TSTP Solution File: SWV681-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV681-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:14:24 EDT 2022
% Result : Timeout 300.02s 300.29s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV681-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 15 09:28:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.39/1.65 ============================== Prover9 ===============================
% 1.39/1.65 Prover9 (32) version 2009-11A, November 2009.
% 1.39/1.65 Process 30893 was started by sandbox2 on n022.cluster.edu,
% 1.39/1.65 Wed Jun 15 09:28:04 2022
% 1.39/1.65 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30739_n022.cluster.edu".
% 1.39/1.65 ============================== end of head ===========================
% 1.39/1.65
% 1.39/1.65 ============================== INPUT =================================
% 1.39/1.65
% 1.39/1.65 % Reading from file /tmp/Prover9_30739_n022.cluster.edu
% 1.39/1.65
% 1.39/1.65 set(prolog_style_variables).
% 1.39/1.65 set(auto2).
% 1.39/1.65 % set(auto2) -> set(auto).
% 1.39/1.65 % set(auto) -> set(auto_inference).
% 1.39/1.65 % set(auto) -> set(auto_setup).
% 1.39/1.65 % set(auto_setup) -> set(predicate_elim).
% 1.39/1.65 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.39/1.65 % set(auto) -> set(auto_limits).
% 1.39/1.65 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.39/1.65 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.39/1.65 % set(auto) -> set(auto_denials).
% 1.39/1.65 % set(auto) -> set(auto_process).
% 1.39/1.65 % set(auto2) -> assign(new_constants, 1).
% 1.39/1.65 % set(auto2) -> assign(fold_denial_max, 3).
% 1.39/1.65 % set(auto2) -> assign(max_weight, "200.000").
% 1.39/1.65 % set(auto2) -> assign(max_hours, 1).
% 1.39/1.65 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.39/1.65 % set(auto2) -> assign(max_seconds, 0).
% 1.39/1.65 % set(auto2) -> assign(max_minutes, 5).
% 1.39/1.65 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.39/1.65 % set(auto2) -> set(sort_initial_sos).
% 1.39/1.65 % set(auto2) -> assign(sos_limit, -1).
% 1.39/1.65 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.39/1.65 % set(auto2) -> assign(max_megs, 400).
% 1.39/1.65 % set(auto2) -> assign(stats, some).
% 1.39/1.65 % set(auto2) -> clear(echo_input).
% 1.39/1.65 % set(auto2) -> set(quiet).
% 1.39/1.65 % set(auto2) -> clear(print_initial_clauses).
% 1.39/1.65 % set(auto2) -> clear(print_given).
% 1.39/1.65 assign(lrs_ticks,-1).
% 1.39/1.65 assign(sos_limit,10000).
% 1.39/1.65 assign(order,kbo).
% 1.39/1.65 set(lex_order_vars).
% 1.39/1.65 clear(print_given).
% 1.39/1.65
% 1.39/1.65 % formulas(sos). % not echoed (1002 formulas)
% 1.39/1.65
% 1.39/1.65 ============================== end of input ==========================
% 1.39/1.65
% 1.39/1.65 % From the command line: assign(max_seconds, 300).
% 1.39/1.65
% 1.39/1.65 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.39/1.65
% 1.39/1.65 % Formulas that are not ordinary clauses:
% 1.39/1.65
% 1.39/1.65 ============================== end of process non-clausal formulas ===
% 1.39/1.65
% 1.39/1.65 ============================== PROCESS INITIAL CLAUSES ===============
% 1.39/1.65
% 1.39/1.65 ============================== PREDICATE ELIMINATION =================
% 1.39/1.65 1 -class_RealVector_Ometric__space(A) | -class_RealVector_Ometric__space(B) | c_Lim_OisCont(C,D,A,B) | -c_Lim_OisUCont(C,A,B) # label(cls_isUCont__isCont_0) # label(axiom). [assumption].
% 1.39/1.65 2 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OisUCont(C,A,B) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_OisUCont_0) # label(axiom). [assumption].
% 1.39/1.65 3 -class_RealVector_Oreal__normed__vector(A) | c_Lim_OisUCont(c_RealVector_OscaleR__class_OscaleR(B,A),A,A) # label(cls_scaleR__right_OisUCont_0) # label(axiom). [assumption].
% 1.39/1.65 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(A) | -class_RealVector_Ometric__space(A) | c_Lim_OisCont(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A). [resolve(3,b,1,d)].
% 1.39/1.65 4 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OisUCont(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A) # label(cls_mult__right_OisUCont_0) # label(axiom). [assumption].
% 1.39/1.65 5 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.39/1.65 6 -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].
% 1.39/1.65 7 -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].
% 1.39/1.65 8 -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].
% 1.39/1.65 9 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 1.39/1.65 10 -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].
% 1.39/1.65 11 -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].
% 1.39/1.65 12 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 1.39/1.65 13 -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].
% 1.39/1.65 14 -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].
% 1.39/1.65 15 -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].
% 1.39/1.65 16 -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].
% 1.39/1.65 17 -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].
% 1.39/1.65 18 -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].
% 1.39/1.65 19 -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].
% 1.39/1.65 20 -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),c_HOL_Ouminus__class_Ouminus(B,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) # label(cls_square__eq__iff_1) # label(axiom). [assumption].
% 1.39/1.65 21 -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C) | B = c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_square__eq__iff_0) # label(axiom). [assumption].
% 1.39/1.65 22 -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].
% 1.39/1.65 23 -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].
% 1.39/1.65 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(5,a,6,a)].
% 1.39/1.65 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),B),tc_RealDef_Oreal). [resolve(5,a,7,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(5,a,8,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_HOL_Ominus__class_Ominus(A,A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(5,a,9,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(5,a,10,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B = C. [resolve(5,a,11,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(5,a,12,a)].
% 1.39/1.65 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal). [resolve(5,a,13,a)].
% 1.39/1.65 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal). [resolve(5,a,14,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(5,a,15,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | B = D | A = C. [resolve(5,a,16,a)].
% 1.39/1.65 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal). [resolve(5,a,18,a)].
% 1.39/1.65 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_RealDef_Oreal). [resolve(5,a,19,a)].
% 1.39/1.65 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A). [resolve(5,a,20,a)].
% 1.39/1.65 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B) | A = c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal) | A = B. [resolve(5,a,21,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)). [resolve(5,a,22,a)].
% 1.39/1.65 24 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.39/1.65 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),tc_Complex_Ocomplex). [resolve(24,a,6,a)].
% 1.39/1.65 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),B),tc_Complex_Ocomplex). [resolve(24,a,7,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(24,a,8,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(24,a,9,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(24,a,10,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(24,a,11,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(24,a,12,a)].
% 1.39/1.65 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex). [resolve(24,a,13,a)].
% 1.39/1.65 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex). [resolve(24,a,14,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(24,a,15,a)].
% 1.39/1.65 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) | B = D | A = C. [resolve(24,a,16,a)].
% 1.43/1.68 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(24,a,18,a)].
% 1.43/1.68 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Complex_Ocomplex). [resolve(24,a,19,a)].
% 1.43/1.68 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A). [resolve(24,a,20,a)].
% 1.43/1.68 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),B) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex) | A = B. [resolve(24,a,21,a)].
% 1.43/1.68 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)). [resolve(24,a,22,a)].
% 1.43/1.68 25 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.43/1.68 26 -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].
% 1.43/1.68 27 -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].
% 1.43/1.68 28 -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].
% 1.43/1.68 29 -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].
% 1.43/1.68 30 -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].
% 1.43/1.68 31 -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].
% 1.43/1.68 32 -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].
% 1.43/1.68 33 -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].
% 1.43/1.68 34 -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].
% 1.43/1.68 35 -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].
% 1.43/1.68 36 -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].
% 1.43/1.68 37 -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].
% 1.43/1.68 38 -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].
% 1.43/1.68 39 -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].
% 1.43/1.68 40 -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].
% 1.43/1.68 41 -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].
% 1.43/1.68 42 -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].
% 1.43/1.68 43 -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].
% 1.43/1.68 44 -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].
% 1.43/1.68 45 -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].
% 1.43/1.68 46 -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].
% 1.43/1.68 47 -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].
% 1.43/1.68 48 -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].
% 1.43/1.68 49 -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].
% 1.43/1.68 50 -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].
% 1.43/1.68 51 -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].
% 1.43/1.68 52 -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].
% 1.43/1.68 53 -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].
% 1.43/1.68 54 -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].
% 1.43/1.68 55 -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].
% 1.43/1.68 56 -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].
% 1.43/1.68 57 -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].
% 1.43/1.68 58 -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].
% 1.43/1.68 59 -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].
% 1.43/1.68 60 -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].
% 1.43/1.68 61 -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].
% 1.43/1.68 62 -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].
% 1.43/1.68 63 -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].
% 1.43/1.68 64 -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].
% 1.43/1.68 65 -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].
% 1.43/1.68 66 -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].
% 1.43/1.68 67 -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].
% 1.43/1.68 68 -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].
% 1.43/1.68 69 -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].
% 1.43/1.68 70 -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].
% 1.43/1.68 71 -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].
% 1.43/1.68 72 -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].
% 1.43/1.68 73 -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].
% 1.43/1.68 74 -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].
% 1.43/1.68 75 -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].
% 1.43/1.68 76 -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].
% 1.43/1.68 77 -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].
% 1.43/1.68 78 -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].
% 1.43/1.68 79 -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].
% 1.43/1.69 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(25,a,26,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_nat). [resolve(25,a,27,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(25,a,28,a)].
% 1.43/1.69 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(25,a,30,a)].
% 1.43/1.69 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(25,a,31,a)].
% 1.43/1.69 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(25,a,32,a)].
% 1.43/1.69 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(25,a,33,a)].
% 1.43/1.69 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(25,a,34,a)].
% 1.43/1.69 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(25,a,36,a)].
% 1.43/1.69 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(25,a,38,a)].
% 1.43/1.69 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(25,a,39,a)].
% 1.43/1.69 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(25,a,40,a)].
% 1.43/1.69 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(25,a,41,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(25,a,42,a)].
% 1.43/1.69 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(25,a,44,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(25,a,45,a)].
% 1.43/1.69 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(25,a,46,a)].
% 1.43/1.69 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(25,a,47,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(25,a,48,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(25,a,49,a)].
% 1.43/1.69 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(25,a,51,a)].
% 1.43/1.69 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(25,a,52,a)].
% 1.43/1.69 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(25,a,53,a)].
% 1.43/1.69 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(25,a,55,a)].
% 1.43/1.69 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(25,a,56,a)].
% 1.43/1.69 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(25,a,57,a)].
% 1.43/1.69 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(25,a,58,a)].
% 1.43/1.69 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(25,a,59,a)].
% 1.43/1.69 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(25,a,60,a)].
% 1.43/1.69 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(25,a,61,a)].
% 1.43/1.69 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(25,a,62,a)].
% 1.43/1.69 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(25,a,63,a)].
% 1.43/1.69 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(25,a,64,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(25,a,65,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(25,a,66,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A),tc_nat). [resolve(25,a,68,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat). [resolve(25,a,69,a)].
% 1.43/1.69 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(25,a,70,a)].
% 1.43/1.69 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(25,a,71,a)].
% 1.43/1.69 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(25,a,73,a)].
% 1.43/1.69 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(25,a,74,a)].
% 1.43/1.69 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(25,a,77,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(25,a,78,a)].
% 1.43/1.69 80 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal). [resolve(80,a,26,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_RealDef_Oreal). [resolve(80,a,27,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(80,a,28,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(80,a,30,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),D)). [resolve(80,a,31,a)].
% 1.43/1.69 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(80,a,32,a)].
% 1.43/1.69 Derived: c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_RealDef_Oreal). [resolve(80,a,33,a)].
% 1.43/1.69 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal)). [resolve(80,a,34,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C). [resolve(80,a,36,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),B). [resolve(80,a,38,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)). [resolve(80,a,39,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)). [resolve(80,a,40,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),c_Power_Opower__class_Opower(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal). [resolve(80,a,41,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),A). [resolve(80,a,42,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal))),A). [resolve(80,a,44,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(80,a,45,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal))),B). [resolve(80,a,46,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),c_HOL_Oone__class_Oone(tc_RealDef_Oreal))),A). [resolve(80,a,47,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = A. [resolve(80,a,48,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(80,a,49,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal). [resolve(80,a,51,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(80,a,52,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(80,a,53,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal)) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_RealDef_Oreal). [resolve(80,a,55,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal)),A) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_RealDef_Oreal). [resolve(80,a,56,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),B). [resolve(80,a,57,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(80,a,58,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(80,a,59,a)].
% 1.43/1.69 Derived: c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,C,tc_RealDef_Oreal)),c_Power_Opower__class_Opower(B,C,tc_RealDef_Oreal)). [resolve(80,a,60,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),B,tc_RealDef_Oreal). [resolve(80,a,61,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B,tc_RealDef_Oreal). [resolve(80,a,62,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(80,a,63,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal). [resolve(80,a,64,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),A) = A. [resolve(80,a,65,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(80,a,66,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),tc_RealDef_Oreal). [resolve(80,a,68,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal). [resolve(80,a,69,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C). [resolve(80,a,70,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(80,a,71,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(80,a,73,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),B). [resolve(80,a,74,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)). [resolve(80,a,77,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A). [resolve(80,a,78,a)].
