2.54 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),C) | A = B. [resolve(354,a,360,a)].
% 2.27/2.54 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C) | B = C. [resolve(354,a,361,a)].
% 2.27/2.54 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(354,a,362,a)].
% 2.27/2.54 363 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.27/2.54 364 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 2.27/2.54 365 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.27/2.54 366 class_OrderedGroup_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.27/2.54 367 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.27/2.54 368 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D)) # label(cls_right__distrib__number__of_0) # label(axiom). [assumption].
% 2.27/2.54 369 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C)),E) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 2.27/2.54 370 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_Int_Onumber__class_Onumber__of(D,A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Int_Onumber__class_Onumber__of(D,A))) # label(cls_left__distrib__number__of_0) # label(axiom). [assumption].
% 2.34/2.62 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B)),D). [resolve(367,a,369,a)].
% 2.34/2.62 371 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.34/2.62 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B)),D). [resolve(371,a,369,a)].
% 2.34/2.62 372 class_Ring__and__Field_Osemiring(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.34/2.62 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C)),B)),D). [resolve(372,a,369,a)].
% 2.34/2.62 373 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 2.34/2.62 374 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom). [assumption].
% 2.34/2.62 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(373,a,374,a)].
% 2.34/2.62 375 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.34/2.62 376 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Olist_ONil(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_listsum_Osimps_I1_J_0) # label(axiom). [assumption].
% 2.34/2.62 377 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 2.34/2.62 378 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 2.34/2.62 379 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(B,A) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A) # label(cls_listsum_0) # label(axiom). [assumption].
% 2.34/2.62 380 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) # label(cls_foldl__absorb0_0) # label(axiom). [assumption].
% 2.34/2.62 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(375,a,376,a)].
% 2.34/2.62 Derived: c_List_Olistsum(A,tc_nat) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat). [resolve(375,a,379,a)].
% 2.34/2.62 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,tc_nat)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat). [resolve(375,a,380,a)].
% 2.34/2.62 381 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.34/2.62 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(381,a,376,a)].
% 2.34/2.67 Derived: c_List_Olistsum(A,tc_Int_Oint) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint). [resolve(381,a,379,a)].
% 2.34/2.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint,tc_Int_Oint)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,B,tc_Int_Oint,tc_Int_Oint). [resolve(381,a,380,a)].
% 2.34/2.67 382 class_OrderedGroup_Omonoid__add(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.34/2.67 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral) = c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(382,a,376,a)].
% 2.34/2.67 Derived: c_List_Olistsum(A,tc_Code__Numeral_Ocode__numeral) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral). [resolve(382,a,379,a)].
% 2.34/2.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),B,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A,B,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral). [resolve(382,a,380,a)].
% 2.34/2.67 383 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.34/2.67 384 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 2.34/2.67 385 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 2.34/2.67 386 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 2.34/2.67 387 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 2.34/2.67 388 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 2.34/2.67 389 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.34/2.67 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(383,a,384,a)].
% 2.49/2.76 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(383,a,385,a)].
% 2.49/2.76 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(383,a,389,a)].
% 2.49/2.76 390 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.49/2.76 391 class_Ring__and__Field_Opordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.49/2.76 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(391,a,384,a)].
% 2.49/2.76 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(391,a,385,a)].
% 2.49/2.76 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(391,a,389,a)].
% 2.49/2.76 392 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.49/2.76 393 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 2.49/2.76 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(392,a,393,a)].
% 2.49/2.76 394 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.49/2.76 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(394,a,393,a)].
% 2.49/2.76 395 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.49/2.76 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C) | B = C. [resolve(395,a,393,a)].
% 2.49/2.76 396 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.49/2.76 397 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 2.59/2.88 398 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 2.59/2.88 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(396,a,398,a)].
% 2.59/2.88 399 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.59/2.88 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B) | A = C. [resolve(399,a,398,a)].
