TSTP Solution File: SWV687-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV687-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 21:14:26 EDT 2022
% Result : Unsatisfiable 27.60s 27.83s
% Output : Refutation 27.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV687-1 : TPTP v8.1.0. Released v4.1.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 21:24:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.69/1.95 ============================== Prover9 ===============================
% 1.69/1.95 Prover9 (32) version 2009-11A, November 2009.
% 1.69/1.95 Process 19210 was started by sandbox2 on n028.cluster.edu,
% 1.69/1.95 Wed Jun 15 21:24:12 2022
% 1.69/1.95 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19057_n028.cluster.edu".
% 1.69/1.95 ============================== end of head ===========================
% 1.69/1.95
% 1.69/1.95 ============================== INPUT =================================
% 1.69/1.95
% 1.69/1.95 % Reading from file /tmp/Prover9_19057_n028.cluster.edu
% 1.69/1.95
% 1.69/1.95 set(prolog_style_variables).
% 1.69/1.95 set(auto2).
% 1.69/1.95 % set(auto2) -> set(auto).
% 1.69/1.95 % set(auto) -> set(auto_inference).
% 1.69/1.95 % set(auto) -> set(auto_setup).
% 1.69/1.95 % set(auto_setup) -> set(predicate_elim).
% 1.69/1.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.69/1.95 % set(auto) -> set(auto_limits).
% 1.69/1.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.69/1.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.69/1.95 % set(auto) -> set(auto_denials).
% 1.69/1.95 % set(auto) -> set(auto_process).
% 1.69/1.95 % set(auto2) -> assign(new_constants, 1).
% 1.69/1.95 % set(auto2) -> assign(fold_denial_max, 3).
% 1.69/1.95 % set(auto2) -> assign(max_weight, "200.000").
% 1.69/1.95 % set(auto2) -> assign(max_hours, 1).
% 1.69/1.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.69/1.95 % set(auto2) -> assign(max_seconds, 0).
% 1.69/1.95 % set(auto2) -> assign(max_minutes, 5).
% 1.69/1.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.69/1.95 % set(auto2) -> set(sort_initial_sos).
% 1.69/1.95 % set(auto2) -> assign(sos_limit, -1).
% 1.69/1.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.69/1.95 % set(auto2) -> assign(max_megs, 400).
% 1.69/1.95 % set(auto2) -> assign(stats, some).
% 1.69/1.95 % set(auto2) -> clear(echo_input).
% 1.69/1.95 % set(auto2) -> set(quiet).
% 1.69/1.95 % set(auto2) -> clear(print_initial_clauses).
% 1.69/1.95 % set(auto2) -> clear(print_given).
% 1.69/1.95 assign(lrs_ticks,-1).
% 1.69/1.95 assign(sos_limit,10000).
% 1.69/1.95 assign(order,kbo).
% 1.69/1.95 set(lex_order_vars).
% 1.69/1.95 clear(print_given).
% 1.69/1.95
% 1.69/1.95 % formulas(sos). % not echoed (1402 formulas)
% 1.69/1.95
% 1.69/1.95 ============================== end of input ==========================
% 1.69/1.95
% 1.69/1.95 % From the command line: assign(max_seconds, 300).
% 1.69/1.95
% 1.69/1.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.69/1.95
% 1.69/1.95 % Formulas that are not ordinary clauses:
% 1.69/1.95
% 1.69/1.95 ============================== end of process non-clausal formulas ===
% 1.69/1.95
% 1.69/1.95 ============================== PROCESS INITIAL CLAUSES ===============
% 1.69/1.95
% 1.69/1.95 ============================== PREDICATE ELIMINATION =================
% 1.69/1.95 1 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.69/1.95 2 -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].
% 1.69/1.95 3 -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].
% 1.69/1.95 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(1,a,2,a)].
% 1.69/1.95 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(1,a,3,a)].
% 1.69/1.95 4 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.69/1.95 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(4,a,2,a)].
% 1.69/1.95 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(4,a,3,a)].
% 1.69/1.95 5 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.69/1.95 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(5,a,2,a)].
% 1.69/1.95 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(5,a,3,a)].
% 1.69/1.95 6 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.69/1.95 7 -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].
% 1.69/1.95 8 -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].
% 1.69/1.95 9 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.69/1.95 10 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.69/1.95 11 -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].
% 1.69/1.95 12 -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].
% 1.69/1.95 13 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))),hAPP(B,D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_setsum__op__ivl__Suc_1) # label(axiom). [assumption].
% 1.69/1.95 14 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),D,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) # label(cls_setsum__head__upt__Suc_0) # label(axiom). [assumption].
% 1.69/1.95 15 -class_HOL_Oord(A) | -class_OrderedGroup_Ocomm__monoid__add(B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,B),C),c_SetInterval_Oord__class_OatLeastLessThan(D,E,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,B),F),c_SetInterval_Oord__class_OatLeastLessThan(D,E,A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(D,E,C,F,A,B),A),E)) # label(cls_setsum__ivl__cong_1) # label(axiom). [assumption].
% 1.69/1.95 16 -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].
% 1.69/1.95 17 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,hAPP(c_Suc,D),tc_nat)) = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_setsum__op__ivl__Suc_0) # label(axiom). [assumption].
% 1.69/1.95 18 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(c_COMBB(B,tc_nat,A,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),D))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat))) # label(cls_sumr__offset3_0) # label(axiom). [assumption].
% 1.69/1.95 19 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.69/1.95 20 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.69/1.95 21 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),B),C),D,B,A,A)),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),E)),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),D),E)) # label(cls_setsum__addf_0) # label(axiom). [assumption].
% 1.69/1.95 22 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(D,B) # label(cls_setsum__infinite_0) # label(axiom). [assumption].
% 1.69/1.95 23 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(D,B) # label(cls_setsum__def_1) # label(axiom). [assumption].
% 1.69/1.95 24 -class_HOL_Oord(A) | -class_OrderedGroup_Ocomm__monoid__add(B) | hAPP(C,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(D,E,C,F,A,B)) != hAPP(F,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(D,E,C,F,A,B)) | hAPP(hAPP(c_Finite__Set_Osetsum(A,B),C),c_SetInterval_Oord__class_OatLeastLessThan(D,E,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,B),F),c_SetInterval_Oord__class_OatLeastLessThan(D,E,A)) # label(cls_setsum__ivl__cong_2) # label(axiom). [assumption].
% 1.69/1.95 25 -class_HOL_Oord(A) | -class_OrderedGroup_Ocomm__monoid__add(B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,B),C),c_SetInterval_Oord__class_OatLeastLessThan(D,E,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,B),F),c_SetInterval_Oord__class_OatLeastLessThan(D,E,A)) | hBOOL(hAPP(c_lessequals(D,A),c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(D,E,C,F,A,B))) # label(cls_setsum__ivl__cong_0) # label(axiom). [assumption].
% 1.69/1.95 26 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(D,E,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),E)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_setsum__add__nat__ivl_0) # label(axiom). [assumption].
% 1.69/1.95 27 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(A),tc_bool,tc_fun(A,tc_fun(A,A)),B),c_fequal(C,B)),D,B,A,tc_fun(A,A))),c_HOL_Ozero__class_Ozero(A))),E) = c_HOL_Ozero__class_Ozero(A) | c_in(C,E,B) | -c_Finite__Set_Ofinite(E,B) # label(cls_setsum__delta_H_1) # label(axiom). [assumption].
% 1.69/1.95 28 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(A),tc_bool,tc_fun(A,tc_fun(A,A)),B),c_fequal(C,B)),D,B,A,tc_fun(A,A))),c_HOL_Ozero__class_Ozero(A))),E) = hAPP(D,C) | -c_in(C,E,B) | -c_Finite__Set_Ofinite(E,B) # label(cls_setsum__delta_H_0) # label(axiom). [assumption].
% 1.69/1.95 29 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(c_COMBB(B,tc_nat,A,tc_nat),c_Suc)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat)) # label(cls_setsum__shift__bounds__Suc__ivl_0) # label(axiom). [assumption].
% 1.69/1.95 30 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) # label(cls_setsum__shift__lb__Suc0__0__upt_0) # label(axiom). [assumption].
% 1.69/1.95 31 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),E),D),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(c_COMBB(B,tc_nat,A,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),D))),c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat)) # label(cls_setsum__shift__bounds__nat__ivl_0) # label(axiom). [assumption].
% 1.69/1.95 32 -class_Power_Opower(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),hAPP(c_Power_Opower__class_Opower(A),B)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(A),C),tc_nat,A,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D)),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(A),B),tc_nat,A,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D))),hAPP(c_Power_Opower__class_Opower(A),C),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat)) # label(cls_lemma__realpow__rev__sumr_0) # label(axiom). [assumption].
% 1.69/1.95 33 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,tc_fun(C,tc_bool),A),hAPP(c_COMBB(c_Finite__Set_Osetsum(C,A),tc_fun(C,A),tc_fun(tc_fun(C,tc_bool),A),B),D)),E)),F) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(hAPP(c_COMBC(C,tc_fun(B,tc_bool),A),hAPP(c_COMBB(c_Finite__Set_Osetsum(B,A),tc_fun(B,A),tc_fun(tc_fun(B,tc_bool),A),C),hAPP(c_COMBC(B,C,A),D))),F)),E) # label(cls_setsum__commute_0) # label(axiom). [assumption].
% 1.69/1.95 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(6,a,9,b)].
% 1.69/1.95 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(6,a,10,b)].
% 1.69/1.95 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(6,a,11,a)].
% 1.69/1.95 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(6,a,12,a)].
% 1.69/1.95 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(A,C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(6,a,13,a)].
% 1.69/1.95 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(6,a,14,a)].
% 1.69/1.95 Derived: -class_HOL_Oord(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_nat),A),D)). [resolve(6,a,15,b)].
% 1.69/1.95 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(6,a,16,a)].
% 1.69/1.95 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(6,a,17,a)].
% 1.69/1.95 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(c_COMBB(A,tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))). [resolve(6,a,18,a)].
% 1.69/1.95 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(6,a,19,b)].
% 1.69/1.95 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)). [resolve(6,a,20,b)].
% 1.69/1.95 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),A),B),C,A,tc_nat,tc_nat)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),C),D)). [resolve(6,a,21,a)].
% 1.69/1.95 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Ofinite(C,A). [resolve(6,a,22,a)].
% 1.69/1.95 Derived: -class_HOL_Oord(A) | hAPP(B,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_nat)) != hAPP(E,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_nat)) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)). [resolve(6,a,24,b)].
% 1.69/1.95 Derived: -class_HOL_Oord(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) | hBOOL(hAPP(c_lessequals(C,A),c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_nat))). [resolve(6,a,25,b)].
% 1.69/1.95 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(6,a,26,a)].
% 1.69/1.95 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(6,a,27,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(C,B) | -c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(6,a,28,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(c_COMBB(A,tc_nat,tc_nat,tc_nat),c_Suc)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)). [resolve(6,a,29,a)].
% 1.69/1.96 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(6,a,30,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(c_COMBB(A,tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)). [resolve(6,a,31,a)].
% 1.69/1.96 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),B),tc_nat,tc_nat,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_nat,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),hAPP(c_Power_Opower__class_Opower(tc_nat),B),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)). [resolve(6,a,32,b)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_bool),tc_nat),hAPP(c_COMBB(c_Finite__Set_Osetsum(B,tc_nat),tc_fun(B,tc_nat),tc_fun(tc_fun(B,tc_bool),tc_nat),A),C)),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_bool),tc_nat),hAPP(c_COMBB(c_Finite__Set_Osetsum(A,tc_nat),tc_fun(A,tc_nat),tc_fun(tc_fun(A,tc_bool),tc_nat),B),hAPP(c_COMBC(A,B,tc_nat),C))),E)),D). [resolve(6,a,33,a)].
% 1.69/1.96 34 class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.69/1.96 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(34,a,9,b)].
% 1.69/1.96 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(34,a,10,b)].
% 1.69/1.96 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)). [resolve(34,a,11,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)). [resolve(34,a,12,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(A,C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(34,a,13,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(A,B)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(34,a,14,a)].
% 1.69/1.96 Derived: -class_HOL_Oord(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Int_Oint),A),D)). [resolve(34,a,15,b)].