% 1.43/1.69 81 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(81,a,26,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_Complex_Ocomplex). [resolve(81,a,27,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(81,a,28,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex). [resolve(81,a,30,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),D)). [resolve(81,a,31,a)].
% 1.43/1.69 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(81,a,32,a)].
% 1.43/1.69 Derived: c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_Complex_Ocomplex). [resolve(81,a,33,a)].
% 1.43/1.69 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex)). [resolve(81,a,34,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C). [resolve(81,a,36,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(81,a,38,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)). [resolve(81,a,39,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)). [resolve(81,a,40,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(81,a,41,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),A). [resolve(81,a,42,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(81,a,44,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(81,a,45,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),B). [resolve(81,a,46,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(81,a,47,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(81,a,48,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(81,a,49,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(81,a,51,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(81,a,52,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(81,a,53,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex)) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_Complex_Ocomplex). [resolve(81,a,55,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex)),A) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_Complex_Ocomplex). [resolve(81,a,56,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(81,a,57,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(81,a,58,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(81,a,59,a)].
% 1.43/1.69 Derived: c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex)),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex)). [resolve(81,a,60,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),A),B,tc_Complex_Ocomplex). [resolve(81,a,61,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),B,tc_Complex_Ocomplex). [resolve(81,a,62,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex). [resolve(81,a,63,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(81,a,64,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(81,a,65,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(81,a,66,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),tc_Complex_Ocomplex). [resolve(81,a,68,a)].
% 1.43/1.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex). [resolve(81,a,69,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C). [resolve(81,a,70,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(81,a,71,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(81,a,73,a)].
% 1.43/1.69 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),B). [resolve(81,a,74,a)].
% 1.43/1.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)). [resolve(81,a,77,a)].
% 1.43/1.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A). [resolve(81,a,78,a)].
% 1.43/1.73 82 class_RealVector_Oreal__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__vector) # label(axiom). [assumption].
% 1.43/1.73 83 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ominus__class_Ominus(C,D,A)) = c_HOL_Ominus__class_Ominus(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D),A) # label(cls_scaleR__right_Odiff_0) # label(axiom). [assumption].
% 1.43/1.73 84 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A) # label(cls_scaleR__minus__right_0) # label(axiom). [assumption].
% 1.43/1.73 85 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR__eq__0__iff_2) # label(axiom). [assumption].
% 1.43/1.73 86 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__left__commute_0) # label(axiom). [assumption].
% 1.43/1.73 87 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__right_Oadd_0) # label(axiom). [assumption].
% 1.43/1.73 88 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),c_HOL_Ozero__class_Ozero(A)) # label(cls_scaleR__cancel__right_1) # label(axiom). [assumption].
% 1.43/1.73 89 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C) != hAPP(c_RealVector_OscaleR__class_OscaleR(D,A),C) | C = c_HOL_Ozero__class_Ozero(A) | B = D # label(cls_scaleR__cancel__right_0) # label(axiom). [assumption].
% 1.43/1.73 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal). [resolve(82,a,83,a)].
% 1.43/1.73 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal). [resolve(82,a,84,a)].
% 1.43/1.73 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(82,a,85,a)].
% 1.43/1.73 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)). [resolve(82,a,86,a)].
% 1.43/1.73 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)). [resolve(82,a,87,a)].
% 1.43/1.73 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(82,a,88,a)].
% 1.51/1.76 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B) != hAPP(c_RealVector_OscaleR__class_OscaleR(C,tc_RealDef_Oreal),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = C. [resolve(82,a,89,a)].
% 1.51/1.76 90 class_RealVector_Oreal__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__vector) # label(axiom). [assumption].
% 1.51/1.76 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex). [resolve(90,a,83,a)].
% 1.51/1.76 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex). [resolve(90,a,84,a)].
% 1.51/1.76 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(90,a,85,a)].
% 1.51/1.76 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_Complex_Ocomplex),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_Complex_Ocomplex),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),C)). [resolve(90,a,86,a)].
% 1.51/1.76 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B)),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),C)). [resolve(90,a,87,a)].
% 1.51/1.76 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(90,a,88,a)].
% 1.51/1.76 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B) != hAPP(c_RealVector_OscaleR__class_OscaleR(C,tc_Complex_Ocomplex),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = C. [resolve(90,a,89,a)].
% 1.51/1.76 91 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.51/1.76 92 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10) # label(cls_pordered__ring_Oring__simps_I41_J_0) # label(axiom). [assumption].
% 1.51/1.76 93 -class_OrderedGroup_Oab__semigroup__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)) | -c_Ring__and__Field_Opordered__ring(E,F,V6,V7,V8,V9,V10,V11) # label(cls_pordered__ring_Oring__simps_I40_J_0) # label(axiom). [assumption].
% 1.51/1.76 94 -class_OrderedGroup_Oab__semigroup__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)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I34_J_0) # label(axiom). [assumption].
% 1.51/1.76 95 -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].
% 1.51/1.76 96 -class_OrderedGroup_Oab__semigroup__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)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I38_J_0) # label(axiom). [assumption].
% 1.53/1.80 97 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11) # label(cls_field_Ofield__eq__simps_I39_J_0) # label(axiom). [assumption].
% 1.53/1.80 98 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8) # label(cls_ring_Oring__simps_I35_J_0) # label(axiom). [assumption].
% 1.53/1.80 99 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.53/1.80 100 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.53/1.80 101 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 1.53/1.80 102 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 1.53/1.80 103 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_abs__less__iff_2) # label(axiom). [assumption].
% 1.53/1.80 104 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_abs__one_0) # label(axiom). [assumption].
% 1.53/1.80 105 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__less__iff_1) # label(axiom). [assumption].
% 1.53/1.80 106 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__less__0__iff_0) # label(axiom). [assumption].
% 1.53/1.80 107 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__less__0__iff_1) # label(axiom). [assumption].
% 1.53/1.80 108 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(C,A),E,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),D,A) # label(cls_abs__mult__less_0) # label(axiom). [assumption].
% 1.53/1.80 109 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq_1) # label(axiom). [assumption].
% 1.53/1.80 110 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_power__abs_0) # label(axiom). [assumption].
% 1.53/1.80 111 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(D,B,A),A),C,A) # label(cls_abs__diff__less__iff_0) # label(axiom). [assumption].
% 1.53/1.80 112 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__less__iff_0) # label(axiom). [assumption].
% 1.53/1.80 113 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(B,A),C,A),A) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(B,C,A),A) # label(cls_abs__power__minus_0) # label(axiom). [assumption].
% 1.53/1.80 114 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__dvd__iff_0) # label(axiom). [assumption].
% 1.53/1.80 115 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_abs__dvd__iff_1) # label(axiom). [assumption].
% 1.53/1.80 116 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_dvd__abs__iff_0) # label(axiom). [assumption].
% 1.53/1.80 117 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oabs__class_Oabs(C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__abs__iff_1) # label(axiom). [assumption].
% 1.53/1.80 118 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),D,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(C,D,A),B,A) # label(cls_abs__diff__less__iff_2) # label(axiom). [assumption].
% 1.53/1.80 119 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(B,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) # label(cls_abs__mult__self_0) # label(axiom). [assumption].
% 1.53/1.80 120 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),D,A) # label(cls_abs__diff__less__iff_1) # label(axiom). [assumption].
% 1.53/1.80 121 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__minus__self__iff_0) # label(axiom). [assumption].
% 1.53/1.80 122 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__minus__self__iff_1) # label(axiom). [assumption].
% 1.53/1.80 123 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,A) != c_HOL_Oabs__class_Oabs(C,A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__if__abs__eq_0) # label(axiom). [assumption].
% 1.53/1.80 124 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)) # label(cls_abs__mult_0) # label(axiom). [assumption].
% 1.53/1.80 125 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(B,A),A) = c_Nat_Osemiring__1__class_Oof__nat(B,A) # label(cls_abs__of__nat_0) # label(axiom). [assumption].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | B = A. [resolve(101,a,102,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(101,a,103,a)].
% 1.53/1.80 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(101,a,104,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(101,a,105,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(101,a,106,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(101,a,107,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal)),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(101,a,108,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(101,a,109,a)].
% 1.53/1.80 Derived: c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(101,a,110,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(101,a,111,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(101,a,112,a)].
% 1.53/1.80 Derived: c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(101,a,113,a)].
% 1.53/1.80 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(101,a,114,a)].
% 1.53/1.80 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(101,a,115,a)].
% 1.53/1.80 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(101,a,116,a)].
% 1.53/1.80 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(101,a,117,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(101,a,118,a)].
% 1.53/1.80 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal)),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A). [resolve(101,a,119,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(101,a,120,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(101,a,121,a)].
% 1.53/1.80 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(101,a,122,a)].
% 1.53/1.80 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) != c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal) | c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(101,a,123,a)].
% 1.59/1.87 Derived: c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal)),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal)). [resolve(101,a,124,a)].
% 1.59/1.87 Derived: c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal). [resolve(101,a,125,a)].
% 1.59/1.87 126 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.59/1.87 127 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.59/1.87 128 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.59/1.87 129 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.59/1.87 130 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.59/1.87 131 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_0) # label(axiom). [assumption].
% 1.59/1.87 132 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.59/1.87 133 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_1) # label(axiom). [assumption].
% 1.59/1.87 134 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.59/1.87 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(126,a,127,a)].
% 1.59/1.87 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | c_HOL_Oabs__class_Oabs(A,tc_nat) = c_HOL_Ouminus__class_Ouminus(A,tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(126,a,131,a)].
% 1.59/1.87 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(126,a,132,a)].
% 1.59/1.87 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | c_HOL_Oabs__class_Oabs(A,tc_nat) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(126,a,133,a)].
% 1.59/1.87 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(126,a,134,a)].
% 1.59/1.87 135 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 1.59/1.87 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(135,a,131,a)].
% 1.59/1.87 Derived: -c_HOL_Oord__class_Oless(A,A,tc_RealDef_Oreal). [resolve(135,a,132,a)].
% 1.59/1.87 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(135,a,133,a)].
% 1.59/1.87 Derived: -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(135,a,134,a)].
% 1.59/1.87 136 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.59/1.87 137 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__algebra__1(B) | C = D | -c_Lim_OLIM(E,F,D,B,A) | -c_Lim_OLIM(E,F,C,B,A) # label(cls_LIM__unique_0) # label(axiom). [assumption].
% 1.59/1.90 Derived: -class_RealVector_Ometric__space(A) | B = C | -c_Lim_OLIM(D,E,C,tc_RealDef_Oreal,A) | -c_Lim_OLIM(D,E,B,tc_RealDef_Oreal,A). [resolve(136,a,137,b)].
% 1.59/1.90 138 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.59/1.90 Derived: -class_RealVector_Ometric__space(A) | B = C | -c_Lim_OLIM(D,E,C,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(D,E,B,tc_Complex_Ocomplex,A). [resolve(138,a,137,b)].
% 1.59/1.90 139 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.59/1.90 140 -class_RealVector_Oreal__normed__field(A) | B = C | -c_Deriv_Oderiv(D,E,C,A) | -c_Deriv_Oderiv(D,E,B,A) # label(cls_DERIV__unique_0) # label(axiom). [assumption].
% 1.59/1.90 141 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A),D,A) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,C,A),D,A))),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)),A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_DERIV__inverse__lemma_0) # label(axiom). [assumption].
% 1.59/1.90 142 -class_RealVector_Oreal__normed__field(A) | c_Lim_OisCont(B,C,A,A) | -c_Deriv_Oderiv(B,C,D,A) # label(cls_DERIV__isCont_0) # label(axiom). [assumption].
% 1.59/1.90 143 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_divide_Odiff_0) # label(axiom). [assumption].
% 1.59/1.90 144 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),D,A) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_divide_OscaleR_0) # label(axiom). [assumption].
% 1.59/1.90 145 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_divide_Ominus_0) # label(axiom). [assumption].
% 1.59/1.90 146 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom). [assumption].
% 1.59/1.90 147 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_divide_Oadd_0) # label(axiom). [assumption].
% 1.59/1.90 148 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,B,A) # label(cls_DERIV__cmult__Id_0) # label(axiom). [assumption].
% 1.59/1.90 Derived: A = B | -c_Deriv_Oderiv(C,D,B,tc_RealDef_Oreal) | -c_Deriv_Oderiv(C,D,A,tc_RealDef_Oreal). [resolve(139,a,140,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal))),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(139,a,141,a)].
% 1.59/1.90 Derived: c_Lim_OisCont(A,B,tc_RealDef_Oreal,tc_RealDef_Oreal) | -c_Deriv_Oderiv(A,B,C,tc_RealDef_Oreal). [resolve(139,a,142,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(139,a,143,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B),C,tc_RealDef_Oreal) = hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)). [resolve(139,a,144,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(139,a,145,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(139,a,146,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)). [resolve(139,a,147,a)].