% 2.59/2.88 400 class_OrderedGroup_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.59/2.88 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B) | A = C. [resolve(400,a,398,a)].
% 2.59/2.88 401 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 2.59/2.88 402 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__right__le__one__le_0) # label(axiom). [assumption].
% 2.59/2.88 403 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__left__le__one__le_0) # label(axiom). [assumption].
% 2.59/2.88 404 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_0) # label(axiom). [assumption].
% 2.59/2.88 405 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_1) # label(axiom). [assumption].
% 2.59/2.88 406 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 2.59/2.88 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(401,a,402,a)].
% 2.59/2.88 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(401,a,403,a)].
% 2.59/2.88 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | B = A. [resolve(401,a,406,a)].
% 2.59/2.88 407 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 2.59/2.88 408 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 2.59/2.88 409 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 2.59/2.88 410 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 2.59/2.88 411 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 2.59/2.88 412 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 2.59/2.88 413 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 2.59/2.88 414 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 2.59/2.88 415 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) | hBOOL(hAPP(c_lessequals(B,A),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 2.59/2.88 416 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 2.59/2.88 417 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 2.59/2.88 418 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 2.59/2.88 419 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 2.59/2.88 420 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 2.59/2.88 421 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 2.59/2.88 422 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | C = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 2.59/2.88 423 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 2.59/2.88 424 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 2.59/2.88 425 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 2.59/2.88 Derived: -class_Int_Onumber(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat))) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat))). [resolve(407,a,408,a)].
% 2.59/2.88 Derived: -class_Int_Onumber(tc_nat) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat))). [resolve(407,a,409,a)].
% 2.59/2.88 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(407,a,410,a)].
% 2.59/2.89 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(407,a,412,a)].
% 2.59/2.89 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(407,a,413,a)].
% 2.59/2.89 Derived: -hBOOL(hAPP(c_lessequals(A,tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)). [resolve(407,a,414,a)].
% 2.59/2.89 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(407,a,416,a)].
% 2.59/2.89 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)). [resolve(407,a,420,a)].
% 2.59/2.89 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)). [resolve(407,a,421,a)].
% 2.59/2.89 426 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 2.59/2.89 Derived: -class_Int_Onumber(tc_Int_Oint) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))). [resolve(426,a,408,a)].
% 2.59/2.89 Derived: -class_Int_Onumber(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))). [resolve(426,a,409,a)].
% 2.59/2.89 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(426,a,410,a)].
% 2.59/2.89 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(426,a,412,a)].
% 2.59/2.89 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(426,a,413,a)].
% 2.59/2.89 Derived: -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),A)). [resolve(426,a,414,a)].
% 2.59/2.89 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(426,a,416,a)].
% 2.59/2.89 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)). [resolve(426,a,420,a)].
% 2.59/2.89 427 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) # label(axiom). [assumption].
% 2.59/2.89 Derived: -class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(B,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(A,tc_Code__Numeral_Ocode__numeral))). [resolve(427,a,408,a)].
% 2.59/2.89 Derived: -class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(B,tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),c_Int_Onumber__class_Onumber__of(A,tc_Code__Numeral_Ocode__numeral))). [resolve(427,a,409,a)].
% 2.59/2.89 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),B)). [resolve(427,a,410,a)].
% 2.59/2.89 Derived: hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),B)) | hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),A)). [resolve(427,a,412,a)].
% 2.59/2.89 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),B)) | hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),A)). [resolve(427,a,413,a)].
% 2.65/2.93 Derived: -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),A)). [resolve(427,a,414,a)].
% 2.65/2.93 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),A)). [resolve(427,a,416,a)].
% 2.65/2.93 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),A)). [resolve(427,a,420,a)].
% 2.65/2.93 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),A)). [resolve(427,a,421,a)].
% 2.65/2.93 428 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.65/2.93 429 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 2.65/2.93 430 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 2.65/2.93 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(428,a,429,a)].