% 1.69/1.96 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),A). [resolve(34,a,16,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(34,a,17,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),hAPP(c_COMBB(A,tc_nat,tc_Int_Oint,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))). [resolve(34,a,18,a)].
% 1.69/1.96 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(34,a,19,b)].
% 1.69/1.96 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)). [resolve(34,a,20,b)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),B),C,A,tc_Int_Oint,tc_Int_Oint)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),C),D)). [resolve(34,a,21,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Finite__Set_Ofinite(C,A). [resolve(34,a,22,a)].
% 1.69/1.96 Derived: -class_HOL_Oord(A) | hAPP(B,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Int_Oint)) != hAPP(E,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Int_Oint)) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)). [resolve(34,a,24,b)].
% 1.69/1.96 Derived: -class_HOL_Oord(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) | hBOOL(hAPP(c_lessequals(C,A),c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Int_Oint))). [resolve(34,a,25,b)].
% 1.69/1.96 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(34,a,26,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(34,a,27,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(34,a,28,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),hAPP(c_COMBB(A,tc_nat,tc_Int_Oint,tc_nat),c_Suc)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)). [resolve(34,a,29,a)].
% 1.69/1.96 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(34,a,30,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),hAPP(c_COMBB(A,tc_nat,tc_Int_Oint,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)). [resolve(34,a,31,a)].
% 1.69/1.96 Derived: -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),tc_nat,tc_Int_Oint,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)),tc_nat,tc_Int_Oint,tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),tc_nat,tc_Int_Oint,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),tc_nat,tc_Int_Oint,tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)). [resolve(34,a,32,b)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_bool),tc_Int_Oint),hAPP(c_COMBB(c_Finite__Set_Osetsum(B,tc_Int_Oint),tc_fun(B,tc_Int_Oint),tc_fun(tc_fun(B,tc_bool),tc_Int_Oint),A),C)),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Int_Oint),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_bool),tc_Int_Oint),hAPP(c_COMBB(c_Finite__Set_Osetsum(A,tc_Int_Oint),tc_fun(A,tc_Int_Oint),tc_fun(tc_fun(A,tc_bool),tc_Int_Oint),B),hAPP(c_COMBC(A,B,tc_Int_Oint),C))),E)),D). [resolve(34,a,33,a)].
% 1.69/1.96 35 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.69/1.96 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B)). [resolve(35,a,9,b)].
% 1.69/1.96 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Complex_Ocomplex),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B)). [resolve(35,a,10,b)].
% 1.69/1.96 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(35,a,11,a)].
% 1.69/1.96 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(35,a,12,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(A,C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(35,a,13,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(A,B)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(35,a,14,a)].
% 1.69/1.96 Derived: -class_HOL_Oord(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Complex_Ocomplex),A),D)). [resolve(35,a,15,b)].
% 1.69/1.96 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(35,a,16,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(35,a,17,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBB(A,tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))). [resolve(35,a,18,a)].
% 1.69/1.96 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B)). [resolve(35,a,19,b)].
% 1.69/1.96 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Complex_Ocomplex),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),C)). [resolve(35,a,20,b)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),C),D)). [resolve(35,a,21,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Finite__Set_Ofinite(C,A). [resolve(35,a,22,a)].
% 1.69/1.96 Derived: -class_HOL_Oord(A) | hAPP(B,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Complex_Ocomplex)) != hAPP(E,c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Complex_Ocomplex)) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)). [resolve(35,a,24,b)].
% 1.69/1.96 Derived: -class_HOL_Oord(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) | hBOOL(hAPP(c_lessequals(C,A),c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1(C,D,B,E,A,tc_Complex_Ocomplex))). [resolve(35,a,25,b)].
% 1.69/1.96 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(35,a,26,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(35,a,27,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(35,a,28,a)].
% 1.69/1.96 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBB(A,tc_nat,tc_Complex_Ocomplex,tc_nat),c_Suc)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)). [resolve(35,a,29,a)].
% 1.77/2.07 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(35,a,30,a)].
% 1.77/2.07 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBB(A,tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)). [resolve(35,a,31,a)].
% 1.77/2.07 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)). [resolve(35,a,32,b)].
% 1.77/2.07 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_bool),tc_Complex_Ocomplex),hAPP(c_COMBB(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),tc_fun(B,tc_Complex_Ocomplex),tc_fun(tc_fun(B,tc_bool),tc_Complex_Ocomplex),A),C)),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_bool),tc_Complex_Ocomplex),hAPP(c_COMBB(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),tc_fun(A,tc_Complex_Ocomplex),tc_fun(tc_fun(A,tc_bool),tc_Complex_Ocomplex),B),hAPP(c_COMBC(A,B,tc_Complex_Ocomplex),C))),E)),D). [resolve(35,a,33,a)].
% 1.77/2.07 36 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.77/2.07 37 -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].
% 1.77/2.07 38 -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].
% 1.77/2.07 39 -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].
% 1.77/2.07 40 -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].
% 1.77/2.07 41 -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].
% 1.77/2.07 42 -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].
% 1.77/2.07 43 -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].
% 1.77/2.07 44 -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].
% 1.77/2.07 45 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 1.77/2.07 46 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 1.77/2.07 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)). [resolve(36,a,37,a)].
% 1.77/2.07 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(36,a,38,a)].
% 1.77/2.07 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)) | B = D | A = C. [resolve(36,a,39,a)].
% 1.77/2.07 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(36,a,43,a)].
% 1.77/2.07 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(36,a,44,a)].
% 1.77/2.07 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(36,a,45,a)].
% 1.77/2.07 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(36,a,46,a)].
% 1.77/2.07 47 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.77/2.07 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(47,a,37,a)].
% 1.77/2.07 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(47,a,38,a)].
% 1.89/2.15 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(47,a,39,a)].
% 1.89/2.15 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(47,a,43,a)].
% 1.89/2.15 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(47,a,44,a)].
% 1.89/2.15 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(47,a,45,a)].
% 1.89/2.15 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(47,a,46,a)].
% 1.89/2.15 48 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.89/2.15 49 -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].
% 1.89/2.15 50 -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].
% 1.89/2.15 51 -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].
% 1.89/2.15 52 -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].
% 1.89/2.15 53 -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].
% 1.89/2.15 54 -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].
% 1.89/2.15 55 -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].
% 1.89/2.15 56 -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].
% 1.89/2.15 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].
% 1.89/2.15 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].
% 1.89/2.15 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].
% 1.89/2.15 60 -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].
% 1.89/2.15 61 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) # label(cls_class__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 1.89/2.15 62 -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].
% 1.89/2.15 63 -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].
% 1.89/2.15 64 -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].
% 1.89/2.15 65 -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].
% 1.89/2.15 66 -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].
% 1.89/2.15 67 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 1.89/2.15 68 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 1.89/2.15 69 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) # label(cls_class__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 1.89/2.15 70 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 1.89/2.15 71 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 1.89/2.15 72 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_class__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 1.89/2.15 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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.89/2.15 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),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.89/2.15 75 -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].
% 1.89/2.15 76 -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].
% 1.89/2.15 77 -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].
% 1.89/2.15 78 -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].
% 1.89/2.15 79 -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].
% 1.89/2.15 80 -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].
% 1.89/2.15 81 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 1.89/2.15 82 -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].
% 1.89/2.15 83 -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].
% 1.89/2.15 84 -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].
% 1.89/2.15 85 -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].
% 1.89/2.15 86 -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].
% 1.89/2.15 87 -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].
% 1.89/2.15 88 -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].
% 1.89/2.15 89 -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].
% 1.89/2.15 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(48,a,54,a)].
% 1.89/2.15 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(48,a,55,a)].
% 1.89/2.15 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(48,a,57,a)].
% 1.89/2.15 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(48,a,58,a)].
% 1.89/2.15 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(48,a,59,a)].
% 1.89/2.15 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(48,a,60,a)].
% 1.89/2.15 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(48,a,61,a)].
% 1.89/2.15 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(48,a,64,a)].
% 1.89/2.15 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(48,a,65,a)].
% 1.89/2.15 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(48,a,66,a)].
% 1.89/2.15 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(48,a,67,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(48,a,69,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)). [resolve(48,a,70,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)). [resolve(48,a,71,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(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_Power_Opower__class_Opower(tc_nat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C)). [resolve(48,a,72,a)].
% 1.89/2.16 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(48,a,73,a)].
% 1.89/2.16 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(48,a,74,a)].
% 1.89/2.16 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(48,a,75,a)].
% 1.89/2.16 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(48,a,76,a)].
% 1.89/2.16 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(48,a,78,a)].
% 1.89/2.16 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(48,a,79,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(48,a,81,a)].
% 1.89/2.16 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(48,a,84,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(48,a,85,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(48,a,86,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(48,a,88,a)].
% 1.89/2.16 90 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(90,a,54,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C). [resolve(90,a,55,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(90,a,57,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(90,a,58,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(90,a,59,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D)). [resolve(90,a,60,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(90,a,61,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint))),A). [resolve(90,a,64,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint))),B). [resolve(90,a,65,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),c_HOL_Oone__class_Oone(tc_Int_Oint))),A). [resolve(90,a,66,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(90,a,67,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(90,a,69,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)). [resolve(90,a,70,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)). [resolve(90,a,71,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)). [resolve(90,a,72,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),B). [resolve(90,a,73,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(90,a,74,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C). [resolve(90,a,75,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(90,a,76,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(90,a,78,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(90,a,79,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(90,a,81,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(90,a,84,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(90,a,85,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(90,a,86,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A). [resolve(90,a,88,a)].
% 1.89/2.16 91 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.89/2.16 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(91,a,54,a)].
% 1.89/2.16 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(91,a,55,a)].
% 1.89/2.16 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(91,a,57,a)].
% 1.89/2.16 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(91,a,58,a)].
% 1.89/2.16 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(91,a,59,a)].
% 1.89/2.16 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(91,a,60,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(91,a,61,a)].
% 1.89/2.16 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(91,a,64,a)].
% 1.89/2.16 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(91,a,65,a)].
% 1.89/2.16 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(91,a,66,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(91,a,67,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(91,a,69,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B)). [resolve(91,a,70,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B)). [resolve(91,a,71,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(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_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)). [resolve(91,a,72,a)].
% 1.89/2.16 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(91,a,73,a)].
% 1.89/2.16 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(91,a,74,a)].
% 1.89/2.16 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(91,a,75,a)].
% 1.89/2.16 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(91,a,76,a)].
% 1.89/2.16 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(91,a,78,a)].
% 1.89/2.16 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(91,a,79,a)].
% 1.89/2.16 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(91,a,81,a)].
% 1.89/2.16 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(91,a,84,a)].
% 2.00/2.29 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(91,a,85,a)].
% 2.00/2.29 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(91,a,86,a)].
% 2.00/2.29 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(91,a,88,a)].
% 2.00/2.29 92 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.00/2.29 93 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 2.00/2.29 94 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 2.00/2.29 95 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 2.00/2.29 96 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 2.00/2.29 97 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 2.00/2.29 98 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 2.00/2.29 99 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 2.00/2.29 100 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 2.00/2.29 101 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 2.00/2.29 102 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.00/2.29 103 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 2.00/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(92,a,93,a)].
% 2.00/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(92,a,94,a)].
% 2.00/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(92,a,95,a)].
% 2.00/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(92,a,96,a)].
% 2.00/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(92,a,97,a)].
% 2.00/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(92,a,98,a)].
% 2.00/2.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(92,a,100,a)].
% 2.00/2.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(92,a,101,a)].
% 2.00/2.29 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(92,a,102,a)].
% 2.00/2.29 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(92,a,103,a)].
% 2.00/2.29 104 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.09/2.34 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(104,a,93,a)].
% 2.09/2.34 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(104,a,94,a)].
% 2.09/2.34 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(104,a,95,a)].
% 2.09/2.34 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(104,a,96,a)].
% 2.09/2.34 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(104,a,97,a)].
% 2.09/2.34 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(104,a,98,a)].
% 2.09/2.34 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(104,a,100,a)].
% 2.09/2.34 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(104,a,101,a)].
% 2.09/2.34 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(104,a,102,a)].
% 2.09/2.34 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(104,a,103,a)].