% 1.59/1.90 Derived: c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B,A,tc_RealDef_Oreal). [resolve(139,a,148,a)].
% 1.59/1.90 149 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.59/1.90 Derived: A = B | -c_Deriv_Oderiv(C,D,B,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(C,D,A,tc_Complex_Ocomplex). [resolve(149,a,140,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex))),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(149,a,141,a)].
% 1.59/1.90 Derived: c_Lim_OisCont(A,B,tc_Complex_Ocomplex,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex). [resolve(149,a,142,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(149,a,143,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex) = hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex)). [resolve(149,a,144,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(149,a,145,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(149,a,146,a)].
% 1.59/1.90 Derived: c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B),C,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex)). [resolve(149,a,147,a)].
% 1.59/1.90 Derived: c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,A,tc_Complex_Ocomplex). [resolve(149,a,148,a)].
% 1.67/1.93 150 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.67/1.93 151 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 1.67/1.93 152 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.67/1.93 153 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.67/1.93 154 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 1.67/1.93 155 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 1.67/1.93 156 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 1.67/1.93 157 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),A),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.67/1.93 158 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.67/1.93 159 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.67/1.93 160 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.67/1.93 161 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,c_Suc(C),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.67/1.93 162 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.67/1.93 163 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_nat) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.67/1.93 164 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.67/1.93 165 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 1.67/1.93 166 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.67/1.93 167 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.67/1.93 168 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.67/1.93 169 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.67/1.93 170 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.67/1.93 171 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Power_Opower__class_Opower(A,B,tc_nat)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(150,a,151,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(150,a,152,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(150,a,153,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Power_Opower__class_Opower(A,B,tc_nat)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(150,a,154,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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)),tc_nat). [resolve(150,a,155,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(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,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(150,a,156,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(150,a,157,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(150,a,158,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(150,a,159,a)].
% 1.67/1.93 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(150,a,160,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(150,a,161,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(150,a,162,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(150,a,163,a)].
% 1.67/1.93 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(150,a,164,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(150,a,165,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(150,a,166,a)].
% 1.67/1.93 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | B = C. [resolve(150,a,167,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(150,a,168,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(150,a,169,a)].
% 1.67/1.93 172 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal)),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(172,a,151,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(172,a,152,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(172,a,153,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal)),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(172,a,154,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(172,a,155,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal)),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(172,a,156,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(172,a,157,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(172,a,158,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(172,a,159,a)].
% 1.67/1.96 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(172,a,160,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,c_Suc(B),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(172,a,161,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal),c_Nat_Osemiring__1__class_Oof__nat(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(172,a,162,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal),c_Nat_Osemiring__1__class_Oof__nat(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(172,a,163,a)].
% 1.67/1.96 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(172,a,164,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(172,a,165,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(172,a,166,a)].
% 1.67/1.96 Derived: c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal) != c_Power_Opower__class_Opower(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | B = C. [resolve(172,a,167,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_RealDef_Oreal),c_Power_Opower__class_Opower(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(172,a,168,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(172,a,169,a)].
% 1.67/1.96 173 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.67/1.96 174 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__divide_0) # label(axiom). [assumption].
% 1.67/1.96 175 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),B,A) # label(cls_eq__divide__imp_0) # label(axiom). [assumption].
% 1.67/1.96 176 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),B,A) = C # label(cls_divide__eq__imp_0) # label(axiom). [assumption].
% 1.67/1.96 177 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom). [assumption].
% 1.67/1.96 178 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom). [assumption].
% 1.67/1.96 179 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Oinverse__class_Odivide(B,C,A)) = c_HOL_Oinverse__class_Odivide(C,B,A) # label(cls_inverse__divide_0) # label(axiom). [assumption].
% 1.67/1.96 180 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oone__class_Oone(A) | C = c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__inverse__eq_0) # label(axiom). [assumption].
% 1.67/1.96 181 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__divide__right_0) # label(axiom). [assumption].
% 1.67/1.96 182 -class_Ring__and__Field_Ofield(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__divide__left_0) # label(axiom). [assumption].
% 1.67/1.96 183 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__divide_0) # label(axiom). [assumption].
% 1.67/1.96 184 -class_Ring__and__Field_Ofield(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__frac__eq_0) # label(axiom). [assumption].
% 1.67/1.96 185 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__inverse_0) # label(axiom). [assumption].
% 1.67/1.96 186 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_diff__divide__distrib_0) # label(axiom). [assumption].
% 1.67/1.96 187 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(c_HOL_Oinverse__class_Oinverse(A),B))),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__add_0) # label(axiom). [assumption].
% 1.67/1.96 188 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,C,A)),D) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom). [assumption].
% 1.67/1.96 189 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oinverse__class_Odivide(C,D,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),D,A) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom). [assumption].
% 1.67/1.96 190 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oinverse__class_Odivide(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__divide_0) # label(axiom). [assumption].
% 1.67/1.96 191 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_divide__1_0) # label(axiom). [assumption].
% 1.67/1.96 192 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom). [assumption].
% 1.67/1.96 193 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_inverse__eq__divide_0) # label(axiom). [assumption].
% 1.67/1.96 194 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_class__fieldgb_Oinverse__divide_0) # label(axiom). [assumption].
% 1.67/1.96 195 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),C,A) # label(cls_power__one__over_0) # label(axiom). [assumption].
% 1.67/1.96 196 -class_Ring__and__Field_Ofield(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__right_0) # label(axiom). [assumption].
% 1.67/1.96 197 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) # label(cls_right__inverse__eq_1) # label(axiom). [assumption].
% 1.67/1.96 198 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self_0) # label(axiom). [assumption].
% 1.67/1.96 199 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_1) # label(axiom). [assumption].
% 1.67/1.96 200 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oinverse__class_Odivide(B,C,A) # label(cls_minus__divide__divide_0) # label(axiom). [assumption].
% 1.67/1.96 201 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),A),c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),E),C),A),A) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(B,E,A),A),C,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__divides__special_0) # label(axiom). [assumption].
% 1.67/1.96 202 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom). [assumption].
% 1.67/1.96 203 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom). [assumption].
% 1.67/1.96 204 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom). [assumption].
% 1.67/1.96 205 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) != c_HOL_Oone__class_Oone(A) | B = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_0) # label(axiom). [assumption].
% 1.67/1.96 206 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),B,A) # label(cls_eq__divide__eq_4) # label(axiom). [assumption].
% 1.67/1.96 207 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,C,A)),c_HOL_Oinverse__class_Odivide(D,E,A)) = c_HOL_Oinverse__class_Odivide(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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom). [assumption].
% 1.67/1.96 208 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,C,A)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom). [assumption].
% 1.67/1.96 209 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,C,A)),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom). [assumption].
% 1.67/1.96 210 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Oone__class_Oone(A)) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_1) # label(axiom). [assumption].
% 1.67/1.96 211 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) = c_HOL_Oinverse__class_Odivide(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom). [assumption].
% 1.67/1.96 212 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = c_HOL_Oinverse__class_Odivide(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom). [assumption].
% 1.67/1.96 213 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_add__divide__distrib_0) # label(axiom). [assumption].
% 1.67/1.96 214 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) # label(cls_divide__inverse_0) # label(axiom). [assumption].
% 1.67/1.96 215 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) # label(cls_class__fieldgb_Odivide__inverse_0) # label(axiom). [assumption].
% 1.67/1.96 216 -class_Ring__and__Field_Ofield(A) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__divide_0) # label(axiom). [assumption].
% 1.67/1.96 217 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_eq__divide__eq_2) # label(axiom). [assumption].
% 1.67/1.96 218 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oinverse__class_Odivide(D,E,A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C) # label(cls_frac__eq__eq_0) # label(axiom). [assumption].
% 1.67/1.96 219 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E) | C = c_HOL_Ozero__class_Ozero(A) | E = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,E,A) = c_HOL_Oinverse__class_Odivide(D,C,A) # label(cls_frac__eq__eq_1) # label(axiom). [assumption].
% 1.67/1.96 220 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom). [assumption].
% 1.67/1.96 221 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) # label(cls_inverse__mult__distrib_0) # label(axiom). [assumption].
% 1.67/1.96 222 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,C,A)),c_HOL_Oinverse__class_Odivide(D,E,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E),A) # label(cls_mult__frac__frac_0) # label(axiom). [assumption].
% 1.67/1.96 223 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,C,A)),D) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) # label(cls_mult__frac__num_0) # label(axiom). [assumption].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_RealDef_Oreal),c_Power_Opower__class_Opower(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(173,a,174,a)].
% 1.67/1.96 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),A,tc_RealDef_Oreal). [resolve(173,a,175,a)].
% 1.67/1.96 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),A,tc_RealDef_Oreal) = B. [resolve(173,a,176,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal). [resolve(173,a,179,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(173,a,180,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(173,a,181,a)].
% 1.67/1.96 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(173,a,182,a)].
% 1.67/1.96 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,183,a)].
% 1.67/1.96 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),D),tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,184,a)].
% 1.67/1.96 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),A) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,185,a)].
% 1.67/1.96 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A))),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,187,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),C) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)),B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,188,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),C,tc_RealDef_Oreal) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,189,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,190,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(173,a,191,a)].
% 1.67/1.96 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(173,a,193,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(173,a,195,a)].
% 1.67/1.96 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,196,a)].
% 1.67/1.96 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,A,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(173,a,197,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal). [resolve(173,a,200,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),B),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,D,tc_RealDef_Oreal),tc_RealDef_Oreal),B,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,201,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,203,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | A = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(173,a,205,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A),A,tc_RealDef_Oreal). [resolve(173,a,206,a)].
% 1.67/1.96 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),D),tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,207,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,208,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),B) = A | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,209,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(173,a,210,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,211,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,212,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)). [resolve(173,a,214,a)].
% 1.67/1.96 Derived: c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_RealDef_Oreal),c_Power_Opower__class_Opower(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,216,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(173,a,217,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B). [resolve(173,a,218,a)].
% 1.67/1.96 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,D,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal). [resolve(173,a,219,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(173,a,220,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)). [resolve(173,a,221,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),D),tc_RealDef_Oreal). [resolve(173,a,222,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal)),C) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B,tc_RealDef_Oreal). [resolve(173,a,223,a)].
% 1.67/1.96 224 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(224,a,174,a)].
% 1.67/1.96 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),A,tc_Complex_Ocomplex). [resolve(224,a,175,a)].
% 1.67/1.96 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),A,tc_Complex_Ocomplex) = B. [resolve(224,a,176,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(B,A,tc_Complex_Ocomplex). [resolve(224,a,179,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(224,a,180,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(224,a,181,a)].
% 1.67/1.96 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(224,a,182,a)].
% 1.67/1.96 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,183,a)].
% 1.67/1.96 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D),tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,184,a)].
% 1.67/1.96 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,185,a)].
% 1.67/1.96 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A))),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,187,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),C) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,188,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),C,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,189,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,190,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(224,a,191,a)].
% 1.67/1.96 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(224,a,193,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(224,a,195,a)].
% 1.67/1.96 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,196,a)].
% 1.67/1.96 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(224,a,197,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex). [resolve(224,a,200,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),B),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,201,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,203,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(224,a,205,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A),A,tc_Complex_Ocomplex). [resolve(224,a,206,a)].
% 1.67/1.96 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D),tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,207,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,208,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),B) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,209,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(224,a,210,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,211,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,212,a)].
% 1.67/1.96 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)). [resolve(224,a,214,a)].
% 1.73/2.01 Derived: c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,216,a)].
% 1.73/2.01 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(224,a,217,a)].
% 1.73/2.01 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B). [resolve(224,a,218,a)].
% 1.73/2.01 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,D,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(C,B,tc_Complex_Ocomplex). [resolve(224,a,219,a)].
% 1.73/2.01 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(224,a,220,a)].
% 1.73/2.01 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)). [resolve(224,a,221,a)].
% 1.73/2.01 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D),tc_Complex_Ocomplex). [resolve(224,a,222,a)].
% 1.73/2.01 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),C) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),B,tc_Complex_Ocomplex). [resolve(224,a,223,a)].
% 1.73/2.01 225 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.73/2.01 226 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom). [assumption].
% 1.73/2.01 227 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),C)) = C # label(cls_add__minus__cancel_0) # label(axiom). [assumption].
% 1.73/2.01 228 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom). [assumption].
% 1.73/2.01 229 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 1.73/2.01 230 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 1.73/2.01 231 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 1.73/2.01 232 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ominus__class_Ominus(B,C,A) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8) # label(cls_ring_Oring__simps_I30_J_0) # label(axiom). [assumption].
% 1.73/2.01 233 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ouminus__class_Ouminus(B,A) # label(cls_group__add__class_Odiff__0_0) # label(axiom). [assumption].
% 1.73/2.01 234 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) # label(cls_diff__minus_0) # label(axiom). [assumption].
% 1.73/2.01 235 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ominus__class_Ominus(B,C,A) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11) # label(cls_field_Ofield__eq__simps_I34_J_0) # label(axiom). [assumption].