% 2.65/2.93 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(428,a,430,a)].
% 2.65/2.93 431 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.65/2.93 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(431,a,429,a)].
% 2.65/2.93 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(431,a,430,a)].
% 2.65/2.93 432 class_Ring__and__Field_Opordered__semiring(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.65/2.93 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(432,a,429,a)].
% 2.71/2.98 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(432,a,430,a)].
% 2.71/2.98 433 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.71/2.98 434 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 2.71/2.98 435 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 2.71/2.98 436 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 2.71/2.98 437 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 2.71/2.98 438 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 2.71/2.98 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(433,a,434,a)].
% 2.71/2.98 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(433,a,435,a)].
% 2.71/2.98 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(433,a,438,a)].
% 2.71/2.98 439 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.71/2.98 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(439,a,434,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(439,a,435,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(439,a,438,a)].
% 2.80/3.10 440 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(440,a,434,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(440,a,435,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(440,a,438,a)].
% 2.80/3.10 441 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 2.80/3.10 442 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 2.80/3.10 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(441,a,442,a)].
% 2.80/3.10 443 class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.80/3.10 444 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 2.80/3.10 445 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 2.80/3.10 446 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 2.80/3.10 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(443,a,446,a)].
% 2.80/3.10 447 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.80/3.10 448 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 2.80/3.10 449 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 2.80/3.10 450 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 2.80/3.10 451 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 2.80/3.10 452 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 2.80/3.10 453 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 2.80/3.10 454 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 2.80/3.10 455 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 2.80/3.10 456 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 2.80/3.10 457 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 2.80/3.10 458 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 2.80/3.10 459 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 2.80/3.10 460 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 2.80/3.10 461 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 2.80/3.10 462 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 2.80/3.10 463 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(447,a,448,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(447,a,449,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(447,a,450,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(447,a,451,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))). [resolve(447,a,452,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(447,a,453,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(447,a,454,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))). [resolve(447,a,455,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(447,a,456,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(447,a,457,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))). [resolve(447,a,458,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A))). [resolve(447,a,459,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(447,a,460,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(447,a,461,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(447,a,462,a)].
% 2.80/3.10 464 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(464,a,448,a)].
% 2.80/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(464,a,449,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(464,a,450,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))). [resolve(464,a,451,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C))). [resolve(464,a,452,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(464,a,453,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C))). [resolve(464,a,455,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(464,a,458,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A))). [resolve(464,a,459,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(464,a,460,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(464,a,461,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(464,a,462,a)].
% 2.80/3.11 465 class_Ring__and__Field_Oordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(465,a,448,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(465,a,449,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(465,a,450,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),A),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(465,a,451,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(465,a,452,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(465,a,453,a)].
% 2.80/3.11 Derived: hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),A),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(465,a,454,a)].
% 2.89/3.15 Derived: hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(465,a,455,a)].
% 2.89/3.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(465,a,456,a)].
% 2.89/3.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),C)). [resolve(465,a,457,a)].
% 2.89/3.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(465,a,458,a)].
% 2.89/3.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),A))). [resolve(465,a,459,a)].
% 2.89/3.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(465,a,460,a)].
% 2.89/3.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)). [resolve(465,a,461,a)].
% 2.89/3.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Code__Numeral_Ocode__numeral),c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)). [resolve(465,a,462,a)].
% 2.89/3.15 466 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.95/3.20 467 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 2.95/3.20 468 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 2.95/3.20 469 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.95/3.20 470 class_Ring__and__Field_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.95/3.20 471 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.95/3.20 472 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 2.95/3.20 473 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 2.95/3.20 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(471,a,472,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(471,a,473,a)].
% 2.95/3.20 474 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.95/3.20 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(474,a,472,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)). [resolve(474,a,473,a)].
% 2.95/3.20 475 class_Ring__and__Field_Omult__mono(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.95/3.20 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Code__Numeral_Ocode__numeral),C)). [resolve(475,a,472,a)].