% 2.09/2.34 105 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 2.09/2.34 106 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E))) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 2.09/2.34 107 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 2.09/2.34 108 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 2.09/2.34 109 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 2.09/2.34 110 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 2.09/2.34 111 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 2.09/2.34 112 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_lessequals(C,A),B)) | -hBOOL(hAPP(c_lessequals(E,A),D)) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 2.09/2.34 113 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 2.09/2.34 114 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 2.09/2.34 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D))). [resolve(105,a,106,a)].
% 2.09/2.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(105,a,107,a)].
% 2.09/2.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),D)). [resolve(105,a,108,a)].
% 2.09/2.34 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(105,a,109,a)].
% 2.09/2.34 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(105,a,110,a)].
% 2.09/2.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(105,a,111,a)].
% 2.09/2.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)). [resolve(105,a,112,a)].
% 2.09/2.34 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(105,a,113,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(105,a,114,a)].
% 2.09/2.38 115 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 2.09/2.38 116 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(c_HOL_Oabs__class_Oabs(A),B))) # label(cls_abs__ge__self_0) # label(axiom). [assumption].
% 2.09/2.38 117 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),C)) # label(cls_abs__le__D1_0) # label(axiom). [assumption].
% 2.09/2.38 118 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_1) # label(axiom). [assumption].
% 2.09/2.38 119 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_0) # label(axiom). [assumption].
% 2.09/2.38 120 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_abs__of__pos_0) # label(axiom). [assumption].
% 2.09/2.38 121 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)))) # label(cls_abs__triangle__ineq_0) # label(axiom). [assumption].
% 2.09/2.38 122 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)))) # label(cls_abs__triangle__ineq4_0) # label(axiom). [assumption].
% 2.09/2.38 123 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D))),hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))))) # label(cls_abs__diff__triangle__ineq_0) # label(axiom). [assumption].
% 2.09/2.38 124 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)) = hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),B)) # label(cls_abs__minus__commute_0) # label(axiom). [assumption].
% 2.09/2.38 125 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)) = hAPP(c_HOL_Oabs__class_Oabs(A),B) # label(cls_abs__idempotent_0) # label(axiom). [assumption].
% 2.09/2.38 126 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Oabs__class_Oabs(A),B))) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__abs__iff_1) # label(axiom). [assumption].
% 2.09/2.38 127 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__not__less__zero_0) # label(axiom). [assumption].
% 2.09/2.38 128 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) # label(cls_abs__add__abs_0) # label(axiom). [assumption].
% 2.09/2.38 129 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)))) # label(cls_zero__less__abs__iff_0) # label(axiom). [assumption].
% 2.09/2.38 130 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__le__zero__iff_0) # label(axiom). [assumption].
% 2.09/2.38 131 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_abs__of__nonneg_0) # label(axiom). [assumption].
% 2.09/2.38 132 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__le__zero__iff_1) # label(axiom). [assumption].
% 2.09/2.38 133 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_HOL_Oabs__class_Oabs(A),B))) # label(cls_abs__ge__zero_0) # label(axiom). [assumption].
% 2.09/2.38 134 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C))),A),hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)))) # label(cls_abs__triangle__ineq3_0) # label(axiom). [assumption].
% 2.09/2.38 135 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)),A),hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)))) # label(cls_abs__triangle__ineq2_0) # label(axiom). [assumption].
% 2.09/2.38 136 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(c_COMBB(c_HOL_Oabs__class_Oabs(A),A,A,B),C)),D))) # label(cls_setsum__abs_0) # label(axiom). [assumption].
% 2.09/2.38 137 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(c_COMBB(c_HOL_Oabs__class_Oabs(A),A,A,B),C)),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(c_COMBB(c_HOL_Oabs__class_Oabs(A),A,A,B),C)),D) # label(cls_abs__setsum__abs_0) # label(axiom). [assumption].
% 2.09/2.38 138 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(c_COMBB(c_HOL_Oabs__class_Oabs(A),A,A,B),C)),D))) # label(cls_setsum__abs__ge__zero_0) # label(axiom). [assumption].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A))). [resolve(115,a,116,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),B)). [resolve(115,a,117,a)].
% 2.09/2.38 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(115,a,118,a)].
% 2.09/2.38 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(115,a,119,a)].
% 2.09/2.38 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(115,a,120,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)))). [resolve(115,a,121,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)))). [resolve(115,a,122,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D))),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),C))),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),D))))). [resolve(115,a,123,a)].
% 2.09/2.38 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),A)). [resolve(115,a,124,a)].
% 2.09/2.38 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A). [resolve(115,a,125,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A))) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(115,a,126,a)].
% 2.09/2.38 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(115,a,127,a)].
% 2.09/2.38 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(115,a,128,a)].
% 2.09/2.38 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)))). [resolve(115,a,129,a)].
% 2.09/2.38 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(115,a,130,a)].
% 2.09/2.38 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(115,a,131,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(115,a,132,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A))). [resolve(115,a,133,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B))),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)))). [resolve(115,a,134,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)))). [resolve(115,a,135,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),C)),tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),tc_Int_Oint,tc_Int_Oint,A),B)),C))). [resolve(115,a,136,a)].
% 2.09/2.38 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),tc_Int_Oint,tc_Int_Oint,A),B)),C)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),tc_Int_Oint,tc_Int_Oint,A),B)),C). [resolve(115,a,137,a)].
% 2.09/2.38 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),tc_Int_Oint,tc_Int_Oint,A),B)),C))). [resolve(115,a,138,a)].
% 2.17/2.48 139 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.17/2.48 140 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 2.17/2.48 141 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 2.17/2.48 142 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 2.17/2.48 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(139,a,140,a)].
% 2.17/2.48 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(139,a,141,a)].
% 2.17/2.48 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(139,a,142,a)].
% 2.17/2.48 143 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.17/2.48 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(143,a,140,a)].
% 2.17/2.48 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(143,a,141,a)].
% 2.17/2.48 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)). [resolve(143,a,142,a)].
% 2.17/2.48 144 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 2.17/2.48 145 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 2.17/2.48 146 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 2.17/2.48 147 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 2.17/2.48 148 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 2.17/2.48 149 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) | hBOOL(hAPP(c_lessequals(B,A),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 2.17/2.48 150 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 2.17/2.48 151 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 2.17/2.48 152 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 2.25/2.48 153 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 2.25/2.48 154 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 2.25/2.48 155 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | C = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 2.25/2.48 156 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 2.25/2.48 157 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 2.25/2.48 158 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 2.25/2.48 159 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 2.25/2.48 160 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 2.25/2.48 161 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__if__lattice_1) # label(axiom). [assumption].
% 2.25/2.48 162 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 2.25/2.48 163 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 2.25/2.48 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(144,a,145,a)].
% 2.25/2.48 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(144,a,147,a)].
% 2.25/2.48 Derived: -hBOOL(hAPP(c_lessequals(A,tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)). [resolve(144,a,148,a)].
% 2.25/2.48 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(144,a,150,a)].
% 2.25/2.48 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)) | B = A. [resolve(144,a,154,a)].
% 2.25/2.48 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)). [resolve(144,a,158,a)].
% 2.25/2.48 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | hAPP(c_HOL_Oabs__class_Oabs(tc_nat),A) = A | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(144,a,161,a)].
% 2.25/2.48 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)). [resolve(144,a,162,a)].
% 2.25/2.48 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(144,a,163,a)].
% 2.25/2.48 164 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 2.25/2.48 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(164,a,145,a)].
% 2.29/2.53 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(164,a,147,a)].
% 2.29/2.53 Derived: -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),A)). [resolve(164,a,148,a)].
% 2.29/2.53 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(164,a,150,a)].
% 2.29/2.53 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | B = A. [resolve(164,a,154,a)].
% 2.29/2.53 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),A)). [resolve(164,a,158,a)].
% 2.29/2.53 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(164,a,161,a)].
% 2.29/2.53 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)). [resolve(164,a,162,a)].
% 2.29/2.53 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(164,a,163,a)].
% 2.29/2.53 165 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 2.29/2.53 166 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(c_COMBB(C,A,B,A),hAPP(c_HOL_Oplus__class_Oplus(A),D)),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) | -c_Lim_OLIM(C,D,hAPP(C,D),A,B) # label(cls_LIM__isCont__iff_0) # label(axiom). [assumption].
% 2.29/2.53 167 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(C,D,hAPP(C,D),A,B) | -c_Lim_OLIM(hAPP(c_COMBB(C,A,B,A),hAPP(c_HOL_Oplus__class_Oplus(A),D)),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) # label(cls_LIM__isCont__iff_1) # label(axiom). [assumption].
% 2.29/2.53 168 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(hAPP(c_COMBB(C,B,A,B),hAPP(c_HOL_Oplus__class_Oplus(B),D)),c_HOL_Ozero__class_Ozero(B),E,B,A) | -c_Lim_OLIM(C,D,E,B,A) # label(cls_LIM__offset__zero_0) # label(axiom). [assumption].
% 2.29/2.53 169 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(C,D,E,B,A) | -c_Lim_OLIM(hAPP(c_COMBB(C,B,A,B),hAPP(c_HOL_Oplus__class_Oplus(B),D)),c_HOL_Ozero__class_Ozero(B),E,B,A) # label(cls_LIM__offset__zero__cancel_0) # label(axiom). [assumption].
% 2.29/2.53 170 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),B),C),D,B,A,A),E,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),V6),B,A) | -c_Lim_OLIM(D,E,V6,B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__add_0) # label(axiom). [assumption].
% 2.29/2.53 171 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OisCont(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(B),B,tc_fun(B,B),A),C),D,A,B,B),E,A,B) | -c_Lim_OisCont(D,E,A,B) | -c_Lim_OisCont(C,E,A,B) # label(cls_isCont__add_0) # label(axiom). [assumption].
% 2.29/2.53 172 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),B),C),D,B,A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),F),V6,B,A) | -c_Limits_Otendsto(D,F,V6,B,A) | -c_Limits_Otendsto(C,E,V6,B,A) # label(cls_tendsto__add_0) # label(axiom). [assumption].
% 2.29/2.53 173 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OisCont(C,D,A,B) | -c_Lim_OLIM(hAPP(c_COMBB(C,A,B,A),hAPP(c_HOL_Oplus__class_Oplus(A),D)),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) # label(cls_isCont__iff_1) # label(axiom). [assumption].
% 2.29/2.53 174 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(c_COMBB(C,A,B,A),hAPP(c_HOL_Oplus__class_Oplus(A),D)),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) | -c_Lim_OisCont(C,D,A,B) # label(cls_isCont__iff_0) # label(axiom). [assumption].
% 2.29/2.53 175 -class_RealVector_Oreal__normed__vector(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Series_Osuminf(B,A)),c_Series_Osuminf(C,A)) = c_Series_Osuminf(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),A) | -c_Series_Osummable(C,A) | -c_Series_Osummable(B,A) # label(cls_suminf__add_0) # label(axiom). [assumption].
% 2.29/2.53 176 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(B,A) | -c_Series_Osums(B,C,A) # label(cls_sums__summable_0) # label(axiom). [assumption].
% 2.29/2.53 177 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(B,A) | -c_Series_Osums(B,C,A) # label(cls_sums__iff_0) # label(axiom). [assumption].
% 2.29/2.53 178 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_Series_Osums(C,E,A) | -c_Series_Osums(B,D,A) # label(cls_sums__add_0) # label(axiom). [assumption].
% 2.29/2.53 179 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),A) | -c_Series_Osummable(C,A) | -c_Series_Osummable(B,A) # label(cls_summable__add_0) # label(axiom). [assumption].
% 2.29/2.53 180 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__add_0) # label(axiom). [assumption].
% 2.29/2.53 181 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),A) | -c_SEQ_OZseq(C,A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__add_0) # label(axiom). [assumption].
% 2.29/2.53 182 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),tc_nat),B)),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__add__const_0) # label(axiom). [assumption].
% 2.29/2.53 183 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,c_HOL_Ozero__class_Ozero(A),A) | -c_Series_Osummable(B,A) # label(cls_summable__LIMSEQ__zero_0) # label(axiom). [assumption].
% 2.29/2.53 184 -class_RealVector_Oreal__normed__vector(A) | B = c_Series_Osuminf(C,A) | -c_Series_Osums(C,B,A) # label(cls_sums__unique_0) # label(axiom). [assumption].