% 1.73/2.01 236 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ominus__class_Ominus(B,C,A)),C) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 1.73/2.01 237 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Ouminus__class_Ouminus(B,A) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom). [assumption].
% 1.73/2.01 238 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__neg__iff__add__eq__0_0) # label(axiom). [assumption].
% 1.73/2.01 239 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ouminus__class_Ouminus(B,A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus_0) # label(axiom). [assumption].
% 1.73/2.01 240 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_left__minus_0) # label(axiom). [assumption].
% 1.73/2.01 241 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 1.73/2.01 242 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ouminus__class_Ouminus(B,A) = C # label(cls_minus__unique_0) # label(axiom). [assumption].
% 1.73/2.01 243 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ouminus__class_Ouminus(C,A) # label(cls_eq__neg__iff__add__eq__0_1) # label(axiom). [assumption].
% 1.73/2.01 244 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = C # label(cls_minus__add__cancel_0) # label(axiom). [assumption].
% 1.73/2.01 245 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) # label(cls_diff__minus__eq__add_0) # label(axiom). [assumption].
% 1.73/2.01 246 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 1.73/2.01 247 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__equation__iff_1) # label(axiom). [assumption].
% 1.73/2.01 248 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_1) # label(axiom). [assumption].
% 1.73/2.01 249 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_0) # label(axiom). [assumption].
% 1.73/2.01 250 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__minus_0) # label(axiom). [assumption].
% 1.73/2.01 251 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ominus__class_Ominus(B,C,A) | -c_Ring__and__Field_Opordered__ring(D,E,F,V6,V7,V8,V9,V10) # label(cls_pordered__ring_Oring__simps_I36_J_0) # label(axiom). [assumption].
% 1.73/2.01 252 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__equal__iff__equal_1) # label(axiom). [assumption].
% 1.73/2.01 253 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom). [assumption].
% 1.73/2.01 254 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(C,A)),c_HOL_Ouminus__class_Ouminus(B,A)) # label(cls_minus__add_0) # label(axiom). [assumption].
% 1.73/2.01 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal) | A = B. [resolve(225,a,226,a)].
% 1.73/2.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),B)) = B. [resolve(225,a,227,a)].
% 1.73/2.01 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(225,a,228,a)].
% 1.73/2.01 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(225,a,229,a)].
% 1.73/2.01 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(225,a,230,a)].
% 1.73/2.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Oring(C,D,E,F,V6,V7). [resolve(225,a,232,a)].
% 1.73/2.01 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal). [resolve(225,a,233,a)].
% 1.73/2.01 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)). [resolve(225,a,234,a)].
% 1.73/2.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Ofield(C,D,E,F,V6,V7,V8,V9,V10). [resolve(225,a,235,a)].
% 1.73/2.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal)),B) = A. [resolve(225,a,236,a)].
% 1.73/2.01 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(225,a,237,a)].
% 1.73/2.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(225,a,238,a)].
% 1.73/2.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(225,a,239,a)].
% 1.73/2.01 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(225,a,241,a)].
% 1.73/2.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) = B. [resolve(225,a,242,a)].
% 1.73/2.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal). [resolve(225,a,243,a)].
% 1.73/2.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)) = B. [resolve(225,a,244,a)].
% 1.73/2.01 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B). [resolve(225,a,245,a)].
% 1.73/2.02 Derived: c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),B,tc_RealDef_Oreal) = A. [resolve(225,a,246,a)].
% 1.73/2.02 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(225,a,247,a)].
% 1.73/2.02 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(225,a,248,a)].
% 1.73/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Opordered__ring(C,D,E,F,V6,V7,V8,V9). [resolve(225,a,251,a)].
% 1.73/2.02 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(225,a,252,a)].
% 1.73/2.02 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(225,a,253,a)].
% 1.73/2.02 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)). [resolve(225,a,254,a)].
% 1.73/2.02 255 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.73/2.02 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex) | A = B. [resolve(255,a,226,a)].
% 1.73/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B)) = B. [resolve(255,a,227,a)].
% 1.73/2.02 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(255,a,228,a)].
% 1.73/2.02 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(255,a,229,a)].
% 1.73/2.02 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(255,a,230,a)].
% 1.73/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Oring(C,D,E,F,V6,V7). [resolve(255,a,232,a)].
% 1.73/2.02 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex). [resolve(255,a,233,a)].
% 1.73/2.02 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)). [resolve(255,a,234,a)].
% 1.73/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Ofield(C,D,E,F,V6,V7,V8,V9,V10). [resolve(255,a,235,a)].
% 1.73/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex)),B) = A. [resolve(255,a,236,a)].
% 1.73/2.02 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(255,a,237,a)].
% 1.73/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(255,a,238,a)].
% 1.73/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(255,a,239,a)].
% 1.73/2.02 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(255,a,241,a)].
% 1.73/2.02 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) = B. [resolve(255,a,242,a)].
% 1.73/2.04 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex). [resolve(255,a,243,a)].
% 1.73/2.04 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)) = B. [resolve(255,a,244,a)].
% 1.73/2.04 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B). [resolve(255,a,245,a)].
% 1.73/2.04 Derived: c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B),B,tc_Complex_Ocomplex) = A. [resolve(255,a,246,a)].
% 1.73/2.04 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(255,a,247,a)].
% 1.73/2.04 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(255,a,248,a)].
% 1.73/2.04 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Opordered__ring(C,D,E,F,V6,V7,V8,V9). [resolve(255,a,251,a)].
% 1.73/2.04 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(255,a,252,a)].
% 1.73/2.04 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(255,a,253,a)].
% 1.73/2.04 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)). [resolve(255,a,254,a)].
% 1.73/2.04 256 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) # label(axiom). [assumption].
% 1.73/2.04 257 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) # label(cls_one__less__inverse__iff_0) # label(axiom). [assumption].
% 1.73/2.04 258 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | B = c_HOL_Ozero__class_Ozero(A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_inverse__negative__imp__negative_0) # label(axiom). [assumption].
% 1.73/2.04 259 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,D,A),C,A) # label(cls_divide__less__eq_0) # label(axiom). [assumption].
% 1.73/2.04 260 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_divide__less__eq_6) # label(axiom). [assumption].
% 1.73/2.04 261 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(D,C,A),A) # label(cls_less__divide__eq_0) # label(axiom). [assumption].
% 1.73/2.04 262 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) # label(cls_less__divide__eq_6) # label(axiom). [assumption].
% 1.73/2.04 263 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__imp__div__pos__less_0) # label(axiom). [assumption].
% 1.73/2.04 264 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__imp__less__div__pos_0) # label(axiom). [assumption].
% 1.73/2.04 265 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_zero__less__divide__iff_0) # label(axiom). [assumption].
% 1.73/2.04 266 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(C,B,A),A) # label(cls_zero__less__divide__iff_1) # label(axiom). [assumption].
% 1.73/2.04 267 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_zero__less__divide__iff_2) # label(axiom). [assumption].
% 1.73/2.04 268 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(C,B,A),A) # label(cls_zero__less__divide__iff_3) # label(axiom). [assumption].
% 1.73/2.04 269 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(D,C,A),B,A) # label(cls_divide__less__eq_2) # label(axiom). [assumption].
% 1.73/2.04 270 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_divide__less__eq_3) # label(axiom). [assumption].
% 1.73/2.04 271 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),B,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_divide__less__eq_8) # label(axiom). [assumption].
% 1.73/2.04 272 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),B,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_divide__less__eq_9) # label(axiom). [assumption].
% 1.73/2.04 273 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(D,C,A),A) # label(cls_less__divide__eq_2) # label(axiom). [assumption].
% 1.73/2.04 274 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_less__divide__eq_3) # label(axiom). [assumption].
% 1.73/2.04 275 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) # label(cls_less__divide__eq_8) # label(axiom). [assumption].
% 1.73/2.04 276 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) # label(cls_less__divide__eq_9) # label(axiom). [assumption].
% 1.73/2.04 277 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),C,A) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_abs__div__pos_0) # label(axiom). [assumption].
% 1.73/2.04 278 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__neg__neg_0) # label(axiom). [assumption].
% 1.73/2.04 279 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide__pos__pos_0) # label(axiom). [assumption].
% 1.73/2.04 280 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__divide__iff_4) # label(axiom). [assumption].
% 1.73/2.04 281 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__less__divide__iff_5) # label(axiom). [assumption].
% 1.73/2.04 282 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) # label(cls_one__less__inverse__iff_1) # label(axiom). [assumption].
% 1.73/2.04 283 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A),C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_gt__half__sum_0) # label(axiom). [assumption].
% 1.73/2.04 284 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__half__sum_0) # label(axiom). [assumption].
% 1.73/2.04 285 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_divide__strict__right__mono_0) # label(axiom). [assumption].
% 1.73/2.04 286 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_divide__strict__right__mono__neg_0) # label(axiom). [assumption].
% 1.73/2.04 287 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs__class_Oabs(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) = hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Oabs__class_Oabs(B,A)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__abs__inverse_0) # label(axiom). [assumption].
% 1.73/2.04 288 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__abs__divide_0) # label(axiom). [assumption].
% 1.73/2.04 289 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) # label(cls_inverse__positive__imp__positive_0) # label(axiom). [assumption].
% 1.73/2.04 290 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(A),C),hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) # label(cls_inverse__less__imp__less_0) # label(axiom). [assumption].
% 1.73/2.04 291 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_less__imp__inverse__less_0) # label(axiom). [assumption].
% 1.73/2.04 292 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(A),C),hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) # label(cls_inverse__less__imp__less__neg_0) # label(axiom). [assumption].
% 1.73/2.04 293 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_less__imp__inverse__less__neg_0) # label(axiom). [assumption].
% 1.73/2.04 294 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__1__iff_0) # label(axiom). [assumption].
% 1.73/2.04 295 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__1__iff_1) # label(axiom). [assumption].
% 1.73/2.04 296 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(D,C,A),B,A) # label(cls_divide__less__eq_1) # label(axiom). [assumption].
% 1.73/2.04 297 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),B,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_divide__less__eq_4) # label(axiom). [assumption].
% 1.73/2.04 298 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),B,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_divide__less__eq_5) # label(axiom). [assumption].
% 1.73/2.04 299 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_divide__less__eq_7) # label(axiom). [assumption].
% 1.73/2.04 300 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Oinverse__class_Odivide(B,D,A),A) # label(cls_less__divide__eq_1) # label(axiom). [assumption].
% 1.73/2.04 301 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_less__divide__eq_4) # label(axiom). [assumption].
% 1.73/2.04 302 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_less__divide__eq_5) # label(axiom). [assumption].
% 1.73/2.04 303 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) # label(cls_less__divide__eq_7) # label(axiom). [assumption].
% 1.73/2.04 304 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_inverse__negative__iff__negative_0) # label(axiom). [assumption].
% 1.73/2.04 305 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_inverse__negative__iff__negative_1) # label(axiom). [assumption].
% 1.73/2.04 306 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_negative__imp__inverse__negative_0) # label(axiom). [assumption].
% 1.73/2.04 307 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_one__less__inverse__iff_2) # label(axiom). [assumption].
% 1.73/2.04 308 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oabs__class_Oabs(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) = hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Oabs__class_Oabs(B,A)) # label(cls_abs__inverse_0) # label(axiom). [assumption].
% 1.73/2.04 309 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_abs__divide_0) # label(axiom). [assumption].
% 1.73/2.04 310 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_positive__imp__inverse__positive_0) # label(axiom). [assumption].
% 1.73/2.04 311 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_inverse__positive__iff__positive_1) # label(axiom). [assumption].
% 1.73/2.04 312 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) # label(cls_inverse__positive__iff__positive_0) # label(axiom). [assumption].
% 1.73/2.04 313 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__iff_3) # label(axiom). [assumption].
% 1.73/2.04 314 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__iff_2) # label(axiom). [assumption].
% 1.73/2.04 315 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__iff_1) # label(axiom). [assumption].
% 1.73/2.04 316 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__iff_0) # label(axiom). [assumption].
% 1.73/2.04 317 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_divide__strict__left__mono_0) # label(axiom). [assumption].
% 1.73/2.04 318 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_divide__strict__left__mono__neg_0) # label(axiom). [assumption].
% 1.73/2.04 319 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),A) # label(cls_zero__less__divide__1__iff_0) # label(axiom). [assumption].
% 1.73/2.04 320 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__divide__1__iff_1) # label(axiom). [assumption].
% 1.73/2.04 321 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__neg__pos_0) # label(axiom). [assumption].
% 1.73/2.04 322 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide__pos__neg_0) # label(axiom). [assumption].
% 1.73/2.04 323 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide__less__0__iff_4) # label(axiom). [assumption].
% 1.73/2.04 324 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__iff_5) # label(axiom). [assumption].