% 2.95/3.20 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Code__Numeral_Ocode__numeral),C)). [resolve(475,a,473,a)].
% 3.03/3.28 476 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 3.03/3.28 477 -class_Ring__and__Field_Omult__mono1(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 3.03/3.28 478 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 3.03/3.28 479 class_Ring__and__Field_Omult__mono1(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 3.03/3.28 480 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 3.03/3.28 481 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E))) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 3.03/3.28 482 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_lessequals(C,A),B)) | -hBOOL(hAPP(c_lessequals(E,A),D)) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 3.03/3.28 483 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 3.03/3.28 484 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 3.03/3.28 485 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 3.03/3.28 486 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 3.03/3.28 487 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 3.03/3.28 488 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 3.03/3.28 489 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 3.03/3.28 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D))). [resolve(480,a,481,a)].
% 3.03/3.28 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)). [resolve(480,a,482,a)].
% 3.11/3.41 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(480,a,483,a)].
% 3.11/3.41 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(480,a,484,a)].
% 3.11/3.41 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(480,a,485,a)].
% 3.11/3.41 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),D)). [resolve(480,a,486,a)].
% 3.11/3.41 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(480,a,487,a)].
% 3.11/3.41 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(480,a,488,a)].
% 3.11/3.41 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(480,a,489,a)].
% 3.11/3.41 490 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.11/3.41 491 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 3.11/3.41 492 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.11/3.41 493 class_OrderedGroup_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.11/3.41 494 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.11/3.41 495 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 3.11/3.41 496 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.11/3.41 497 class_Ring__and__Field_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.11/3.41 498 class_Divides_Oring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 3.11/3.41 499 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),F),D),C,A) # label(cls_mod__diff__cong_0) # label(axiom). [assumption].
% 3.11/3.41 500 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__diff__left__eq_0) # label(axiom). [assumption].
% 3.24/3.49 501 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__diff__right__eq_0) # label(axiom). [assumption].
% 3.24/3.49 502 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__diff__eq_0) # label(axiom). [assumption].
% 3.24/3.49 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),E),C),B,tc_Int_Oint). [resolve(498,a,499,a)].
% 3.24/3.49 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B),C,tc_Int_Oint). [resolve(498,a,500,a)].
% 3.24/3.49 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(498,a,501,a)].
% 3.24/3.49 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(498,a,502,a)].
% 3.24/3.49 503 class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 3.24/3.49 504 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__diff_0) # label(axiom). [assumption].
% 3.24/3.49 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(503,a,504,a)].
% 3.24/3.49 505 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 3.24/3.49 506 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),C) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 3.24/3.49 507 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),C) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 3.24/3.49 508 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 3.24/3.49 509 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 3.24/3.49 510 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 3.24/3.49 511 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 3.24/3.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),B) = A. [resolve(505,a,506,a)].
% 3.53/3.79 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),B) = A. [resolve(505,a,507,a)].
% 3.53/3.79 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(505,a,509,a)].
% 3.53/3.79 512 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.53/3.79 513 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 3.53/3.79 514 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.53/3.79 515 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.53/3.79 516 class_Ring__and__Field_Oring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 3.53/3.79 517 -class_Ring__and__Field_Oring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) # label(cls_of__nat__diff_0) # label(axiom). [assumption].
% 3.53/3.79 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(516,a,517,a)].
% 3.53/3.79 518 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 3.53/3.79 519 -class_OrderedGroup_Osemigroup__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A)) # label(cls_foldl__assoc_0) # label(axiom). [assumption].
% 3.53/3.79 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)). [resolve(518,a,519,a)].
% 3.53/3.79 520 class_OrderedGroup_Osemigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 3.53/3.79 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B,C,tc_Int_Oint,tc_Int_Oint)). [resolve(520,a,519,a)].