% 2.29/2.53 185 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osuminf(B,A) = C | -c_Series_Osums(B,C,A) # label(cls_sums__iff_1) # label(axiom). [assumption].
% 2.29/2.53 186 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(B,c_Series_Osuminf(B,A),A) | -c_Series_Osummable(B,A) # label(cls_summable__sums_0) # label(axiom). [assumption].
% 2.29/2.53 187 -class_RealVector_Oreal__normed__vector(A) | -c_Series_Osummable(B,A) | c_Series_Osums(B,c_Series_Osuminf(B,A),A) # label(cls_sums__iff_2) # label(axiom). [assumption].
% 2.29/2.53 188 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat))),A) | -c_Series_Osums(hAPP(c_COMBB(B,tc_nat,A,tc_nat),c_Suc),C,A) # label(cls_sums__Suc_0) # label(axiom). [assumption].
% 2.29/2.53 189 -class_RealVector_Oreal__normed__vector(A) | hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) | c_Series_Osums(B,C,A) | -c_Series_Osums(hAPP(c_COMBB(B,tc_nat,A,tc_nat),c_Suc),C,A) # label(cls_sums__Suc__imp_0) # label(axiom). [assumption].
% 2.29/2.53 190 -class_RealVector_Oreal__normed__vector(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Series_Osuminf(B,A)),c_Series_Osuminf(C,A)) = c_Series_Osuminf(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),A) | -c_Series_Osummable(C,A) | -c_Series_Osummable(B,A) # label(cls_suminf__diff_0) # label(axiom). [assumption].
% 2.29/2.53 191 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),B)),C),A) # label(cls_LIMSEQ__Zseq__iff_1) # label(axiom). [assumption].
% 2.29/2.53 192 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_LIMSEQ__Zseq__iff_0) # label(axiom). [assumption].
% 2.29/2.53 193 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(hAPP(c_COMBB(B,tc_nat,A,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C)),A) | -c_Series_Osummable(B,A) # label(cls_summable__ignore__initial__segment_0) # label(axiom). [assumption].
% 2.29/2.53 194 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osuminf(B,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))),c_Series_Osuminf(hAPP(c_COMBB(B,tc_nat,A,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C)),A)) | -c_Series_Osummable(B,A) # label(cls_suminf__split__initial__segment_0) # label(axiom). [assumption].
% 2.29/2.53 195 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),B),C),D,B,A,A),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__add__zero_0) # label(axiom). [assumption].
% 2.29/2.53 196 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(hAPP(c_COMBB(C,B,A,B),hAPP(hAPP(c_COMBC(B,B,B),c_HOL_Oplus__class_Oplus(B)),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(B),E),D),F,B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__offset_0) # label(axiom). [assumption].
% 2.29/2.53 197 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OisCont(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(B),B,tc_fun(B,B),A),C),D,A,B,B),E,A,B) | -c_Lim_OisCont(D,E,A,B) | -c_Lim_OisCont(C,E,A,B) # label(cls_isCont__diff_0) # label(axiom). [assumption].
% 2.29/2.53 198 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),B),C),D,B,A,A),E,hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),F),V6),B,A) | -c_Lim_OLIM(D,E,V6,B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__diff_0) # label(axiom). [assumption].
% 2.29/2.53 199 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),B),C),D,B,A,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),F),V6,B,A) | -c_Limits_Otendsto(D,F,V6,B,A) | -c_Limits_Otendsto(C,E,V6,B,A) # label(cls_tendsto__diff_0) # label(axiom). [assumption].
% 2.29/2.53 200 -class_RealVector_Oreal__normed__vector(A) | -c_Series_Osummable(B,A) | c_Series_Osuminf(hAPP(c_COMBB(B,tc_nat,A,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C)),A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Series_Osuminf(B,A)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))) # label(cls_suminf__minus__initial__segment_0) # label(axiom). [assumption].
% 2.29/2.53 201 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__diff_0) # label(axiom). [assumption].
% 2.29/2.53 202 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),A) | -c_Series_Osummable(C,A) | -c_Series_Osummable(B,A) # label(cls_summable__diff_0) # label(axiom). [assumption].
% 2.29/2.53 203 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),A) | -c_SEQ_OZseq(C,A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__diff_0) # label(axiom). [assumption].
% 2.29/2.53 204 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E),A) | -c_Series_Osums(C,E,A) | -c_Series_Osums(B,D,A) # label(cls_sums__diff_0) # label(axiom). [assumption].
% 2.29/2.53 205 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),B)),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__diff__const_0) # label(axiom). [assumption].
% 2.29/2.53 206 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(hAPP(c_COMBB(B,tc_nat,A,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))),A) | -c_Series_Osums(B,D,A) # label(cls_sums__split__initial__segment_0) # label(axiom). [assumption].
% 2.29/2.53 207 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),B),C)),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,D,B,A) # label(cls_LIM__zero_0) # label(axiom). [assumption].
% 2.29/2.53 208 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(C,D,E,B,A) | -c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),B),C)),E),D,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__zero__iff_0) # label(axiom). [assumption].
% 2.29/2.53 209 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),D),B,tc_nat,A,A),c_HOL_Ozero__class_Ozero(A),A) | -c_SEQ_OLIMSEQ(D,C,A) # label(cls_LIMSEQ__diff__approach__zero2_0) # label(axiom). [assumption].
% 2.29/2.53 210 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),B),D,tc_nat,A,A),c_HOL_Ozero__class_Ozero(A),A) | -c_SEQ_OLIMSEQ(D,C,A) # label(cls_LIMSEQ__diff__approach__zero_0) # label(axiom). [assumption].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(c_COMBB(B,tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(B,C),tc_Complex_Ocomplex,A) | -c_Lim_OLIM(B,C,hAPP(B,C),tc_Complex_Ocomplex,A). [resolve(165,a,166,a)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,hAPP(B,C),tc_Complex_Ocomplex,A) | -c_Lim_OLIM(hAPP(c_COMBB(B,tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(B,C),tc_Complex_Ocomplex,A). [resolve(165,a,167,a)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(c_COMBB(B,tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),D,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(B,C,D,tc_Complex_Ocomplex,A). [resolve(165,a,168,b)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,D,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(hAPP(c_COMBB(B,tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),D,tc_Complex_Ocomplex,A). [resolve(165,a,169,b)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),E),F),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,F,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(165,a,170,a)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OisCont(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,A,tc_Complex_Ocomplex) | -c_Lim_OisCont(C,D,A,tc_Complex_Ocomplex) | -c_Lim_OisCont(B,D,A,tc_Complex_Ocomplex). [resolve(165,a,171,b)].
% 2.29/2.53 Derived: c_Limits_Otendsto(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),D),E),F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(C,E,F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,F,A,tc_Complex_Ocomplex). [resolve(165,a,172,a)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OisCont(B,C,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(hAPP(c_COMBB(B,tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(B,C),tc_Complex_Ocomplex,A). [resolve(165,a,173,a)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(c_COMBB(B,tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(B,C),tc_Complex_Ocomplex,A) | -c_Lim_OisCont(B,C,tc_Complex_Ocomplex,A). [resolve(165,a,174,a)].
% 2.29/2.53 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),c_Series_Osuminf(B,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(165,a,175,a)].
% 2.29/2.53 Derived: c_Series_Osummable(A,tc_Complex_Ocomplex) | -c_Series_Osums(A,B,tc_Complex_Ocomplex). [resolve(165,a,176,a)].
% 2.29/2.53 Derived: c_Series_Osums(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_Series_Osums(B,D,tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(165,a,178,a)].
% 2.29/2.53 Derived: c_Series_Osummable(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(165,a,179,a)].
% 2.29/2.53 Derived: c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(165,a,180,a)].
% 2.29/2.53 Derived: c_SEQ_OZseq(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(165,a,181,a)].
% 2.29/2.53 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(165,a,182,a)].
% 2.29/2.53 Derived: c_SEQ_OLIMSEQ(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(165,a,183,a)].
% 2.29/2.53 Derived: A = c_Series_Osuminf(B,tc_Complex_Ocomplex) | -c_Series_Osums(B,A,tc_Complex_Ocomplex). [resolve(165,a,184,a)].
% 2.29/2.53 Derived: c_Series_Osuminf(A,tc_Complex_Ocomplex) = B | -c_Series_Osums(A,B,tc_Complex_Ocomplex). [resolve(165,a,185,a)].
% 2.29/2.53 Derived: c_Series_Osums(A,c_Series_Osuminf(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(165,a,186,a)].
% 2.29/2.53 Derived: c_Series_Osums(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))),tc_Complex_Ocomplex) | -c_Series_Osums(hAPP(c_COMBB(A,tc_nat,tc_Complex_Ocomplex,tc_nat),c_Suc),B,tc_Complex_Ocomplex). [resolve(165,a,188,a)].
% 2.29/2.53 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Series_Osums(A,B,tc_Complex_Ocomplex) | -c_Series_Osums(hAPP(c_COMBB(A,tc_nat,tc_Complex_Ocomplex,tc_nat),c_Suc),B,tc_Complex_Ocomplex). [resolve(165,a,189,a)].
% 2.29/2.53 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),c_Series_Osuminf(B,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(165,a,190,a)].
% 2.29/2.53 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex). [resolve(165,a,191,a)].
% 2.29/2.53 Derived: c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex). [resolve(165,a,192,a)].
% 2.29/2.53 Derived: c_Series_Osummable(hAPP(c_COMBB(A,tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),B)),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(165,a,193,a)].
% 2.29/2.53 Derived: c_Series_Osuminf(A,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),c_Series_Osuminf(hAPP(c_COMBB(A,tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),B)),tc_Complex_Ocomplex)) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(165,a,194,a)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(165,a,195,a)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(c_COMBB(B,tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),C),E,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(B,D,E,tc_Complex_Ocomplex,A). [resolve(165,a,196,b)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OisCont(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,A,tc_Complex_Ocomplex) | -c_Lim_OisCont(C,D,A,tc_Complex_Ocomplex) | -c_Lim_OisCont(B,D,A,tc_Complex_Ocomplex). [resolve(165,a,197,b)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),E),F),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,F,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(165,a,198,a)].
% 2.29/2.53 Derived: c_Limits_Otendsto(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),E),F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(C,E,F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,F,A,tc_Complex_Ocomplex). [resolve(165,a,199,a)].
% 2.29/2.53 Derived: -c_Series_Osummable(A,tc_Complex_Ocomplex) | c_Series_Osuminf(hAPP(c_COMBB(A,tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),B)),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))). [resolve(165,a,200,a)].
% 2.29/2.53 Derived: c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(165,a,201,a)].
% 2.29/2.53 Derived: c_Series_Osummable(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(165,a,202,a)].
% 2.29/2.53 Derived: c_SEQ_OZseq(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(165,a,203,a)].
% 2.29/2.53 Derived: c_Series_Osums(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_Series_Osums(B,D,tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(165,a,204,a)].
% 2.29/2.53 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(165,a,205,a)].
% 2.29/2.53 Derived: c_Series_Osums(hAPP(c_COMBB(A,tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),B)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(165,a,206,a)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B)),C),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,C,A,tc_Complex_Ocomplex). [resolve(165,a,207,a)].
% 2.29/2.53 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,D,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B)),D),C,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(165,a,208,a)].
% 2.29/2.58 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),C),A,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(C,B,tc_Complex_Ocomplex). [resolve(165,a,209,a)].
% 2.29/2.58 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),C,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(C,B,tc_Complex_Ocomplex). [resolve(165,a,210,a)].
% 2.29/2.58 211 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 2.29/2.58 212 -class_RealVector_Oreal__normed__div__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(c_COMBB(c_HOL_Oinverse__class_Oinverse(A),A,A,B),C),D,hAPP(c_HOL_Oinverse__class_Oinverse(A),E),B,A) | E = c_HOL_Ozero__class_Ozero(A) | -c_Lim_OLIM(C,D,E,B,A) # label(cls_LIM__inverse_0) # label(axiom). [assumption].
% 2.29/2.58 213 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__div__algebra(B) | c_Lim_OisCont(hAPP(c_COMBB(c_HOL_Oinverse__class_Oinverse(B),B,B,A),C),D,A,B) | hAPP(C,D) = c_HOL_Ozero__class_Ozero(B) | -c_Lim_OisCont(C,D,A,B) # label(cls_isCont__inverse_0) # label(axiom). [assumption].