% 1.73/2.04 325 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_inverse__less__1__iff_2) # label(axiom). [assumption].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(256,a,257,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,258,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(256,a,259,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal). [resolve(256,a,260,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,261,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B,tc_RealDef_Oreal). [resolve(256,a,262,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(256,a,263,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(256,a,264,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,265,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,266,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,267,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,268,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(256,a,269,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(256,a,270,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,273,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(256,a,274,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(256,a,277,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,278,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(256,a,279,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(256,a,282,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(256,a,283,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(256,a,284,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(256,a,285,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,A,tc_RealDef_Oreal). [resolve(256,a,286,a)].
% 1.73/2.05 Derived: c_HOL_Oabs__class_Oabs(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal) = hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal)) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(256,a,287,a)].
% 1.73/2.05 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(256,a,288,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(256,a,289,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(256,a,290,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(256,a,291,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(256,a,292,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(256,a,293,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,294,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,295,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(256,a,296,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(256,a,297,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(256,a,298,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal). [resolve(256,a,299,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,300,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(256,a,301,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(256,a,302,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),B,tc_RealDef_Oreal). [resolve(256,a,303,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,304,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,305,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,306,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(256,a,307,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal) = hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal)). [resolve(256,a,308,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,309,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(256,a,310,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(256,a,312,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,313,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,314,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,315,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,316,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal). [resolve(256,a,317,a)].
% 1.73/2.05 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(256,a,318,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,319,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(256,a,320,a)].
% 1.83/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(256,a,321,a)].
% 1.83/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(256,a,322,a)].
% 1.83/2.10 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(256,a,325,a)].
% 1.83/2.10 326 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.83/2.10 327 -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].
% 1.83/2.10 328 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 1.83/2.10 329 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 1.83/2.10 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(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(326,a,327,a)].
% 1.83/2.10 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(326,a,328,a)].
% 1.83/2.10 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(326,a,329,a)].
% 1.83/2.10 330 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.83/2.10 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) | -class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) | -class_Power_Opower(tc_RealDef_Oreal) | c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(330,a,327,a)].
% 1.83/2.10 Derived: c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(330,a,328,a)].
% 1.83/2.10 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(330,a,329,a)].
% 1.83/2.10 331 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.83/2.10 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(331,a,327,a)].
% 1.83/2.10 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(331,a,328,a)].
% 1.83/2.10 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(331,a,329,a)].
% 1.83/2.10 332 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 1.87/2.12 333 -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].
% 1.87/2.12 Derived: c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(332,a,333,a)].
% 1.87/2.12 334 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 1.87/2.12 Derived: c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(334,a,333,a)].
% 1.87/2.12 335 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.87/2.12 336 -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].
% 1.87/2.12 337 -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].
% 1.87/2.12 338 -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].
% 1.87/2.12 339 -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].
% 1.87/2.12 340 -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].
% 1.87/2.12 341 -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].
% 1.87/2.12 342 -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].
% 1.87/2.12 343 -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].
% 1.87/2.12 344 -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].
% 1.87/2.12 345 -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].
% 1.87/2.12 346 -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].
% 1.87/2.12 347 -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].
% 1.87/2.12 348 -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].
% 1.87/2.12 349 -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].
% 1.87/2.12 350 -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].
% 1.87/2.12 351 -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].
% 1.87/2.12 352 -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].
% 1.87/2.12 353 -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].
% 1.87/2.12 354 -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].
% 1.87/2.12 355 -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].
% 1.87/2.12 356 -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].
% 1.87/2.12 357 -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].
% 1.87/2.12 358 -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].
% 1.87/2.12 359 -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].
% 1.87/2.12 360 -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].
% 1.87/2.12 361 -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].
% 1.87/2.12 362 -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].
% 1.87/2.12 363 -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].
% 1.87/2.12 364 -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].
% 1.87/2.13 365 -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].
% 1.87/2.13 366 -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].
% 1.87/2.13 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(335,a,336,a)].
% 1.87/2.13 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(335,a,337,a)].
% 1.87/2.13 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(335,a,338,a)].
% 1.87/2.13 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(335,a,339,a)].
% 1.87/2.13 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(335,a,340,a)].
% 1.87/2.13 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(335,a,341,a)].
% 1.87/2.13 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(335,a,343,a)].
% 1.87/2.13 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(335,a,344,a)].
% 1.87/2.13 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(335,a,345,a)].
% 1.87/2.13 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(335,a,347,a)].
% 1.87/2.13 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(335,a,348,a)].
% 1.87/2.13 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(335,a,349,a)].
% 1.87/2.13 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(335,a,350,a)].
% 1.87/2.13 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(335,a,351,a)].
% 1.87/2.13 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(335,a,352,a)].
% 1.87/2.13 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(335,a,353,a)].
% 1.87/2.13 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(335,a,354,a)].
% 1.87/2.15 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(335,a,355,a)].
% 1.87/2.15 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(335,a,356,a)].
% 1.87/2.15 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(335,a,357,a)].
% 1.87/2.15 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(335,a,358,a)].
% 1.87/2.15 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(335,a,359,a)].
% 1.87/2.15 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(335,a,360,a)].
% 1.87/2.15 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(335,a,361,a)].
% 1.87/2.15 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(335,a,362,a)].
% 1.87/2.15 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(335,a,363,a)].
% 1.87/2.15 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(335,a,364,a)].
% 1.87/2.15 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(335,a,365,a)].
% 1.87/2.15 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(335,a,366,a)].
% 1.87/2.15 367 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.87/2.15 368 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 1.87/2.15 369 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 1.87/2.15 370 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 1.91/2.15 371 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 1.91/2.15 372 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 1.91/2.15 373 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 1.91/2.15 374 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 1.91/2.15 375 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 1.91/2.15 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(367,a,368,a)].
% 1.91/2.15 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(367,a,369,a)].
% 1.91/2.15 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat). [resolve(367,a,371,a)].
% 1.91/2.15 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A),tc_nat). [resolve(367,a,372,a)].
% 1.91/2.15 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(367,a,373,a)].
% 1.91/2.15 Derived: c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(367,a,374,a)].
% 1.91/2.15 Derived: c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(367,a,375,a)].
% 1.91/2.15 376 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.91/2.15 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,368,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(376,a,369,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal). [resolve(376,a,371,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),tc_RealDef_Oreal). [resolve(376,a,372,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(376,a,373,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(376,a,374,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(376,a,375,a)].
% 1.91/2.22 377 -class_OrderedGroup_Oab__semigroup__idem__mult(A) | c_Finite__Set_Ofun__left__comm__idem(c_HOL_Otimes__class_Otimes(A),A,A) # label(cls_fun__left__comm__idem_0) # label(axiom). [assumption].
% 1.91/2.22 378 hAPP(hAPP(A,B),hAPP(hAPP(A,B),C)) = hAPP(hAPP(A,B),C) | -c_Finite__Set_Ofun__left__comm__idem(A,D,E) # label(cls_fun__left__comm__idem_Ofun__left__idem_0) # label(axiom). [assumption].
% 1.91/2.22 379 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 1.91/2.22 380 -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].
% 1.91/2.22 381 -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].
% 1.91/2.22 382 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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))),A) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 1.91/2.22 383 -class_Ring__and__Field_Oordered__ring__strict(A) | -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)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 1.91/2.22 384 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 1.91/2.22 385 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 1.91/2.22 386 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 1.91/2.22 387 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 1.91/2.22 388 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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)),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 1.91/2.22 389 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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)),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 1.91/2.22 390 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(D,B,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 1.91/2.22 391 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 1.91/2.22 392 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 1.91/2.22 393 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 1.91/2.22 394 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 1.91/2.22 395 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 1.91/2.22 396 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 1.91/2.22 397 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 1.91/2.22 398 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 1.91/2.22 399 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 1.91/2.22 400 -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].
% 1.91/2.22 401 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 1.91/2.22 402 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 1.91/2.22 403 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 1.91/2.22 404 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 1.91/2.22 405 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 1.91/2.22 406 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 1.91/2.22 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(379,a,380,a)].
% 1.91/2.22 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(379,a,381,a)].
% 1.91/2.22 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),tc_RealDef_Oreal). [resolve(379,a,382,a)].
% 1.91/2.22 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(379,a,383,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(379,a,384,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal). [resolve(379,a,385,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal). [resolve(379,a,386,a)].
% 1.91/2.22 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(379,a,387,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(379,a,388,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(379,a,389,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(379,a,390,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(379,a,393,a)].
% 1.91/2.22 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(379,a,397,a)].
% 1.99/2.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(379,a,399,a)].
% 1.99/2.24 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(379,a,400,a)].
% 1.99/2.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal). [resolve(379,a,401,a)].
% 1.99/2.24 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal). [resolve(379,a,402,a)].
% 1.99/2.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal). [resolve(379,a,403,a)].
% 1.99/2.24 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal). [resolve(379,a,404,a)].
% 1.99/2.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal). [resolve(379,a,405,a)].
% 1.99/2.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal). [resolve(379,a,406,a)].
% 1.99/2.24 407 class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) # label(axiom). [assumption].
% 1.99/2.24 408 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Oone__class_Oone(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = C # label(cls_inverse__unique_0) # label(axiom). [assumption].
% 1.99/2.24 409 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) != hAPP(c_HOL_Oinverse__class_Oinverse(A),C) | B = C # label(cls_inverse__eq__iff__eq_0) # label(axiom). [assumption].
% 1.99/2.24 410 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) != hAPP(c_HOL_Oinverse__class_Oinverse(A),C) | B = C | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__imp__eq_0) # label(axiom). [assumption].
% 1.99/2.24 411 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_1) # label(axiom). [assumption].
% 1.99/2.24 412 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_Power_Opower__class_Opower(B,C,A)) = c_Power_Opower__class_Opower(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),C,A) # label(cls_power__inverse_0) # label(axiom). [assumption].
% 1.99/2.24 413 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Ouminus__class_Ouminus(B,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) # label(cls_inverse__minus__eq_0) # label(axiom). [assumption].
% 1.99/2.24 414 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_left__inverse_0) # label(axiom). [assumption].
% 1.99/2.24 415 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_right__inverse_0) # label(axiom). [assumption].
% 1.99/2.24 416 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_division__ring__inverse__add_0) # label(axiom). [assumption].
% 1.99/2.24 417 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),c_HOL_Ominus__class_Ominus(B,C,A))),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)),A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_Deriv_Oinverse__diff__inverse_0) # label(axiom). [assumption].
% 1.99/2.24 418 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__mult__distrib_0) # label(axiom). [assumption].
% 1.99/2.24 419 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)) = B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__inverse__eq_0) # label(axiom). [assumption].
% 1.99/2.24 420 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)) = B # label(cls_inverse__inverse__eq_0) # label(axiom). [assumption].
% 1.99/2.24 421 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_Power_Opower__class_Opower(B,C,A)) = c_Power_Opower__class_Opower(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),C,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__inverse_0) # label(axiom). [assumption].
% 1.99/2.24 422 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Ouminus__class_Ouminus(B,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__minus__eq_0) # label(axiom). [assumption].
% 1.99/2.24 423 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_HOL_Oone__class_Oone(A)) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__1_0) # label(axiom). [assumption].
% 1.99/2.24 424 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_0) # label(axiom). [assumption].
% 1.99/2.24 425 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__zero__imp__zero_0) # label(axiom). [assumption].
% 1.99/2.24 426 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(A),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),c_HOL_Ominus__class_Ominus(C,B,A))),hAPP(c_HOL_Oinverse__class_Oinverse(A),C)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_division__ring__inverse__diff_0) # label(axiom). [assumption].
% 1.99/2.24 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) = B. [resolve(407,a,408,a)].
% 1.99/2.24 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) != hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B) | A = B. [resolve(407,a,409,a)].
% 1.99/2.24 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) != hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B) | A = B | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,410,a)].
% 1.99/2.24 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,411,a)].
% 1.99/2.24 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal)) = c_Power_Opower__class_Opower(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal). [resolve(407,a,412,a)].
% 1.99/2.24 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(407,a,413,a)].
% 1.99/2.24 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,415,a)].
% 1.99/2.24 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B))),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,416,a)].
% 1.99/2.24 Derived: c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal))),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,417,a)].
% 1.99/2.24 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,418,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)) = A | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,419,a)].
% 1.99/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)) = A. [resolve(407,a,420,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal)) = c_Power_Opower__class_Opower(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,421,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,422,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(407,a,423,a)].
% 1.99/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,424,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,425,a)].
% 1.99/2.25 Derived: c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A)),c_HOL_Ominus__class_Ominus(B,A,tc_RealDef_Oreal))),hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),B)) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(407,a,426,a)].
% 1.99/2.25 427 class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) # label(axiom). [assumption].
% 1.99/2.25 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = B. [resolve(427,a,408,a)].
% 1.99/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) != hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B) | A = B. [resolve(427,a,409,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) != hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B) | A = B | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,410,a)].
% 1.99/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,411,a)].
% 1.99/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex)) = c_Power_Opower__class_Opower(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex). [resolve(427,a,412,a)].
% 1.99/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex). [resolve(427,a,413,a)].
% 1.99/2.25 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,415,a)].
% 1.99/2.25 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B))),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,416,a)].
% 1.99/2.25 Derived: c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex))),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,417,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,418,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = A | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,419,a)].