% 3.53/3.79 521 class_OrderedGroup_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) # label(clsarity_Code____Numeral__Ocode____numeral__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 3.53/3.79 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),C,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B,C,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)). [resolve(521,a,519,a)].
% 3.53/3.79
% 3.53/3.79 ============================== end predicate elimination =============
% 3.53/3.79
% 3.53/3.79 Auto_denials: (non-Horn, no changes).
% 3.53/3.79
% 3.53/3.79 Term ordering decisions:
% 3.53/3.79 Function symbol KB weights: tc_nat=1. tc_Int_Oint=1. tc_Code__Numeral_Ocode__numeral=1. tc_Lambda_OdB=1. c_Lambda_OdB_OApp=1. c_Lambda_OdB_OVar=1. c_Lambda_Osubst=1. c_Lambda_Olift=1. tc_bool=1. c_InductTermi_OIT=1. v_ja=1. v_n=1. v_ia=1. v_rs=1. t_a=1. c_and=1. tc_Type_Otype=1. v_x=1. hAPP=1. c_HOL_Oord__class_Oless=1. c_lessequals=1. c_Nat_Osemiring__1__class_Oof__nat=1. tc_fun=1. c_Int_Onumber__class_Onumber__of=1. c_List_Olistsum=1. c_Nat_Osize__class_Osize=1. c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__iff__1__1=1. c_ATP__Linkup_Osko__Nat__XSuc__lessE__1__1=1. c_ATP__Linkup_Osko__Nat__XlessE__1__1=1. c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1=1. c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__1__1=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Oplus__class_Oplus=1. c_Suc=1. c_HOL_Ominus__class_Ominus=1. c_HOL_Oone__class_Oone=1. c_Lambda_OdB_OAbs=1. c_List_Olist_ONil=1. c_Code__Numeral_Onat__of=1. c_Code__Numeral_Oof__nat=1. c_Lambda_OdB_OdB__size=1. c_fequal=1. c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1=1. c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1=1. c_All=1. v_sko__List__Xlexn__Xinduct__1=1. c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1=1. c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1=1. c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1=1. c_Divides_Odiv__class_Omod=1. c_Power_Opower__class_Opower=1. c_Divides_Odiv__class_Odiv=1. c_COMBB=1. c_Lambda_Oliftn=1. c_Lambda_Osubstn=1. c_List_Olistsp=1. c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1=1. c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1=1. c_List_Ofilter=1. c_List_Omap=1. c_Type_Oshift=1. c_Finite__Set_Osetsum=1. c_List_Osko__List__Xfoldl__apply__inv__1__1=1. c_List_Ofoldl=1. c_COMBC=1. c_COMBS=1.
% 46.21/46.47
% 46.21/46.47 ============================== end of process initial clauses ========
% 46.21/46.47
% 46.21/46.47 ============================== CLAUSES FOR SEARCH ====================
% 46.21/46.47
% 46.21/46.47 ============================== end of clauses for search =============
% 46.21/46.47
% 46.21/46.47 ============================== SEARCH ================================
% 46.21/46.47
% 46.21/46.47 % Starting search at 2.36 seconds.
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=72.000, iters=3781
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=67.000, iters=3684
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=52.000, iters=3426
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=51.000, iters=3367
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=48.000, iters=3335
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=46.000, iters=3346
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=45.000, iters=3532
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=42.000, iters=3363
% 46.21/46.47
% 46.21/46.47 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 54 (0.00 of 2.89 sec).