% 2.29/2.58 214 -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].
% 2.29/2.58 215 -class_RealVector_Oreal__normed__div__algebra(A) | c_Limits_Otendsto(hAPP(c_COMBB(c_HOL_Oinverse__class_Oinverse(A),A,A,B),C),hAPP(c_HOL_Oinverse__class_Oinverse(A),D),E,B,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Limits_Otendsto(C,D,E,B,A) # label(cls_tendsto__inverse_0) # label(axiom). [assumption].
% 2.29/2.58 216 -class_RealVector_Oreal__normed__div__algebra(A) | c_SEQ_OLIMSEQ(hAPP(c_COMBB(c_HOL_Oinverse__class_Oinverse(A),A,A,tc_nat),B),hAPP(c_HOL_Oinverse__class_Oinverse(A),C),A) | C = c_HOL_Ozero__class_Ozero(A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_LIMSEQ__inverse_0) # label(axiom). [assumption].
% 2.29/2.58 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(c_COMBB(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),B),C,hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),D),A,tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Lim_OLIM(B,C,D,A,tc_Complex_Ocomplex). [resolve(211,a,212,a)].
% 2.29/2.58 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OisCont(hAPP(c_COMBB(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),B),C,A,tc_Complex_Ocomplex) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Lim_OisCont(B,C,A,tc_Complex_Ocomplex). [resolve(211,a,213,b)].
% 2.29/2.58 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(211,a,214,a)].
% 2.29/2.58 Derived: c_Limits_Otendsto(hAPP(c_COMBB(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),B),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),C),D,A,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,C,D,A,tc_Complex_Ocomplex). [resolve(211,a,215,a)].
% 2.29/2.58 Derived: c_SEQ_OLIMSEQ(hAPP(c_COMBB(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex). [resolve(211,a,216,a)].
% 2.39/2.62 217 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 2.39/2.62 218 -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].
% 2.39/2.62 219 -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].
% 2.39/2.62 220 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 2.39/2.62 221 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 2.39/2.62 222 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 2.39/2.62 223 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 2.39/2.62 224 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 2.39/2.62 225 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 2.39/2.62 226 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 2.39/2.62 227 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 2.39/2.62 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(217,a,219,a)].
% 2.39/2.62 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(217,a,220,a)].
% 2.39/2.62 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))). [resolve(217,a,222,a)].
% 2.39/2.67 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))). [resolve(217,a,224,a)].
% 2.39/2.67 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(217,a,226,a)].
% 2.39/2.67 228 class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) # label(axiom). [assumption].
% 2.39/2.67 229 -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].
% 2.39/2.67 230 -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].
% 2.39/2.67 231 -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].
% 2.39/2.67 232 -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].
% 2.39/2.67 233 -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].
% 2.39/2.67 234 -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].
% 2.39/2.67 235 -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].
% 2.39/2.67 236 -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].
% 2.39/2.67 237 -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].
% 2.39/2.67 238 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),C) # label(cls_power__inverse_0) # label(axiom). [assumption].
% 2.39/2.67 239 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(A),C),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_division__ring__inverse__diff_0) # label(axiom). [assumption].
% 2.39/2.67 240 -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].
% 2.39/2.67 241 -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].
% 2.39/2.67 242 -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].
% 2.39/2.67 243 -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].
% 2.39/2.67 244 -class_Ring__and__Field_Odivision__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),C) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__inverse_0) # label(axiom). [assumption].
% 2.39/2.67 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(228,a,229,a)].
% 2.39/2.67 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(228,a,230,a)].
% 2.39/2.67 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(228,a,231,a)].
% 2.39/2.67 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(228,a,232,a)].
% 2.39/2.67 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(228,a,233,a)].
% 2.39/2.67 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(228,a,234,a)].
% 2.39/2.67 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(228,a,235,a)].
% 2.39/2.67 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(228,a,236,a)].
% 2.39/2.67 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(228,a,237,a)].
% 2.47/2.71 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),B). [resolve(228,a,238,a)].
% 2.47/2.71 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(tc_Complex_Ocomplex),B),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(228,a,239,a)].
% 2.47/2.71 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(228,a,240,a)].
% 2.47/2.71 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(228,a,241,a)].
% 2.47/2.71 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(228,a,242,a)].
% 2.47/2.71 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(228,a,243,a)].
% 2.47/2.71 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),B) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(228,a,244,a)].
% 2.47/2.71 245 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.47/2.71 246 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 2.47/2.71 247 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 2.47/2.71 248 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 2.47/2.71 249 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 2.47/2.71 250 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(245,a,246,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(245,a,247,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(245,a,248,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(245,a,249,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(245,a,250,a)].
% 2.47/2.76 251 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(251,a,246,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(251,a,247,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(251,a,248,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)). [resolve(251,a,249,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(251,a,250,a)].
% 2.47/2.76 252 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 2.47/2.76 253 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D),A),B)) # label(cls_abs__diff__less__iff_2) # label(axiom). [assumption].
% 2.47/2.76 254 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B)),A),C)) # label(cls_abs__diff__less__iff_0) # label(axiom). [assumption].
% 2.47/2.76 255 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__even__abs_0) # label(axiom). [assumption].
% 2.47/2.76 256 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_power__less__zero__eq__number__of_2) # label(axiom). [assumption].
% 2.47/2.76 257 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),C),A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),D)) # label(cls_abs__mult__less_0) # label(axiom). [assumption].
% 2.47/2.76 258 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) # label(cls_abs__mult__self_0) # label(axiom). [assumption].
% 2.47/2.76 259 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) # label(cls_abs__mult_0) # label(axiom). [assumption].
% 2.47/2.76 260 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_4) # label(axiom). [assumption].
% 2.47/2.76 261 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_5) # label(axiom). [assumption].
% 2.47/2.76 262 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__less__zero__eq_2) # label(axiom). [assumption].
% 2.47/2.76 263 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq_0) # label(axiom). [assumption].
% 2.47/2.76 264 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq__number__of_1) # label(axiom). [assumption].
% 2.47/2.76 265 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),D))) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__even_0) # label(axiom). [assumption].
% 2.47/2.76 266 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_1) # label(axiom). [assumption].
% 2.47/2.76 267 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) # label(cls_zero__less__power__eq__number__of_0) # label(axiom). [assumption].
% 2.47/2.76 268 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Oone__class_Oone(A)) = c_HOL_Oone__class_Oone(A) # label(cls_abs__one_0) # label(axiom). [assumption].
% 2.47/2.76 269 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_1) # label(axiom). [assumption].
% 2.47/2.76 270 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_0) # label(axiom). [assumption].
% 2.47/2.76 271 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 2.47/2.76 272 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq__number__of_0) # label(axiom). [assumption].
% 2.47/2.76 273 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),C) # label(cls_power__abs_0) # label(axiom). [assumption].
% 2.47/2.76 274 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B) # label(cls_abs__of__nat_0) # label(axiom). [assumption].
% 2.47/2.76 275 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),C)) # label(cls_abs__less__iff_0) # label(axiom). [assumption].
% 2.47/2.76 276 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_Int_Onumber__class_Onumber__of(B,A)) = c_Int_Onumber__class_Onumber__of(B,A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__number__of_1) # label(axiom). [assumption].
% 2.47/2.76 277 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_5) # label(axiom). [assumption].
% 2.47/2.76 278 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),A),D)) # label(cls_abs__diff__less__iff_1) # label(axiom). [assumption].
% 2.47/2.76 279 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_4) # label(axiom). [assumption].
% 2.47/2.76 280 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),c_Int_Onumber__class_Onumber__of(C,tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_power__even__abs__number__of_0) # label(axiom). [assumption].
% 2.47/2.76 281 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_1) # label(axiom). [assumption].
% 2.47/2.76 282 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__le__power__eq__number__of_1) # label(axiom). [assumption].
% 2.47/2.76 283 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__le__power__eq__number__of_2) # label(axiom). [assumption].
% 2.47/2.76 284 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) # label(cls_zero__le__power__eq__number__of_0) # label(axiom). [assumption].
% 2.47/2.76 285 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_2) # label(axiom). [assumption].
% 2.47/2.76 286 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__less__power__eq__number__of_2) # label(axiom). [assumption].
% 2.47/2.76 287 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B))) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_zero__less__power__eq_1) # label(axiom). [assumption].
% 2.47/2.76 288 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) # label(cls_zero__less__power__eq__number__of_3) # label(axiom). [assumption].
% 2.47/2.76 289 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(cls_zero__less__power__eq_0) # label(axiom). [assumption].
% 2.47/2.76 290 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),C) = hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_abs__mult__pos_0) # label(axiom). [assumption].
% 2.47/2.76 291 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_5) # label(axiom). [assumption].
% 2.47/2.76 292 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__le__zero__eq__number__of_4) # label(axiom). [assumption].
% 2.47/2.76 293 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(cls_zero__le__power__eq_0) # label(axiom). [assumption].
% 2.47/2.76 294 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_2) # label(axiom). [assumption].
% 2.47/2.76 295 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_0) # label(axiom). [assumption].
% 2.47/2.76 296 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_1) # label(axiom). [assumption].
% 2.47/2.76 297 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B))) # label(cls_zero__le__power__iff_0) # label(axiom). [assumption].
% 2.47/2.76 298 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_2) # label(axiom). [assumption].
% 2.47/2.76 299 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),C))) # label(cls_zero__le__power__abs_0) # label(axiom). [assumption].
% 2.47/2.76 300 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_3) # label(axiom). [assumption].
% 2.47/2.76 301 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_1) # label(axiom). [assumption].
% 2.47/2.76 302 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_1) # label(axiom). [assumption].
% 2.47/2.76 303 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__iff_2) # label(axiom). [assumption].
% 2.47/2.76 304 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)))) # label(cls_zero__less__power__eq_3) # label(axiom). [assumption].
% 2.47/2.76 305 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__less__power__eq_2) # label(axiom). [assumption].
% 2.47/2.76 306 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq_1) # label(axiom). [assumption].
% 2.47/2.76 307 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__odd_0) # label(axiom). [assumption].
% 2.47/2.76 308 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__le__zero__eq_4) # label(axiom). [assumption].
% 2.47/2.76 309 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_0) # label(axiom). [assumption].
% 2.47/2.76 310 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_5) # label(axiom). [assumption].
% 2.47/2.76 311 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__left__le__one__le_0) # label(axiom). [assumption].
% 2.47/2.76 312 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__right__le__one__le_0) # label(axiom). [assumption].
% 2.47/2.76 313 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__power__iff_1) # label(axiom). [assumption].
% 2.47/2.76 314 -class_Ring__and__Field_Oordered__idom(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_0) # label(axiom). [assumption].
% 2.47/2.76 315 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_3) # label(axiom). [assumption].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C),tc_Int_Oint),A)). [resolve(252,a,253,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),A)),tc_Int_Oint),B)). [resolve(252,a,254,a)].
% 2.47/2.76 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(252,a,255,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(252,a,256,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),C)). [resolve(252,a,257,a)].
% 2.47/2.76 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A). [resolve(252,a,258,a)].
% 2.47/2.76 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(252,a,259,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(252,a,260,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(252,a,261,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(252,a,262,a)].
% 2.47/2.76 Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,263,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,264,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),C))) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(252,a,265,a)].
% 2.47/2.76 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_nat)))) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat). [resolve(252,a,266,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)))). [resolve(252,a,267,a)].
% 2.47/2.76 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(252,a,268,a)].
% 2.47/2.76 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),B). [resolve(252,a,273,a)].
% 2.47/2.76 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A). [resolve(252,a,274,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint),B)). [resolve(252,a,275,a)].
% 2.47/2.76 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)) = c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,276,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),tc_Int_Oint),C)). [resolve(252,a,278,a)].
% 2.47/2.76 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,281,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(252,a,282,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(252,a,283,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)))). [resolve(252,a,284,a)].
% 2.47/2.76 Derived: c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,285,a)].
% 2.47/2.76 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_nat)))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,286,a)].
% 2.47/2.76 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A))) | -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(252,a,287,a)].
% 2.47/2.76 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)))). [resolve(252,a,288,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(252,a,289,a)].
% 2.47/2.76 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),B) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(252,a,290,a)].