% 1.99/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)) = A. [resolve(427,a,420,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex)) = c_Power_Opower__class_Opower(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,421,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,422,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(427,a,423,a)].
% 1.99/2.25 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,424,a)].
% 1.99/2.25 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,425,a)].
% 1.99/2.25 Derived: c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),c_HOL_Ominus__class_Ominus(B,A,tc_Complex_Ocomplex))),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(427,a,426,a)].
% 1.99/2.29 428 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.99/2.29 429 -class_Ring__and__Field_Osemiring(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)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I18_J_0) # label(axiom). [assumption].
% 1.99/2.29 430 -class_Ring__and__Field_Osemiring(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)) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I17_J_0) # label(axiom). [assumption].
% 1.99/2.29 431 -class_Ring__and__Field_Osemiring(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)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I21_J_0) # label(axiom). [assumption].
% 1.99/2.29 432 -class_Ring__and__Field_Osemiring(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)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I22_J_0) # label(axiom). [assumption].
% 1.99/2.29 433 -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].
% 1.99/2.29 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(428,a,433,a)].
% 1.99/2.29 434 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.99/2.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),B)),D). [resolve(434,a,433,a)].
% 1.99/2.29 435 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.99/2.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B)),D). [resolve(435,a,433,a)].
% 1.99/2.29 436 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.99/2.29 437 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,E,A) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 1.99/2.29 438 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_HOL_Oord__class_Oless(D,E,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 1.99/2.29 439 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_neg__less__iff__less_1) # label(axiom). [assumption].
% 1.99/2.29 440 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__less__iff__less_0) # label(axiom). [assumption].
% 1.99/2.29 441 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__0__iff__less_1) # label(axiom). [assumption].
% 1.99/2.29 442 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__less__0__iff__less_0) # label(axiom). [assumption].
% 1.99/2.29 443 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 1.99/2.29 444 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 1.99/2.29 445 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__less__iff_1) # label(axiom). [assumption].
% 1.99/2.29 446 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__less__iff_0) # label(axiom). [assumption].
% 1.99/2.29 447 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__minus__iff_1) # label(axiom). [assumption].
% 1.99/2.29 448 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__minus__iff_0) # label(axiom). [assumption].
% 1.99/2.29 449 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ominus__class_Ominus(C,D,A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I25_J_1) # label(axiom). [assumption].
% 1.99/2.29 450 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ominus__class_Ominus(D,C,A),A) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I25_J_0) # label(axiom). [assumption].
% 1.99/2.29 451 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I26_J_1) # label(axiom). [assumption].
% 1.99/2.29 452 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,D,A),C,A) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I26_J_0) # label(axiom). [assumption].
% 1.99/2.29 453 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__0__less__iff__less_0) # label(axiom). [assumption].
% 1.99/2.29 454 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__less__iff__less_1) # label(axiom). [assumption].
% 1.99/2.29 455 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,D,A),C,A) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I22_J_0) # label(axiom). [assumption].
% 1.99/2.29 456 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I22_J_1) # label(axiom). [assumption].
% 1.99/2.29 457 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ominus__class_Ominus(D,C,A),A) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I21_J_0) # label(axiom). [assumption].
% 1.99/2.29 458 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ominus__class_Ominus(C,D,A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A) | -c_Ring__and__Field_Oring(E,F,V6,V7,V8,V9) # label(cls_ring_Oring__simps_I21_J_1) # label(axiom). [assumption].
% 1.99/2.29 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,D,tc_RealDef_Oreal). [resolve(436,a,437,a)].
% 1.99/2.29 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(436,a,438,a)].
% 1.99/2.29 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(436,a,439,a)].
% 1.99/2.29 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(436,a,440,a)].
% 1.99/2.29 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(436,a,441,a)].
% 1.99/2.29 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(436,a,442,a)].
% 1.99/2.29 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(436,a,443,a)].
% 1.99/2.29 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(436,a,444,a)].
% 1.99/2.29 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(436,a,445,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(436,a,447,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),B,tc_RealDef_Oreal) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(436,a,449,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(436,a,450,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(436,a,451,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(436,a,452,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(436,a,453,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(436,a,454,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(436,a,455,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(436,a,456,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(436,a,457,a)].
% 2.06/2.31 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),B,tc_RealDef_Oreal) | -c_Ring__and__Field_Oring(D,E,F,V6,V7,V8). [resolve(436,a,458,a)].
% 2.06/2.31 459 class_Ring__and__Field_Odvd(tc_nat) # label(clsarity_nat__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.06/2.31 460 -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_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A)),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].
% 2.06/2.31 461 -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),c_HOL_Ominus__class_Ominus(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),F),A)),D),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,F,A) # label(cls_inf__period_I4_J_1) # label(axiom). [assumption].
% 2.06/2.31 462 -class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Odvd(A) | c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_List_Osko__Presburger__Xunity__coeff__ex__1__1(C,B,A)),c_HOL_Ozero__class_Ozero(A)),A) | -hBOOL(hAPP(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_unity__coeff__ex_0) # label(axiom). [assumption].
% 2.06/2.31 463 -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].
% 2.06/2.31 464 -class_Ring__and__Field_Osemiring__0(A) | -class_Ring__and__Field_Odvd(A) | hBOOL(hAPP(B,c_List_Osko__Presburger__Xunity__coeff__ex__1__1(B,C,A))) | -hBOOL(hAPP(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_unity__coeff__ex_1) # label(axiom). [assumption].
% 2.06/2.31 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),c_HOL_Ominus__class_Ominus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat)),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(459,a,460,a)].
% 2.06/2.31 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),c_HOL_Ominus__class_Ominus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),E),tc_nat)),C),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_nat). [resolve(459,a,461,a)].
% 2.06/2.31 Derived: -class_Ring__and__Field_Osemiring__0(tc_nat) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Osko__Presburger__Xunity__coeff__ex__1__1(B,A,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) | -hBOOL(hAPP(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))). [resolve(459,a,462,b)].
% 2.06/2.31 Derived: -class_Ring__and__Field_Osemiring__0(tc_nat) | hBOOL(hAPP(A,c_List_Osko__Presburger__Xunity__coeff__ex__1__1(A,B,tc_nat))) | -hBOOL(hAPP(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))). [resolve(459,a,464,b)].
% 2.06/2.31 465 class_Ring__and__Field_Odvd(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.06/2.31 Derived: -class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal)),E),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),E),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_RealDef_Oreal). [resolve(465,a,460,a)].
% 2.06/2.31 Derived: -class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),D),E),tc_RealDef_Oreal)),C),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_RealDef_Oreal). [resolve(465,a,461,a)].
% 2.06/2.31 Derived: -class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_List_Osko__Presburger__Xunity__coeff__ex__1__1(B,A,tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_RealDef_Oreal) | -hBOOL(hAPP(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))). [resolve(465,a,462,b)].
% 2.06/2.31 Derived: -class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) | hBOOL(hAPP(A,c_List_Osko__Presburger__Xunity__coeff__ex__1__1(A,B,tc_RealDef_Oreal))) | -hBOOL(hAPP(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C))). [resolve(465,a,464,b)].
% 2.06/2.31 466 class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.06/2.35 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex)),E),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),E),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_Complex_Ocomplex). [resolve(466,a,460,a)].
% 2.06/2.35 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),E),tc_Complex_Ocomplex)),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_Complex_Ocomplex). [resolve(466,a,461,a)].
% 2.06/2.35 Derived: -class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) | c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_List_Osko__Presburger__Xunity__coeff__ex__1__1(B,A,tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) | -hBOOL(hAPP(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C))). [resolve(466,a,462,b)].
% 2.06/2.35 Derived: -class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) | hBOOL(hAPP(A,c_List_Osko__Presburger__Xunity__coeff__ex__1__1(A,B,tc_Complex_Ocomplex))) | -hBOOL(hAPP(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C))). [resolve(466,a,464,b)].
% 2.06/2.35 467 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 2.06/2.35 468 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 2.06/2.35 469 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 2.06/2.35 470 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 2.06/2.35 471 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 2.06/2.35 472 -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].
% 2.06/2.35 473 -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].
% 2.06/2.35 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal). [resolve(467,a,468,a)].
% 2.06/2.35 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(467,a,472,a)].
% 2.06/2.35 474 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 2.06/2.35 475 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,B,A),A) # label(cls_abs__minus__commute_0) # label(axiom). [assumption].
% 2.06/2.35 476 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__neg_0) # label(axiom). [assumption].
% 2.06/2.35 477 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__minus__cancel_0) # label(axiom). [assumption].
% 2.06/2.35 478 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__idempotent_0) # label(axiom). [assumption].
% 2.06/2.35 479 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_1) # label(axiom). [assumption].
% 2.06/2.35 480 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(B,A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__abs__iff_1) # label(axiom). [assumption].
% 2.06/2.35 481 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__not__less__zero_0) # label(axiom). [assumption].
% 2.06/2.35 482 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__pos_0) # label(axiom). [assumption].
% 2.06/2.35 483 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)) # label(cls_abs__add__abs_0) # label(axiom). [assumption].
% 2.06/2.35 484 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_0) # label(axiom). [assumption].
% 2.06/2.35 485 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A),A) # label(cls_zero__less__abs__iff_0) # label(axiom). [assumption].
% 2.06/2.35 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(474,a,475,a)].
% 2.06/2.35 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(474,a,476,a)].
% 2.06/2.35 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal). [resolve(474,a,477,a)].
% 2.06/2.35 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal). [resolve(474,a,478,a)].
% 2.06/2.35 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(474,a,479,a)].
% 2.06/2.35 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(474,a,480,a)].
% 2.06/2.35 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(474,a,481,a)].
% 2.06/2.35 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(474,a,482,a)].
% 2.16/2.41 Derived: c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal)),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal)),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal)),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal)). [resolve(474,a,483,a)].
% 2.16/2.41 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(474,a,484,a)].
% 2.16/2.41 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(474,a,485,a)].
% 2.16/2.41 486 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 2.16/2.41 487 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 2.16/2.41 488 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 2.16/2.41 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != A | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(486,a,487,a)].
% 2.16/2.41 489 class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 2.16/2.41 490 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ominus__class_Ominus(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__diff_0) # label(axiom). [assumption].
% 2.16/2.41 491 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_dvd__minus__iff_0) # label(axiom). [assumption].
% 2.16/2.41 492 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__minus__iff_1) # label(axiom). [assumption].
% 2.16/2.41 493 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__dvd__iff_0) # label(axiom). [assumption].
% 2.16/2.41 494 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_minus__dvd__iff_1) # label(axiom). [assumption].
% 2.16/2.41 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(489,a,490,a)].
% 2.16/2.41 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(489,a,491,a)].
% 2.16/2.41 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(489,a,492,a)].
% 2.16/2.41 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(489,a,493,a)].
% 2.16/2.41 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(489,a,494,a)].
% 2.16/2.41 495 class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 2.20/2.47 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex). [resolve(495,a,490,a)].
% 2.20/2.47 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(495,a,491,a)].
% 2.20/2.47 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex). [resolve(495,a,492,a)].
% 2.20/2.47 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(495,a,493,a)].
% 2.20/2.47 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex). [resolve(495,a,494,a)].
% 2.20/2.47 496 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 2.20/2.47 497 -class_Ring__and__Field_Oabs__if(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_0) # label(axiom). [assumption].
% 2.20/2.47 498 -class_Ring__and__Field_Oabs__if(A) | c_HOL_Oabs__class_Oabs(B,A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_1) # label(axiom). [assumption].
% 2.20/2.47 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(496,a,498,a)].
% 2.20/2.47 499 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Oadditive(c_RealVector_OscaleR__class_OscaleR(B,A),A,A) # label(cls_scaleR_Oadditive__right_0) # label(axiom). [assumption].
% 2.20/2.47 500 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,c_HOL_Ominus__class_Ominus(D,E,A)) = c_HOL_Ominus__class_Ominus(hAPP(C,D),hAPP(C,E),B) | -c_RealVector_Oadditive(C,A,B) # label(cls_additive_Odiff_0) # label(axiom). [assumption].
% 2.20/2.47 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ominus__class_Ominus(C,D,A)) = c_HOL_Ominus__class_Ominus(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D),A). [resolve(499,b,500,d)].
% 2.20/2.47 501 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(B),hAPP(C,D)),hAPP(C,E)) | -c_RealVector_Oadditive(C,A,B) # label(cls_additive_Oadd_0) # label(axiom). [assumption].
% 2.20/2.47 502 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,c_HOL_Ouminus__class_Ouminus(D,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(C,D),B) | -c_RealVector_Oadditive(C,A,B) # label(cls_additive_Ominus_0) # label(axiom). [assumption].
% 2.20/2.47 Derived: -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A) | -class_RealVector_Oreal__normed__vector(A). [resolve(502,d,499,b)].
% 2.20/2.47 503 -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(B) | hAPP(C,c_HOL_Ozero__class_Ozero(B)) = c_HOL_Ozero__class_Ozero(A) | -c_RealVector_Oadditive(C,B,A) # label(cls_additive_Ozero_0) # label(axiom). [assumption].