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=40.000, iters=3350
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=39.000, iters=3361
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=38.000, iters=3384
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=36.000, iters=3378
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=35.000, iters=3345
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=34.000, iters=3366
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=33.000, iters=3344
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=32.000, iters=3347
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=31.000, iters=3382
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=30.000, iters=3362
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=29.000, iters=3514
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=28.000, iters=3356
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=27.000, iters=3336
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=26.000, iters=3412
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=25.000, iters=3334
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=24.000, iters=3406
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=23.000, iters=3334
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=22.000, iters=3367
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=21.000, iters=3371
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=20.000, iters=3452
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=19.000, iters=3333
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=3916, wt=132.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=4862, wt=131.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=3923, wt=112.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=3922, wt=107.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=3921, wt=105.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=3565, wt=102.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=4297, wt=97.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=3839, wt=91.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=3920, wt=89.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=3913, wt=87.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=13661, wt=16.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=13721, wt=14.000
% 46.21/46.47
% 46.21/46.47 Low Water (displace): id=17270, wt=13.000
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=18.000, iters=3340
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=17.000, iters=3334
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=16.000, iters=3339
% 46.21/46.47
% 46.21/46.47 Low Water (keep): wt=15.000, iters=3333
% 278.44/278.76
% 278.44/278.76 ============================== STATISTICS ============================
% 278.44/278.76
% 278.44/278.76 Given=20599. Generated=15092420. Kept=378516. proofs=0.
% 278.44/278.76 Usable=19894. Sos=9999. Demods=2129. Limbo=149, Disabled=350409. Hints=0.
% 278.44/278.76 Kept_by_rule=0, Deleted_by_rule=165.
% 278.44/278.76 Forward_subsumed=2626258. Back_subsumed=96.
% 278.44/278.76 Sos_limit_deleted=12087481. Sos_displaced=346300. Sos_removed=0.
% 278.44/278.76 New_demodulators=5776 (0 lex), Back_demodulated=2055. Back_unit_deleted=22.
% 278.44/278.76 Demod_attempts=362239273. Demod_rewrites=5211924.
% 278.44/278.76 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 278.44/278.76 Nonunit_fsub_feature_tests=1743080. Nonunit_bsub_feature_tests=22493.
% 278.44/278.76 Megabytes=419.43.
% 278.44/278.76 User_CPU=269.07, System_CPU=8.25, Wall_clock=278.
% 278.44/278.76
% 278.44/278.76 Megs malloced by palloc(): 400.
% 278.44/278.76 type (bytes each) gets frees in use bytes
% 278.44/278.76 chunk ( 104) 38986 38986 0 0.0 K
% 278.44/278.76 string_buf ( 8) 33652 33652 0 0.0 K