% 2.47/2.76 Derived: -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,291,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(252,a,292,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(252,a,293,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(252,a,294,a)].
% 2.47/2.76 Derived: c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,298,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),B))). [resolve(252,a,299,a)].
% 2.47/2.76 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,300,a)].
% 2.47/2.76 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,301,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(252,a,302,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)))). [resolve(252,a,304,a)].
% 2.47/2.76 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,305,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,306,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(252,a,307,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(252,a,308,a)].
% 2.47/2.76 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,309,a)].
% 2.47/2.76 Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,310,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(252,a,311,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(252,a,312,a)].
% 2.47/2.76 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(252,a,313,a)].
% 2.47/2.76 Derived: -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,314,a)].
% 2.55/2.81 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(252,a,315,a)].
% 2.55/2.81 316 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_Finite__Set_Ofinite(C,A) | hAPP(B,D) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_in(D,C,A) # label(cls_setsum__eq__0__iff_0) # label(axiom). [assumption].
% 2.55/2.81 317 -class_Finite__Set_Ofinite_Ofinite(A) | c_Finite__Set_Ofinite(B,A) # label(cls_finite_0) # label(axiom). [assumption].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(B,D) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_in(D,C,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(316,b,317,b)].
% 2.55/2.81 318 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Ofinite(C,A). [resolve(6,a,22,a)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),D),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(D,E) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_in(E,C,A). [resolve(318,b,316,b)].
% 2.55/2.81 319 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(6,a,27,a)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(319,c,317,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(319,c,318,b)].
% 2.55/2.81 320 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(C,B) | -c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(6,a,28,a)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(C,B) | -c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(320,c,317,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(320,c,318,b)].
% 2.55/2.81 321 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Finite__Set_Ofinite(C,A). [resolve(34,a,22,a)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),D),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(D,E) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_in(E,C,A). [resolve(321,b,316,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(D,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),C) = hAPP(E,D) | -c_in(D,C,A). [resolve(321,b,320,c)].
% 2.55/2.81 322 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(34,a,27,a)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(322,c,317,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(322,c,318,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(322,c,321,b)].
% 2.55/2.81 323 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(34,a,28,a)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(323,c,317,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(323,c,318,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(323,c,321,b)].
% 2.55/2.81 324 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Finite__Set_Ofinite(C,A). [resolve(35,a,22,a)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),D),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(D,E) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_in(E,C,A). [resolve(324,b,316,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(D,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),C) = hAPP(E,D) | -c_in(D,C,A). [resolve(324,b,320,c)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(D,A)),E,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),C) = hAPP(E,D) | -c_in(D,C,A). [resolve(324,b,323,c)].
% 2.55/2.81 325 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(35,a,27,a)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(325,c,317,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(325,c,318,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(325,c,321,b)].
% 2.55/2.81 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(325,c,324,b)].
% 2.55/2.81 326 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -c_in(B,D,A) | -c_Finite__Set_Ofinite(D,A). [resolve(35,a,28,a)].
% 2.60/2.89 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(326,c,317,b)].
% 2.60/2.89 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(326,c,318,b)].
% 2.60/2.89 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(326,c,321,b)].
% 2.60/2.89 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(326,c,324,b)].
% 2.60/2.89 327 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 2.60/2.89 328 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom). [assumption].
% 2.60/2.89 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(327,a,328,a)].
% 2.60/2.89 329 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption].
% 2.60/2.89 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) | A = B. [resolve(329,a,328,a)].
% 2.60/2.89 330 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.60/2.89 331 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D)) # label(cls_right__distrib__number__of_0) # label(axiom). [assumption].
% 2.60/2.89 332 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C)),E) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 2.70/2.98 333 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_Int_Onumber__class_Onumber__of(D,A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Int_Onumber__class_Onumber__of(D,A))) # label(cls_left__distrib__number__of_0) # label(axiom). [assumption].
% 2.70/2.98 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(330,a,332,a)].
% 2.70/2.98 334 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B)),D). [resolve(334,a,332,a)].
% 2.70/2.98 335 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 2.70/2.98 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(335,a,332,a)].
% 2.70/2.98 336 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.70/2.98 337 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 2.70/2.98 338 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.70/2.98 339 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 2.70/2.98 340 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 2.70/2.98 341 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_add__cancel__21_1) # label(axiom). [assumption].
% 2.70/2.98 342 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)) # label(cls_Deriv_Oadd__diff__add_0) # label(axiom). [assumption].
% 2.70/2.98 343 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 2.70/2.98 344 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(c_COMBB(B,tc_nat,A,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))) # label(cls_sumr__offset_0) # label(axiom). [assumption].
% 2.70/2.98 345 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),B),C),D,B,A,A)),E) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),E)),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),D),E)) # label(cls_setsum__subtractf_0) # label(axiom). [assumption].
% 2.70/2.98 346 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(E,D,tc_nat)) | -hBOOL(hAPP(c_lessequals(E,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),E)) # label(cls_setsum__diff__nat__ivl_0) # label(axiom). [assumption].
% 2.70/2.98 347 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__iff__diff__eq__0_0) # label(axiom). [assumption].
% 2.70/2.98 348 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D) | C = D # label(cls_eq__eqI_0) # label(axiom). [assumption].
% 2.70/2.98 349 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),D) | B = C # label(cls_eq__eqI_1) # label(axiom). [assumption].
% 2.70/2.98 350 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_eq__iff__diff__eq__0_1) # label(axiom). [assumption].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),D)). [resolve(340,a,342,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) = D. [resolve(340,a,343,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),hAPP(c_COMBB(A,tc_nat,tc_Int_Oint,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),B))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))). [resolve(340,a,344,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),B),C,A,tc_Int_Oint,tc_Int_Oint)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),C),D)). [resolve(340,a,345,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(D,C,tc_nat)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)). [resolve(340,a,346,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(340,a,347,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C) | B = C. [resolve(340,a,348,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),C) | A = B. [resolve(340,a,349,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(340,a,350,a)].
% 2.70/2.98 351 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)). [resolve(351,a,342,a)].
% 2.70/2.98 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),D) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) = D. [resolve(351,a,343,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBB(A,tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),B))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))). [resolve(351,a,344,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),C),D)). [resolve(351,a,345,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(D,C,tc_nat)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)). [resolve(351,a,346,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(351,a,347,a)].
% 2.70/2.98 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C) | B = C. [resolve(351,a,348,a)].
% 2.77/3.02 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),C) | A = B. [resolve(351,a,349,a)].
% 2.77/3.02 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(351,a,350,a)].
% 2.77/3.02 352 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 2.77/3.02 353 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(hAPP(c_COMBB(c_HOL_Oinverse__class_Oinverse(A),A,A,A),B),C,A) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(A) | -c_Deriv_Odifferentiable(B,C,A) # label(cls_differentiable__inverse_0) # label(axiom). [assumption].
% 2.77/3.02 354 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(hAPP(c_COMBB(B,A,A,A),C),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,hAPP(C,D),A) # label(cls_differentiable__compose_0) # label(axiom). [assumption].
% 2.77/3.02 355 -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].
% 2.77/3.02 356 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),A),B),C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__sum_0) # label(axiom). [assumption].
% 2.77/3.02 357 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(A),A,tc_fun(A,A),A),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),F),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__add_0) # label(axiom). [assumption].
% 2.77/3.02 358 -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].
% 2.77/3.02 359 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(B,C,A) | -c_Deriv_Oderiv(B,C,D,A) # label(cls_differentiable__def_1) # label(axiom). [assumption].
% 2.77/3.02 360 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(B,C,A) | -c_Deriv_Oderiv(B,C,D,A) # label(cls_differentiableI_0) # label(axiom). [assumption].
% 2.77/3.02 361 -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].
% 2.77/3.02 362 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_divide_Oadd_0) # label(axiom). [assumption].
% 2.77/3.02 363 -class_RealVector_Oreal__normed__field(A) | c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),tc_nat),B)),C),A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Series_Osuminf(B,A)),C) | -c_Series_Osummable(B,A) # label(cls_suminf__divide_0) # label(axiom). [assumption].
% 2.77/3.02 364 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Series_Osuminf(B,A)),C) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_divide_Osuminf_0) # label(axiom). [assumption].
% 2.77/3.02 365 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),A),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(C,D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),hAPP(B,D))),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__mult_0) # label(axiom). [assumption].
% 2.77/3.02 366 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),A),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(B,D)),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),hAPP(C,D))),A) | -c_Deriv_Oderiv(C,D,E,A) | -c_Deriv_Oderiv(B,D,F,A) # label(cls_DERIV__mult_H_0) # label(axiom). [assumption].
% 2.77/3.02 367 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(c_COMBB(B,A,A,A),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),F),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,hAPP(C,D),E,A) # label(cls_DERIV__chain2_0) # label(axiom). [assumption].
% 2.77/3.02 368 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(c_COMBB(B,A,A,A),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),F),A) | -c_Deriv_Oderiv(B,hAPP(C,D),E,A) | -c_Deriv_Oderiv(C,D,F,A) # label(cls_DERIV__chain_H_0) # label(axiom). [assumption].
% 2.77/3.02 369 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,A),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E),A) | -c_Deriv_Oderiv(C,D,E,A) # label(cls_DERIV__cmult_0) # label(axiom). [assumption].
% 2.77/3.02 370 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),A),B),C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__mult_0) # label(axiom). [assumption].
% 2.77/3.02 371 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),A),B),C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__diff_0) # label(axiom). [assumption].
% 2.77/3.02 372 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),A),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),F),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__diff_0) # label(axiom). [assumption].
% 2.77/3.02 373 -class_RealVector_Oreal__normed__field(A) | c_Limits_Otendsto(hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),B),C)),D),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),E),D),F,B,A) | -c_Limits_Otendsto(C,E,F,B,A) # label(cls_divide_Otendsto_0) # label(axiom). [assumption].
% 2.77/3.02 374 -class_RealVector_Oreal__normed__field(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),B),C)),D),E,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),F),D),B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_divide_OLIM_0) # label(axiom). [assumption].
% 2.77/3.02 375 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(hAPP(c_COMBC(A,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),A),B)),C),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),E),C),A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__cdivide_0) # label(axiom). [assumption].
% 2.77/3.02 376 -class_RealVector_Oreal__normed__field(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Oinverse__class_Odivide(A)),B),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),B),A,A) # label(cls_divide_Ocont_0) # label(axiom). [assumption].
% 2.77/3.02 377 -class_RealVector_Oreal__normed__field(A) | c_Lim_OisCont(hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Oinverse__class_Odivide(A)),B),C,A,A) # label(cls_divide_OisCont_0) # label(axiom). [assumption].
% 2.77/3.02 378 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(hAPP(c_COMBC(A,tc_nat,A),hAPP(c_COMBB(c_Power_Opower__class_Opower(A),A,tc_fun(tc_nat,A),A),B)),hAPP(c_Suc,C)),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(B,D)),C))),A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__power__Suc_0) # label(axiom). [assumption].
% 2.77/3.02 379 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(B,C,D,A) | -c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),A),hAPP(hAPP(c_COMBC(A,A,A),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),A),B)),hAPP(B,C))),hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Ominus__class_Ominus(A)),C),A,A,A),C,D,A,A) # label(cls_DERIV__iff2_1) # label(axiom). [assumption].
% 2.77/3.02 380 -class_RealVector_Oreal__normed__field(A) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),A),hAPP(hAPP(c_COMBC(A,A,A),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),A),B)),hAPP(B,C))),hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Ominus__class_Ominus(A)),C),A,A,A),C,D,A,A) | -c_Deriv_Oderiv(B,C,D,A) # label(cls_DERIV__iff2_0) # label(axiom). [assumption].
% 2.77/3.02 381 -class_RealVector_Oreal__normed__field(A) | c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_divide_Osummable_0) # label(axiom). [assumption].
% 2.77/3.02 382 -class_RealVector_Oreal__normed__field(A) | c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_summable__divide_0) # label(axiom). [assumption].
% 2.77/3.02 383 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),tc_nat),B)),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_divide_OLIMSEQ_0) # label(axiom). [assumption].
% 2.77/3.02 384 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_SEQ_OZseq(B,A) # label(cls_divide_OZseq_0) # label(axiom). [assumption].