% 2.20/2.47 Derived: -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) | -class_RealVector_Oreal__normed__vector(A). [resolve(503,d,499,b)].
% 2.20/2.52 504 -class_RealVector_Oreal__normed__algebra(A) | c_RealVector_Oadditive(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A) # label(cls_mult_Oadditive__right_0) # label(axiom). [assumption].
% 2.20/2.52 Derived: -class_RealVector_Oreal__normed__algebra(A) | -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(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)). [resolve(504,b,501,d)].
% 2.20/2.52 Derived: -class_RealVector_Oreal__normed__algebra(A) | -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A). [resolve(504,b,502,d)].
% 2.20/2.52 Derived: -class_RealVector_Oreal__normed__algebra(A) | -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A). [resolve(504,b,503,d)].
% 2.20/2.52 505 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.20/2.52 506 -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].
% 2.20/2.52 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(505,a,506,a)].
% 2.20/2.52 507 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.20/2.52 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B = C. [resolve(507,a,506,a)].
% 2.20/2.52 508 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.20/2.52 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(508,a,506,a)].
% 2.20/2.52 509 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.20/2.52 510 -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].
% 2.20/2.52 511 -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].
% 2.20/2.52 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(509,a,511,a)].
% 2.20/2.52 512 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.20/2.52 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B) | A = C. [resolve(512,a,511,a)].
% 2.20/2.52 513 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.20/2.52 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B) | A = C. [resolve(513,a,511,a)].
% 2.20/2.52 514 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.20/2.52 515 -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].
% 2.30/2.54 516 -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].
% 2.30/2.54 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(514,a,515,a)].
% 2.30/2.54 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(514,a,516,a)].
% 2.30/2.54 517 class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.30/2.54 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal)). [resolve(517,a,515,a)].
% 2.30/2.54 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_RealDef_Oreal)). [resolve(517,a,516,a)].
% 2.30/2.54 518 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.30/2.54 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)). [resolve(518,a,515,a)].
% 2.30/2.54 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)). [resolve(518,a,516,a)].
% 2.30/2.54 519 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.30/2.54 520 -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].
% 2.30/2.54 521 -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].
% 2.30/2.54 522 -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].
% 2.30/2.54 523 -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].
% 2.30/2.54 524 -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].
% 2.30/2.54 525 -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].
% 2.30/2.54 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(519,a,520,a)].
% 2.30/2.54 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(519,a,521,a)].
% 2.30/2.54 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(519,a,523,a)].
% 2.30/2.58 526 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.30/2.58 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(526,a,520,a)].
% 2.30/2.58 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal)),A). [resolve(526,a,521,a)].
% 2.30/2.58 Derived: c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(526,a,523,a)].
% 2.30/2.58 527 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.30/2.58 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(527,a,520,a)].
% 2.30/2.58 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex)),A). [resolve(527,a,521,a)].
% 2.30/2.58 Derived: c_Power_Opower__class_Opower(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex). [resolve(527,a,523,a)].
% 2.30/2.58 528 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.30/2.58 529 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(A),A,A) # label(cls_comm__monoid__add_Ofun__left__comm_0) # label(axiom). [assumption].
% 2.30/2.58 530 -class_OrderedGroup_Ocomm__monoid__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_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 2.30/2.58 531 -class_OrderedGroup_Ocomm__monoid__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_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 2.30/2.58 532 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 2.30/2.58 533 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 2.30/2.58 534 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 2.30/2.58 Derived: c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat). [resolve(528,a,529,a)].
% 2.30/2.58 535 class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.30/2.58 Derived: c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(535,a,529,a)].
% 2.30/2.58 536 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.30/2.58 Derived: c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(536,a,529,a)].
% 2.30/2.58 537 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Obounded__linear(c_RealVector_OscaleR__class_OscaleR(B,A),A,A) # label(cls_scaleR_Obounded__linear__right_0) # label(axiom). [assumption].
% 2.36/2.60 538 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | hAPP(C,hAPP(c_RealVector_OscaleR__class_OscaleR(D,A),E)) = hAPP(c_RealVector_OscaleR__class_OscaleR(D,B),hAPP(C,E)) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_OscaleR_0) # label(axiom). [assumption].
% 2.36/2.60 539 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OisCont(C,D,A,B) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_OisCont_0) # label(axiom). [assumption].
% 2.36/2.60 540 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(C,D,hAPP(C,D),A,B) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_Ocont_0) # label(axiom). [assumption].
% 2.36/2.60 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)). [resolve(537,b,538,d)].
% 2.36/2.60 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | c_Lim_OisCont(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A). [resolve(537,b,539,d)].
% 2.36/2.60 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | c_Lim_OLIM(c_RealVector_OscaleR__class_OscaleR(B,A),C,hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A,A). [resolve(537,b,540,d)].
% 2.36/2.60 541 -class_RealVector_Oreal__normed__algebra(A) | c_RealVector_Obounded__linear(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A) # label(cls_mult_Obounded__linear__right_0) # label(axiom). [assumption].
% 2.36/2.60 Derived: -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)). [resolve(541,b,538,d)].
% 2.36/2.60 542 class_RealVector_Oreal__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__field) # label(axiom). [assumption].
% 2.36/2.60 543 -class_RealVector_Oreal__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A),F,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(C,E,A),F,A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,D,A),F,A)),E)) # label(cls_DERIV__mult__lemma_0) # label(axiom). [assumption].
% 2.36/2.60 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal),E,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),E,tc_RealDef_Oreal))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),E,tc_RealDef_Oreal)),D)). [resolve(542,a,543,a)].
% 2.36/2.60 544 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 2.36/2.60 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex),E,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex)),D)). [resolve(544,a,543,a)].
% 2.36/2.61 545 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.36/2.61 546 -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),c_HOL_Ominus__class_Ominus(B,E,A)),C)),D)) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 2.36/2.61 547 -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),c_HOL_Ominus__class_Ominus(D,B,A)),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].
% 2.36/2.61 548 -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),c_HOL_Ominus__class_Ominus(B,E,A)),C)),D) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 2.36/2.61 549 -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),c_HOL_Ominus__class_Ominus(E,B,A)),C)),F) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 2.36/2.61 550 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ominus__class_Ominus(C,D,A)) = c_HOL_Ominus__class_Ominus(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_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I20_J_0) # label(axiom). [assumption].
% 2.36/2.61 551 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,C,A)),D) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I19_J_0) # label(axiom). [assumption].
% 2.36/2.61 552 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 2.36/2.61 553 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),c_HOL_Ouminus__class_Ouminus(C,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 2.36/2.61 554 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 2.36/2.61 555 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 2.36/2.61 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal)),B)),C)). [resolve(545,a,546,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(C,A,tc_RealDef_Oreal)),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)),D). [resolve(545,a,547,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal)),B)),C) = E. [resolve(545,a,548,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E) | C = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(D,A,tc_RealDef_Oreal)),B)),E). [resolve(545,a,549,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(545,a,550,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal)),C) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(545,a,551,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)). [resolve(545,a,552,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B). [resolve(545,a,553,a)].
% 2.36/2.62 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)). [resolve(545,a,554,a)].
% 2.36/2.62 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),B). [resolve(545,a,555,a)].
% 2.36/2.62 556 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(A,D,tc_Complex_Ocomplex)),B)),C)). [resolve(556,a,546,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(C,A,tc_Complex_Ocomplex)),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),D). [resolve(556,a,547,a)].
% 2.36/2.63 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(A,D,tc_Complex_Ocomplex)),B)),C) = E. [resolve(556,a,548,a)].
% 2.36/2.63 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),E) | C = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(D,A,tc_Complex_Ocomplex)),B)),E). [resolve(556,a,549,a)].
% 2.36/2.63 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(556,a,550,a)].
% 2.36/2.63 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex)),C) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11). [resolve(556,a,551,a)].
% 2.36/2.63 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)). [resolve(556,a,552,a)].
% 2.36/2.63 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B). [resolve(556,a,553,a)].
% 2.36/2.63 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)). [resolve(556,a,554,a)].
% 2.36/2.63 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B). [resolve(556,a,555,a)].
% 2.36/2.63 557 -class_RealVector_Ometric__space(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(C,D,hAPP(C,D),A,B) | -c_Lim_OisCont(C,D,A,B) # label(cls_isCont__def_0) # label(axiom). [assumption].
% 2.36/2.63 558 -class_RealVector_Oreal__normed__vector(A) | c_Lim_OisCont(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A) # label(cls_scaleR__right_OisCont_0) # label(axiom). [assumption].
% 2.36/2.63 559 -class_RealVector_Ometric__space(A) | -class_RealVector_Ometric__space(B) | c_Lim_OisCont(C,D,A,B) | -c_Lim_OLIM(C,D,hAPP(C,D),A,B) # label(cls_isCont__def_1) # label(axiom). [assumption].
% 2.36/2.63 560 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OisCont(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A) # label(cls_mult__right_OisCont_0) # label(axiom). [assumption].
% 2.36/2.63 Derived: -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(A) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A,A). [resolve(560,b,557,d)].
% 2.36/2.63 561 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(A) | -class_RealVector_Ometric__space(A) | c_Lim_OisCont(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A). [resolve(3,b,1,d)].
% 2.42/2.69 562 c_Lim_OisCont(A,B,tc_RealDef_Oreal,tc_RealDef_Oreal) | -c_Deriv_Oderiv(A,B,C,tc_RealDef_Oreal). [resolve(139,a,142,a)].
% 2.42/2.69 Derived: -c_Deriv_Oderiv(A,B,C,tc_RealDef_Oreal) | -class_RealVector_Ometric__space(tc_RealDef_Oreal) | -class_RealVector_Ometric__space(tc_RealDef_Oreal) | c_Lim_OLIM(A,B,hAPP(A,B),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(562,a,557,d)].
% 2.42/2.69 563 c_Lim_OisCont(A,B,tc_Complex_Ocomplex,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex). [resolve(149,a,142,a)].
% 2.42/2.69 Derived: -c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(tc_Complex_Ocomplex) | c_Lim_OLIM(A,B,hAPP(A,B),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(563,a,557,d)].
% 2.42/2.69 564 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | c_Lim_OisCont(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A). [resolve(537,b,539,d)].
% 2.42/2.69 565 -class_OrderedGroup_Oab__semigroup__mult(A) | c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(A),A,A) # label(cls_fun__left__comm_0) # label(axiom). [assumption].
% 2.42/2.69 566 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Finite__Set_Ofun__left__comm(A,E,F) # label(cls_fun__left__comm_Ofun__left__comm_0) # label(axiom). [assumption].
% 2.42/2.69 Derived: -class_OrderedGroup_Oab__semigroup__mult(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)). [resolve(565,b,566,b)].
% 2.42/2.69 567 c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat). [resolve(528,a,529,a)].
% 2.42/2.69 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(567,a,566,b)].
% 2.42/2.69 568 c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(535,a,529,a)].
% 2.42/2.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)). [resolve(568,a,566,b)].
% 2.42/2.69 569 c_Finite__Set_Ofun__left__comm(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(536,a,529,a)].
% 2.42/2.69 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)). [resolve(569,a,566,b)].
% 2.42/2.69 570 class_Orderings_Oorder(tc_nat) # label(clsarity_nat__Orderings_Oorder) # label(axiom). [assumption].
% 2.42/2.69 571 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_xt1_I10_J_0) # label(axiom). [assumption].
% 2.42/2.69 572 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__le_1) # label(axiom). [assumption].
% 2.42/2.69 573 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_xt1_I9_J_0) # label(axiom). [assumption].
% 2.42/2.69 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(570,a,571,a)].
% 2.42/2.69 574 class_Orderings_Oorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Oorder) # label(axiom). [assumption].
% 2.42/2.69 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal). [resolve(574,a,571,a)].
% 2.42/2.69 575 class_Orderings_Opreorder(tc_nat) # label(clsarity_nat__Orderings_Opreorder) # label(axiom). [assumption].
% 2.42/2.69 576 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_order__less__trans_0) # label(axiom). [assumption].
% 2.48/2.72 577 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__irrefl_0) # label(axiom). [assumption].
% 2.48/2.72 578 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_0) # label(axiom). [assumption].
% 2.48/2.72 579 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_H_0) # label(axiom). [assumption].
% 2.48/2.72 580 class_Orderings_Opreorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Opreorder) # label(axiom). [assumption].
% 2.48/2.72 581 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 2.48/2.72 582 -class_OrderedGroup_Osemigroup__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)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I40_J_0) # label(axiom). [assumption].
% 2.48/2.72 583 class_OrderedGroup_Osemigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 2.48/2.72 584 class_OrderedGroup_Osemigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 2.48/2.72 585 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 2.48/2.72 586 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),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_HOL_Ominus__class_Ominus(B,D,A)),c_HOL_Ominus__class_Ominus(C,E,A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,D,A)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_HOL_Ominus__class_Ominus(C,E,A))) # label(cls_mult_Oprod__diff__prod_0) # label(axiom). [assumption].