% 278.44/278.76 token ( 20) 73635 73635 0 0.0 K
% 278.44/278.76 pterm ( 16) 50927 50927 0 0.0 K
% 278.44/278.76 hashtab ( 8) 0 0 0 0.0 K
% 278.44/278.76 hashnode ( 8) 0 0 0 0.0 K
% 278.44/278.76 term ( 20) 518089642 509713713 8375929 163592.4 K
% 278.44/278.76 term arg arrays: 42938.2 K
% 278.44/278.76 attribute ( 12) 3004 108 2896 33.9 K
% 278.44/278.76 ilist ( 8) 1376842169 1374461803 2380366 18596.6 K
% 278.44/278.76 plist ( 8) 11595780 11178262 417518 3261.9 K
% 278.44/278.76 i2list ( 12) 92739342 92739342 0 0.0 K
% 278.44/278.76 just ( 12) 20243539 19796971 446568 5233.2 K
% 278.44/278.76 parajust ( 16) 13213242 12866567 346675 5416.8 K
% 278.44/278.76 instancejust ( 8) 0 0 0 0.0 K
% 278.44/278.76 ivyjust ( 24) 0 0 0 0.0 K
% 278.44/278.76 formula ( 28) 6312 6312 0 0.0 K
% 278.44/278.76 formula arg arrays: 0.0 K
% 278.44/278.76 topform ( 52) 15094551 14713904 380647 19329.7 K
% 278.44/278.76 clist_pos ( 20) 1136216 753636 382580 7472.3 K
% 278.44/278.76 clist ( 16) 8 1 7 0.1 K
% 278.44/278.76 context ( 808) 103533804 103533800 4 3.2 K
% 278.44/278.76 trail ( 12) 35779999 35779997 2 0.0 K
% 278.44/278.76 ac_match_pos (70044) 0 0 0 0.0 K
% 278.44/278.76 ac_match_free_vars_pos (20020)
% 278.44/278.76 0 0 0 0.0 K
% 278.44/278.76 btm_state ( 60) 0 0 0 0.0 K
% 278.44/278.76 btu_state ( 60) 0 0 0 0.0 K
% 278.44/278.76 ac_position (285432) 0 0 0 0.0 K
% 278.44/278.76 fpa_trie ( 20) 6432317 5299741 1132576 22120.6 K
% 278.44/278.76 fpa_state ( 28) 6370951 6370945 6 0.2 K
% 278.44/278.76 fpa_index ( 12) 10 0 10 0.1 K
% 278.44/278.76 fpa_chunk ( 20) 6975582 6849988 125594 2453.0 K
% 278.44/278.76 fpa_list ( 16) 5379119 0 5379119 84048.7 K
% 278.44/278.76 fpa_list chunks: 6420.0 K
% 278.44/278.76 discrim ( 12) 5662026 5528841 133185 1560.8 K
% 278.44/278.76 discrim_pos ( 16) 6240698 6240698 0 0.0 K
% 278.44/278.76 flat2 ( 32) 356711348 356711348 0 0.0 K
% 278.44/278.76 flat ( 48) 0 0 0 0.0 K
% 278.44/278.76 flatterm ( 32) 483301507 483301507 0 0.0 K
% 278.44/278.76 mindex ( 28) 13 0 13 0.4 K
% 278.44/278.76 mindex_pos ( 56) 72782471 72782470 1 0.1 K
% 278.44/278.76 lindex ( 12) 5 0 5 0.1 K
% 278.44/278.76 clash ( 40) 0 0 0 0.0 K
% 278.44/278.76 di_tree ( 12) 5344878 3653207 1691671 19824.3 K
% 278.44/278.76 avl_node ( 20) 755150 735152 19998 390.6 K
% 278.44/278.76
% 278.44/278.76 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 278.44/278.76 List 1, length 1427, 5.6 K
% 278.44/278.76 List 2, length 297, 2.3 K
% 278.44/278.76 List 3, length 66315, 777.1 K
% 278.44/278.76 List 8, length 35, 1.1 K
% 278.44/278.76 List 9, length 10, 0.4 K
% 278.44/278.76 List 10, length 1, 0.0 K
% 278.44/278.76 List 14, length 1, 0.1 K
% 278.44/278.76 List 16, length 1330, 83.1 K
% 278.44/278.76 List 26, length 131, 13.3 K
% 278.44/278.76 List 32, length 405, 50.6 K
% 278.44/278.76 List 64, length 72, 18.0 K
% 278.44/278.76 List 128, length 9, 4.5 K
% 278.44/278.76 List 256, length 202, 202.0 K
% 278.44/278.76
% 278.44/278.76 ============================== SELECTOR REPORT =======================
% 278.44/278.76 Sos_deleted=12087481, Sos_displaced=346300, Sos_size=9999
% 278.44/278.76 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 278.44/278.76 I 2147483647 high age 0 1165
% 278.44/278.76 H 1 high weight 0 0
% 278.44/278.76 A 1 low age 9999 2160
% 278.44/278.76 F 4 low weight 1665 8638
% 278.44/278.76 T 4 low weight 8334 8636
% 278.44/278.76 ============================== end of selector report ================
% 278.44/278.76
% 278.44/278.76 ============================== end of statistics =====================
% 278.44/278.76
% 278.44/278.76 Exiting with failure.
% 278.44/278.76
% 278.44/278.76 Process 29972 exit (max_megs) Sat Jul 2 13:21:23 2022
% 278.44/278.76 Prover9 interrupted
%------------------------------------------------------------------------------