% 2.77/3.02 385 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OCauchy(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_SEQ_OCauchy(B,A) # label(cls_divide_OCauchy_0) # label(axiom). [assumption].
% 2.77/3.02 386 -class_RealVector_Oreal__normed__field(A) | c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),tc_nat),B)),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_divide_Osums_0) # label(axiom). [assumption].
% 2.77/3.02 387 -class_RealVector_Oreal__normed__field(A) | c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),tc_nat),B)),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_sums__divide_0) # label(axiom). [assumption].
% 2.77/3.02 388 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBC(A,tc_nat,A),hAPP(c_COMBB(c_Power_Opower__class_Opower(A),A,tc_fun(tc_nat,A),A),B)),C),D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__power_0) # label(axiom). [assumption].
% 2.77/3.02 389 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(hAPP(c_COMBC(A,tc_nat,A),hAPP(c_COMBB(c_Power_Opower__class_Opower(A),A,tc_fun(tc_nat,A),A),B)),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(B,D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))))),A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__power_0) # label(axiom). [assumption].
% 2.77/3.02 390 -class_RealVector_Oreal__normed__field(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),B),C)),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide_OLIM__zero_0) # label(axiom). [assumption].
% 2.77/3.02 391 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),A),B),C,A,A,A),D,A) | hAPP(C,D) = c_HOL_Ozero__class_Ozero(A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__divide_0) # label(axiom). [assumption].
% 2.77/3.02 392 -class_RealVector_Oreal__normed__field(A) | c_Limits_Otendsto(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),B),C),D,B,A,A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),E),F),V6,B,A) | F = c_HOL_Ozero__class_Ozero(A) | -c_Limits_Otendsto(D,F,V6,B,A) | -c_Limits_Otendsto(C,E,V6,B,A) # label(cls_tendsto__divide_0) # label(axiom). [assumption].
% 2.77/3.03 393 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),A),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(C,D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),hAPP(B,D)))),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(C,D)),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))),A) | hAPP(C,D) = c_HOL_Ozero__class_Ozero(A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__quotient_0) # label(axiom). [assumption].
% 2.77/3.03 394 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E),A) | E = c_HOL_Ozero__class_Ozero(A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__divide_0) # label(axiom). [assumption].
% 2.77/3.03 395 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),A),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(C,D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(B,D)),F))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(C,D)),hAPP(C,D))),A) | hAPP(C,D) = c_HOL_Ozero__class_Ozero(A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__divide_0) # label(axiom). [assumption].
% 2.77/3.03 396 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),B),C)),E)),D) # label(cls_divide_Osetsum_0) # label(axiom). [assumption].
% 2.77/3.03 397 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_divide_Odiff_0) # label(axiom). [assumption].
% 2.77/3.03 398 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom). [assumption].
% 2.77/3.03 Derived: c_Deriv_Odifferentiable(hAPP(c_COMBB(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex) | hAPP(A,B) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,B,tc_Complex_Ocomplex). [resolve(352,a,353,a)].
% 2.77/3.03 Derived: c_Deriv_Odifferentiable(hAPP(c_COMBB(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,hAPP(B,C),tc_Complex_Ocomplex). [resolve(352,a,354,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,A,tc_Complex_Ocomplex). [resolve(352,a,355,a)].
% 2.77/3.03 Derived: c_Deriv_Odifferentiable(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(352,a,356,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),D),E),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(352,a,357,a)].
% 2.77/3.03 Derived: A = B | -c_Deriv_Oderiv(C,D,B,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(C,D,A,tc_Complex_Ocomplex). [resolve(352,a,358,a)].
% 2.77/3.03 Derived: c_Deriv_Odifferentiable(A,B,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex). [resolve(352,a,359,a)].
% 2.77/3.03 Derived: c_Lim_OisCont(A,B,tc_Complex_Ocomplex,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex). [resolve(352,a,361,a)].
% 2.77/3.03 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(352,a,362,a)].
% 2.77/3.03 Derived: c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),B) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(352,a,363,a)].
% 2.77/3.03 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),B) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(352,a,364,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(B,C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),hAPP(A,C))),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(352,a,365,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(A,C)),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),hAPP(B,C))),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,D,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,E,tc_Complex_Ocomplex). [resolve(352,a,366,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(hAPP(c_COMBB(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),E),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,hAPP(B,C),D,tc_Complex_Ocomplex). [resolve(352,a,367,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,D,tc_Complex_Ocomplex). [resolve(352,a,369,a)].
% 2.77/3.03 Derived: c_Deriv_Odifferentiable(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(352,a,370,a)].
% 2.77/3.03 Derived: c_Deriv_Odifferentiable(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(352,a,371,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),E),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(352,a,372,a)].
% 2.77/3.03 Derived: c_Limits_Otendsto(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B)),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),C),E,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,E,A,tc_Complex_Ocomplex). [resolve(352,a,373,a)].
% 2.77/3.03 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B)),C),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),E),C),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(352,a,374,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A)),B),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),B),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(352,a,375,a)].
% 2.77/3.03 Derived: c_Lim_OLIM(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A),B,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(352,a,376,a)].
% 2.77/3.03 Derived: c_Lim_OisCont(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(352,a,377,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A)),hAPP(c_Suc,B)),C,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)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),B))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(A,C)),B))),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(352,a,378,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex) | -c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A)),hAPP(A,B))),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(352,a,379,a)].
% 2.77/3.03 Derived: c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A)),hAPP(A,B))),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex). [resolve(352,a,380,a)].
% 2.77/3.03 Derived: c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(352,a,381,a)].
% 2.77/3.03 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(352,a,383,a)].
% 2.77/3.03 Derived: c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(352,a,384,a)].
% 2.77/3.03 Derived: c_SEQ_OCauchy(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(A,tc_Complex_Ocomplex). [resolve(352,a,385,a)].
% 2.77/3.03 Derived: c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(352,a,386,a)].
% 2.77/3.03 Derived: c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A)),B),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(352,a,388,a)].
% 2.77/3.03 Derived: c_Deriv_Oderiv(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A)),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(A,C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))))),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(352,a,389,a)].
% 2.77/3.03 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B)),C),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(352,a,390,a)].
% 2.77/3.03 Derived: c_Deriv_Odifferentiable(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(352,a,391,a)].
% 2.84/3.07 Derived: c_Limits_Otendsto(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),E),F,A,tc_Complex_Ocomplex) | E = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Limits_Otendsto(C,E,F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,F,A,tc_Complex_Ocomplex). [resolve(352,a,392,a)].
% 2.84/3.07 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(B,C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),hAPP(A,C)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(B,C)),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))),tc_Complex_Ocomplex) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(352,a,393,a)].
% 2.84/3.07 Derived: c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(352,a,394,a)].
% 2.84/3.07 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(B,C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(A,C)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(B,C)),hAPP(B,C))),tc_Complex_Ocomplex) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(352,a,395,a)].
% 2.84/3.07 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B)),D)),C). [resolve(352,a,396,a)].
% 2.84/3.07 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(352,a,397,a)].
% 2.84/3.07 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(352,a,398,a)].
% 2.84/3.07 399 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 2.84/3.07 400 -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].
% 2.84/3.07 401 -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].
% 2.84/3.07 402 -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].
% 2.84/3.07 403 -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].
% 2.84/3.07 404 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),c_Int_Onumber__class_Onumber__of(B,A)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),c_Int_Onumber__class_Onumber__of(B,A)) # label(cls_inverse__eq__divide__number__of_0) # label(axiom). [assumption].
% 2.84/3.07 405 -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_Oinverse__class_Odivide(A),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),B) # label(cls_inverse__divide_0) # label(axiom). [assumption].
% 2.84/3.07 406 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_add__divide__distrib_0) # label(axiom). [assumption].
% 2.84/3.07 407 -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].
% 2.84/3.07 408 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) != c_Int_Onumber__class_Onumber__of(D,A) | B = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_0) # label(axiom). [assumption].
% 2.84/3.07 409 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,A))),c_Int_Onumber__class_Onumber__of(B,A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_4) # label(axiom). [assumption].
% 2.84/3.07 410 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),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)) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom). [assumption].
% 2.84/3.07 411 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C) = c_Int_Onumber__class_Onumber__of(B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_3) # label(axiom). [assumption].
% 2.84/3.07 412 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(C,A))),c_Int_Onumber__class_Onumber__of(C,A)) = B | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of1_0) # label(axiom). [assumption].
% 2.84/3.07 413 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | B = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(C,A))),c_Int_Onumber__class_Onumber__of(C,A)) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_0) # label(axiom). [assumption].
% 2.84/3.07 414 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_3) # label(axiom). [assumption].
% 2.84/3.07 415 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C) = c_Int_Onumber__class_Onumber__of(B,A) # label(cls_divide__eq__eq__number__of_4) # label(axiom). [assumption].
% 2.84/3.07 416 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))),D) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom). [assumption].
% 2.84/3.07 417 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom). [assumption].
% 2.84/3.07 418 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C) # label(cls_eq__divide__eq__number__of_4) # label(axiom). [assumption].
% 2.84/3.07 419 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D) = C | D = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_0) # label(axiom). [assumption].
% 2.84/3.07 420 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | B = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(C,A))),c_Int_Onumber__class_Onumber__of(C,A)) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of1_3) # label(axiom). [assumption].
% 2.84/3.07 421 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(C,A))),c_Int_Onumber__class_Onumber__of(C,A)) = B | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_3) # label(axiom). [assumption].
% 2.84/3.07 422 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,A))),c_Int_Onumber__class_Onumber__of(B,A)) # label(cls_eq__divide__eq__number__of1_4) # label(axiom). [assumption].
% 2.84/3.07 423 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__divide_0) # label(axiom). [assumption].
% 2.84/3.07 424 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),E),C))) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),E))),C) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__divides__special_0) # label(axiom). [assumption].
% 2.84/3.07 425 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_Int_Onumber__class_Onumber__of(B,A)) # label(cls_eq__divide__eq__number__of1_2) # label(axiom). [assumption].
% 2.84/3.07 426 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_HOL_Ozero__class_Ozero(A)) # label(cls_eq__divide__eq__number__of_2) # label(axiom). [assumption].
% 2.84/3.07 427 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_HOL_Ozero__class_Ozero(A)) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_1) # label(axiom). [assumption].
% 2.84/3.07 428 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_HOL_Ozero__class_Ozero(A)) = c_Int_Onumber__class_Onumber__of(B,A) # label(cls_divide__eq__eq__number__of_2) # label(axiom). [assumption].
% 2.84/3.07 429 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) != c_Int_Onumber__class_Onumber__of(C,A) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_1) # label(axiom). [assumption].
% 2.84/3.07 430 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_Int_Onumber__class_Onumber__of(B,A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_1) # label(axiom). [assumption].
% 2.84/3.07 431 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) = 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].
% 2.84/3.07 432 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) = 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].
% 2.84/3.07 433 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B) # label(cls_class__fieldgb_Oinverse__divide_0) # label(axiom). [assumption].
% 2.84/3.07 434 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Oinverse__class_Oinverse(A),B) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B) # label(cls_inverse__eq__divide_0) # label(axiom). [assumption].
% 2.84/3.07 435 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oinverse__class_Oinverse(A),B)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff__inverse_0) # label(axiom). [assumption].
% 2.84/3.07 436 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) != c_HOL_Oone__class_Oone(A) | C = c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__inverse__eq_0) # label(axiom). [assumption].
% 2.84/3.07 437 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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)) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__frac__eq_0) # label(axiom). [assumption].
% 2.84/3.07 438 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),C)) | hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff__rev__if_1) # label(axiom). [assumption].
% 2.84/3.07 439 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_divide__1_0) # label(axiom). [assumption].
% 2.84/3.07 440 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom). [assumption].
% 2.84/3.07 441 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Oinverse__class_Odivide(A),A,tc_fun(A,A),B),C)),E)),D) # label(cls_setsum__divide__distrib_0) # label(axiom). [assumption].
% 2.84/3.07 442 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)),B) # label(cls_eq__divide__eq_4) # label(axiom). [assumption].
% 2.84/3.07 443 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom). [assumption].
% 2.84/3.07 444 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom). [assumption].
% 2.84/3.07 445 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff__rev__if_0) # label(axiom). [assumption].