% 2.48/2.72 587 -class_RealVector_Oreal__normed__algebra(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__right_Ozero_0) # label(axiom). [assumption].
% 2.48/2.72 588 -class_RealVector_Oreal__normed__algebra(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_Ozero__right_0) # label(axiom). [assumption].
% 2.48/2.72 589 -class_RealVector_Oreal__normed__algebra(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_Ozero__left_0) # label(axiom). [assumption].
% 2.48/2.72 590 -class_RealVector_Oreal__normed__algebra(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__left_Ozero_0) # label(axiom). [assumption].
% 2.48/2.72 591 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult__right_OscaleR_0) # label(axiom). [assumption].
% 2.48/2.72 592 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult_OscaleR__right_0) # label(axiom). [assumption].
% 2.48/2.72 593 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult__left_OscaleR_0) # label(axiom). [assumption].
% 2.48/2.72 594 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult_OscaleR__left_0) # label(axiom). [assumption].
% 2.48/2.72 595 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 2.48/2.72 596 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 2.48/2.72 597 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 2.48/2.72 598 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 2.48/2.72 599 -class_RealVector_Oreal__normed__algebra(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_mult_Oadd__left_0) # label(axiom). [assumption].
% 2.48/2.72 600 -class_RealVector_Oreal__normed__algebra(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_mult__left_Oadd_0) # label(axiom). [assumption].
% 2.48/2.72 601 -class_RealVector_Oreal__normed__algebra(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_mult_Oadd__right_0) # label(axiom). [assumption].
% 2.48/2.72 602 -class_RealVector_Oreal__normed__algebra(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_mult__right_Oadd_0) # label(axiom). [assumption].
% 2.48/2.72 603 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A,A) # label(cls_mult__right_Ocont_0) # label(axiom). [assumption].
% 2.48/2.72 604 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ominus__class_Ominus(C,D,A)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__right_Odiff_0) # label(axiom). [assumption].
% 2.48/2.72 605 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ominus__class_Ominus(C,D,A)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult_Odiff__right_0) # label(axiom). [assumption].
% 2.48/2.72 606 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,C,A)),D) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult_Odiff__left_0) # label(axiom). [assumption].
% 2.48/2.72 607 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,C,A)),D) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__left_Odiff_0) # label(axiom). [assumption].
% 2.48/2.73 Derived: c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal)),c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal)),D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal))). [resolve(585,a,586,a)].
% 2.48/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(585,a,591,a)].
% 2.48/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)),C) = hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(585,a,593,a)].
% 2.48/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal). [resolve(585,a,595,a)].
% 2.48/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),B) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal). [resolve(585,a,597,a)].
% 2.48/2.73 Derived: c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(585,a,603,a)].
% 2.48/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal). [resolve(585,a,604,a)].
% 2.48/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal)),C) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal). [resolve(585,a,606,a)].
% 2.48/2.73 608 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 2.48/2.73 Derived: c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex)),D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex))). [resolve(608,a,586,a)].
% 2.48/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_Complex_Ocomplex),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(608,a,591,a)].
% 2.48/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B)),C) = hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(608,a,593,a)].
% 2.48/2.74 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex). [resolve(608,a,595,a)].
% 2.48/2.74 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex). [resolve(608,a,597,a)].
% 2.48/2.74 Derived: c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(608,a,603,a)].
% 2.48/2.74 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex). [resolve(608,a,604,a)].
% 2.48/2.74 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex)),C) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex). [resolve(608,a,606,a)].
% 2.48/2.74 609 -class_RealVector_Oreal__normed__algebra(A) | -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(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)). [resolve(504,b,501,d)].
% 2.48/2.74 Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(609,a,585,a)].
% 2.48/2.74 Derived: -class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) | -class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(609,a,608,a)].
% 2.48/2.74 610 -class_RealVector_Oreal__normed__algebra(A) | -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A). [resolve(504,b,502,d)].
% 2.48/2.74 611 -class_RealVector_Oreal__normed__algebra(A) | -class_OrderedGroup_Oab__group__add(A) | -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A). [resolve(504,b,503,d)].
% 2.48/2.74 Derived: -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | -class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(611,a,585,a)].
% 2.48/2.74 Derived: -class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) | -class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(611,a,608,a)].
% 2.48/2.74 612 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)). [resolve(541,b,538,d)].
% 2.52/2.76 613 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(A) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A,A). [resolve(560,b,557,d)].
% 2.52/2.76 614 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.52/2.76 615 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 2.52/2.76 616 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 2.52/2.76 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(614,a,615,a)].
% 2.52/2.76 617 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.52/2.76 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(617,a,615,a)].
% 2.52/2.76 618 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 2.52/2.76 619 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,C,A)),D)),E),F,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F),A) # label(cls_less__add__iff1_0) # label(axiom). [assumption].
% 2.52/2.76 620 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(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),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,E,A)),C)),D),F,A) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 2.52/2.76 621 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(C,D,A)),E)),F),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F),A) # label(cls_less__add__iff2_0) # label(axiom). [assumption].
% 2.52/2.76 622 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(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),A) | -c_HOL_Oord__class_Oless(D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(E,B,A)),C)),F),A) # label(cls_less__add__iff2_1) # label(axiom). [assumption].
% 2.52/2.76 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal)),C)),D),E,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)),E),tc_RealDef_Oreal). [resolve(618,a,619,a)].
% 2.52/2.78 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal)),B)),C),E,tc_RealDef_Oreal). [resolve(618,a,620,a)].
% 2.52/2.78 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal)),D)),E),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)),E),tc_RealDef_Oreal). [resolve(618,a,621,a)].
% 2.52/2.78 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),D),B)),E),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(D,A,tc_RealDef_Oreal)),B)),E),tc_RealDef_Oreal). [resolve(618,a,622,a)].
% 2.52/2.78 623 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.52/2.78 624 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 2.52/2.78 625 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 2.52/2.78 626 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 2.52/2.78 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(623,a,624,a)].
% 2.52/2.78 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(623,a,625,a)].
% 2.52/2.78 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(623,a,626,a)].
% 2.52/2.78 627 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.52/2.78 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(627,a,624,a)].
% 2.52/2.84 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(627,a,625,a)].
% 2.52/2.84 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(627,a,626,a)].
% 2.52/2.84 628 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 2.52/2.84 629 -class_RealVector_Oreal__normed__div__algebra(A) | c_Lim_OLIM(c_HOL_Oinverse__class_Oinverse(A),B,hAPP(c_HOL_Oinverse__class_Oinverse(A),B),A,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_LIM__inverse__fun_0) # label(axiom). [assumption].
% 2.52/2.84 Derived: c_Lim_OLIM(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A,hAPP(c_HOL_Oinverse__class_Oinverse(tc_RealDef_Oreal),A),tc_RealDef_Oreal,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(628,a,629,a)].
% 2.52/2.84 630 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 2.52/2.84 Derived: c_Lim_OLIM(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A,hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(630,a,629,a)].
% 2.52/2.84 631 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 2.52/2.84 632 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 2.52/2.84 633 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 2.52/2.84 634 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.52/2.84 635 -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].
% 2.52/2.84 636 -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].
% 2.52/2.84 637 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.52/2.84 638 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.52/2.84 639 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.52/2.84 640 -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].
% 2.52/2.84 641 -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].
% 2.52/2.84 642 -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].
% 2.61/2.88 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(639,a,642,a)].
% 2.61/2.88 643 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.61/2.88 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(643,a,642,a)].
% 2.61/2.88 644 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.61/2.88 645 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 2.61/2.88 646 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 2.61/2.88 647 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 2.61/2.88 648 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 2.61/2.88 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(644,a,645,a)].
% 2.61/2.88 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(644,a,647,a)].
% 2.61/2.88 649 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.61/2.88 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal). [resolve(649,a,645,a)].
% 2.61/2.88 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal). [resolve(649,a,647,a)].
% 2.61/2.88 650 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.61/2.88 651 -class_OrderedGroup_Oab__semigroup__mult(A) | c_OrderedGroup_Oab__semigroup__mult__axioms(c_HOL_Otimes__class_Otimes(A),A) # label(cls_ab__semigroup__mult__class_Oaxioms_0) # label(axiom). [assumption].
% 2.61/2.88 652 -class_OrderedGroup_Oab__semigroup__mult(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)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I35_J_0) # label(axiom). [assumption].
% 2.61/2.88 653 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) | -c_Ring__and__Field_Ofield(D,E,F,V6,V7,V8,V9,V10,V11) # label(cls_field_Ofield__eq__simps_I36_J_0) # label(axiom). [assumption].
% 2.66/2.92 654 -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].
% 2.66/2.92 Derived: c_OrderedGroup_Oab__semigroup__mult__axioms(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat). [resolve(650,a,651,a)].
% 2.66/2.92 655 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.66/2.92 Derived: c_OrderedGroup_Oab__semigroup__mult__axioms(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(655,a,651,a)].
% 2.66/2.92 656 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.66/2.92 Derived: c_OrderedGroup_Oab__semigroup__mult__axioms(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(656,a,651,a)].
% 2.66/2.92 657 -class_OrderedGroup_Oab__semigroup__mult(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)). [resolve(565,b,566,b)].
% 2.66/2.92 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(657,a,650,a)].
% 2.66/2.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(657,a,655,a)].
% 2.66/2.92 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(657,a,656,a)].
% 2.66/2.92 658 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra) # label(axiom). [assumption].
% 2.66/2.92 659 -class_RealVector_Oreal__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult__scaleR__right_0) # label(axiom). [assumption].
% 2.66/2.92 660 -class_RealVector_Oreal__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult__scaleR__left_0) # label(axiom). [assumption].
% 2.66/2.92 661 class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) # label(axiom). [assumption].
% 2.66/2.92 662 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.66/2.92 663 -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].
% 2.66/2.92 664 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.66/2.92 665 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.66/2.92 666 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.66/2.92 667 -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].
% 3.31/3.55 668 -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].
% 3.31/3.55 669 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.31/3.55 670 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.31/3.55 671 class_OrderedGroup_Osemigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__mult) # label(axiom). [assumption].
% 3.31/3.55 672 -class_OrderedGroup_Osemigroup__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)) | -c_Ring__and__Field_Ofield(E,F,V6,V7,V8,V9,V10,V11,V12) # label(cls_field_Ofield__eq__simps_I37_J_0) # label(axiom). [assumption].
% 3.31/3.55 673 class_OrderedGroup_Osemigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__mult) # label(axiom). [assumption].
% 3.31/3.55 674 class_OrderedGroup_Osemigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Osemigroup__mult) # label(axiom). [assumption].
% 3.31/3.55 675 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 3.31/3.55 676 -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].
% 3.31/3.55 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(675,a,676,a)].
% 3.31/3.55 677 class_Nat_Osemiring__char__0(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 3.31/3.55 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_RealDef_Oreal) | A = B. [resolve(677,a,676,a)].
% 3.31/3.55 678 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 3.31/3.55 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex) | A = B. [resolve(678,a,676,a)].
% 3.31/3.55 679 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 3.31/3.55 680 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 3.31/3.55 Derived: A = A. [resolve(679,b,680,a)].
% 3.31/3.55
% 3.31/3.55 ============================== end predicate elimination =============
% 3.31/3.55
% 3.31/3.55 Auto_denials: (non-Horn, no changes).
% 3.31/3.55
% 3.31/3.55 Term ordering decisions:
% 3.31/3.55 Function symbol KB weights: tc_RealDef_Oreal=1. tc_Complex_Ocomplex=1. tc_nat=1. v_n=1. t_a=1. v_c=1. v_i=1. v_a=1. hAPP=1. c_HOL_Ouminus__class_Ouminus=1. c_RealVector_OscaleR__class_OscaleR=1. c_HOL_Oabs__class_Oabs=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_FFT__Mirabelle_ODFT=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Oinverse__class_Oinverse=1. c_HOL_Oone__class_Oone=1. c_Suc=1. c_Complex_Ocnj=1. c_HOL_Oinverse__class_Odivide=1. c_HOL_Ominus__class_Ominus=1. c_Power_Opower__class_Opower=1. c_Divides_Odiv__class_Omod=1. c_List_Osko__Presburger__Xunity__coeff__ex__1__1=1. c_Transcendental_Odiffs=1. c_FFT__Mirabelle_OIDFT=1.
% 3.31/3.55
% 3.31/3.55 ============================== end of process initial clauses ========
% 3.31/3.55
% 3.31/3.55 ============================== CLAUSES FOR SEARCH ====================
% 3.31/3.55
% 3.31/3.55 ============================== end of clauses for search =============
% 3.31/3.55
% 3.31/3.55 ============================== SEARCH ================================
% 3.31/3.55
% 3.31/3.55 % Starting search at 1.63 seconds.
% 3.31/3.55
% 3.31/3.55 Low Water (keep): wt=64.000, iters=3556
% 3.31/3.55
% 3.31/3.55 Low Water (keep): wt=58.000, iters=3461
% 3.31/3.55
% 3.31/3.55 Low Water (keep): wt=52.0Cputime limit exceeded (core dumped)
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