% 2.84/3.07 446 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__divide_0) # label(axiom). [assumption].
% 2.84/3.07 447 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_eq__divide__eq_2) # label(axiom). [assumption].
% 2.84/3.07 448 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E) | 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].
% 2.84/3.07 449 -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) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),E) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C) # label(cls_frac__eq__eq_1) # label(axiom). [assumption].
% 2.84/3.07 450 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom). [assumption].
% 2.84/3.07 451 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_mult__frac__frac_0) # label(axiom). [assumption].
% 2.84/3.07 452 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_power__divide_0) # label(axiom). [assumption].
% 2.84/3.07 453 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),B) # label(cls_eq__divide__imp_0) # label(axiom). [assumption].
% 2.84/3.07 454 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),B) = C # label(cls_divide__eq__imp_0) # label(axiom). [assumption].
% 2.84/3.07 455 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom). [assumption].
% 2.84/3.07 456 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom). [assumption].
% 2.84/3.07 457 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_diff__divide__distrib_0) # label(axiom). [assumption].
% 2.84/3.07 458 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B)),C) # label(cls_power__one__over_0) # label(axiom). [assumption].
% 2.84/3.07 459 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) # label(cls_right__inverse__eq_1) # label(axiom). [assumption].
% 2.84/3.07 460 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self_0) # label(axiom). [assumption].
% 2.84/3.07 461 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_1) # label(axiom). [assumption].
% 2.84/3.07 462 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff_0) # label(axiom). [assumption].
% 2.84/3.07 463 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom). [assumption].
% 2.84/3.07 464 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom). [assumption].
% 2.84/3.07 465 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom). [assumption].
% 2.84/3.07 466 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(A),B),D) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom). [assumption].
% 2.84/3.07 467 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(A),C),D) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom). [assumption].
% 2.84/3.07 468 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_mult__frac__num_0) # label(axiom). [assumption].
% 2.84/3.07 469 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(c_Power_Opower__class_Opower(A),B)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),c_HOL_Oone__class_Oone(A))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Oone__class_Oone(A))) | B = c_HOL_Oone__class_Oone(A) # label(cls_geometric__sum_0) # label(axiom). [assumption].
% 2.84/3.07 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(399,a,400,a)].
% 2.84/3.07 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(399,a,401,a)].
% 2.84/3.07 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(399,a,403,a)].
% 2.84/3.07 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)). [resolve(399,a,404,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A). [resolve(399,a,405,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,408,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,409,a)].
% 2.84/3.07 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),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)) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,410,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),B)),B) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,411,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) = A | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,412,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,413,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),B)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,414,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),B)),B) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex). [resolve(399,a,415,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C))),C) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,416,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B))),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,417,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),B)),B). [resolve(399,a,418,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),C) = B | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,419,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,420,a)].
% 2.84/3.07 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) = A | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,421,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)). [resolve(399,a,422,a)].
% 2.84/3.08 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,423,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),B))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),D))),B) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,424,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)). [resolve(399,a,425,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(399,a,426,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,427,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex). [resolve(399,a,428,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,429,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,430,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),B)). [resolve(399,a,431,a)].
% 2.84/3.08 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A). [resolve(399,a,433,a)].
% 2.84/3.08 Derived: hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A). [resolve(399,a,434,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),A)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,435,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(399,a,436,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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)) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,437,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),B)) | hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,438,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(399,a,439,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A)),A). [resolve(399,a,442,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,443,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),B) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,444,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,445,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,446,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(399,a,447,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D) | 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(399,a,448,a)].
% 2.84/3.08 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) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B). [resolve(399,a,449,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,450,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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(399,a,451,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)). [resolve(399,a,452,a)].
% 2.84/3.08 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)),A). [resolve(399,a,453,a)].
% 2.84/3.08 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)),A) = B. [resolve(399,a,454,a)].
% 2.84/3.08 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A)),B). [resolve(399,a,458,a)].
% 2.84/3.08 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(399,a,459,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,462,a)].
% 2.87/3.12 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,464,a)].
% 2.87/3.12 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,466,a)].
% 2.87/3.12 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(399,a,467,a)].
% 2.87/3.12 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),B). [resolve(399,a,468,a)].
% 2.87/3.12 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))) | A = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(399,a,469,a)].
% 2.87/3.12 470 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 2.87/3.12 471 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))))) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 2.87/3.12 472 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 2.87/3.12 473 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)))) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 2.87/3.12 474 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)))) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 2.87/3.12 475 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 2.87/3.12 476 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 2.87/3.12 477 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 2.87/3.12 478 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)))) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 2.87/3.12 479 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 2.87/3.12 480 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 2.87/3.12 481 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 2.87/3.12 482 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 2.87/3.12 483 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 2.87/3.12 484 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 2.87/3.12 485 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 2.87/3.12 486 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 2.87/3.12 487 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 2.87/3.12 488 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 2.87/3.12 489 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 2.87/3.12 490 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 2.87/3.12 491 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 2.87/3.12 492 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 2.87/3.12 493 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 2.87/3.12 494 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 2.87/3.12 495 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 2.87/3.12 496 -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].
% 2.87/3.12 497 -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].
% 2.87/3.12 498 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 2.87/3.12 499 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 2.87/3.12 500 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 2.87/3.12 501 -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].
% 2.87/3.12 502 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 2.87/3.12 503 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 2.87/3.12 504 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 2.87/3.12 505 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 2.87/3.12 506 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Omonoid__mult(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__even__power_0) # label(axiom). [assumption].
% 2.87/3.12 507 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 2.87/3.12 508 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 2.87/3.12 509 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 2.87/3.12 510 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 2.87/3.12 511 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B))) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 2.87/3.12 512 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 2.87/3.12 513 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 2.87/3.12 514 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 2.87/3.12 515 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 2.87/3.12 516 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 2.87/3.12 517 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 2.87/3.12 518 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 2.87/3.12 519 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 2.87/3.12 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))))). [resolve(470,a,471,a)].
% 2.87/3.12 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,472,a)].
% 2.87/3.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)))) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(470,a,473,a)].
% 2.87/3.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)))) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(470,a,474,a)].
% 2.87/3.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(470,a,475,a)].
% 2.87/3.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(470,a,476,a)].
% 2.87/3.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,477,a)].
% 2.87/3.12 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)))). [resolve(470,a,478,a)].
% 2.87/3.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(470,a,479,a)].
% 2.87/3.12 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)). [resolve(470,a,480,a)].
% 2.87/3.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,481,a)].
% 2.87/3.12 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,482,a)].
% 2.87/3.12 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,483,a)].
% 2.87/3.12 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,484,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,485,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,486,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)). [resolve(470,a,487,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(470,a,488,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),A)). [resolve(470,a,492,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(470,a,493,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,495,a)].
% 2.87/3.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(470,a,496,a)].
% 2.87/3.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(470,a,497,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(470,a,498,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(470,a,499,a)].
% 2.87/3.13 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,500,a)].
% 2.87/3.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(470,a,501,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(470,a,502,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(470,a,503,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(470,a,504,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(470,a,505,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,508,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,509,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A))). [resolve(470,a,511,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(470,a,512,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,513,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A))). [resolve(470,a,515,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(470,a,516,a)].
% 2.87/3.13 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(470,a,518,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(470,a,519,a)].
% 2.90/3.17 520 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.90/3.17 521 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)))) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 2.90/3.17 522 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)))) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 2.90/3.17 523 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 2.90/3.17 524 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 2.90/3.17 525 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 2.90/3.17 526 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 2.90/3.17 527 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 2.90/3.17 528 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 2.90/3.17 529 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 2.90/3.17 530 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 2.90/3.17 531 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 2.90/3.17 532 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 2.90/3.17 533 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 2.90/3.17 534 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 2.90/3.17 535 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)),A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 2.90/3.17 536 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 2.90/3.17 537 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 2.90/3.17 538 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,D)),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Suc,D)))) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 2.90/3.17 539 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Suc,C)) | B = D | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 2.90/3.17 540 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 2.90/3.17 541 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 2.90/3.17 542 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 2.90/3.17 543 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 2.90/3.17 544 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 2.90/3.17 545 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 2.90/3.17 546 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 2.90/3.17 547 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 2.90/3.17 548 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C) | B = D | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 2.90/3.17 549 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 2.90/3.17 550 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 2.90/3.17 551 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 2.90/3.17 552 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 2.90/3.17 553 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D),tc_nat)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),E)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(E,B,C,A),tc_nat),C)) # label(cls_real__setsum__nat__ivl__bounded2_0) # label(axiom). [assumption].
% 2.90/3.17 554 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D),tc_nat)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),E)) | -hBOOL(hAPP(c_lessequals(hAPP(B,c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(E,B,C,A)),A),E)) # label(cls_real__setsum__nat__ivl__bounded2_1) # label(axiom). [assumption].
% 2.90/3.17 555 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 2.90/3.17 556 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 2.90/3.17 557 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 2.90/3.17 558 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 2.90/3.17 559 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 2.90/3.17 560 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 2.90/3.17 561 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 2.90/3.17 562 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 2.90/3.17 563 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_power__mono_0) # label(axiom). [assumption].
% 2.90/3.17 564 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 2.90/3.17 565 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)))). [resolve(520,a,521,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))). [resolve(520,a,522,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(520,a,523,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(520,a,524,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)). [resolve(520,a,525,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(520,a,528,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A),tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),B))). [resolve(520,a,529,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A),tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(520,a,530,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(520,a,531,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A))). [resolve(520,a,532,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(520,a,533,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(520,a,534,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)),tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(520,a,535,a)].
% 2.90/3.17 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(520,a,536,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(520,a,537,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,C)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),hAPP(c_Suc,C)))). [resolve(520,a,538,a)].
% 2.90/3.17 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),hAPP(c_Suc,B)) | A = C | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(520,a,539,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C))). [resolve(520,a,540,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(520,a,541,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(520,a,542,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(520,a,543,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(520,a,544,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(520,a,545,a)].
% 2.90/3.17 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | B = C. [resolve(520,a,546,a)].
% 2.90/3.17 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(520,a,547,a)].
% 2.90/3.17 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B) | A = C | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(520,a,548,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(520,a,549,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(520,a,550,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)). [resolve(520,a,551,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),B)),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(D,A,B,tc_nat),tc_nat),B)). [resolve(520,a,553,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),B)),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),D)) | -hBOOL(hAPP(c_lessequals(hAPP(A,c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(D,A,B,tc_nat)),tc_nat),D)). [resolve(520,a,554,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(520,a,555,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(520,a,556,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(520,a,557,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(520,a,558,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(520,a,559,a)].
% 2.90/3.17 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(520,a,560,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A),tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),B))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(520,a,561,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A),tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),B))). [resolve(520,a,562,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(520,a,563,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A))). [resolve(520,a,564,a)].
% 2.90/3.17 566 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint)))). [resolve(566,a,521,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)))). [resolve(566,a,522,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(566,a,523,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,524,a)].
% 2.90/3.17 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),C)). [resolve(566,a,525,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,528,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))). [resolve(566,a,529,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(566,a,530,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,531,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))). [resolve(566,a,532,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(566,a,533,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(566,a,534,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,535,a)].
% 2.90/3.18 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(566,a,536,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(566,a,537,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,C)),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Suc,C)))). [resolve(566,a,538,a)].
% 2.90/3.18 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(c_Suc,B)) | A = C | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,539,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C))). [resolve(566,a,540,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,541,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,542,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(566,a,543,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,544,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,545,a)].
% 2.90/3.18 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | B = C. [resolve(566,a,546,a)].
% 2.90/3.18 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(566,a,547,a)].
% 2.90/3.18 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B) | A = C | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,548,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,549,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,550,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),C)). [resolve(566,a,551,a)].
% 2.90/3.18 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),tc_nat)),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(D,A,B,tc_Int_Oint),tc_nat),B)). [resolve(566,a,553,a)].
% 3.01/3.26 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),tc_nat)),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(hAPP(A,c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(D,A,B,tc_Int_Oint)),tc_Int_Oint),D)). [resolve(566,a,554,a)].
% 3.01/3.26 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(566,a,555,a)].
% 3.01/3.26 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(566,a,557,a)].
% 3.01/3.26 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(566,a,558,a)].
% 3.01/3.26 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(566,a,559,a)].
% 3.01/3.26 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(566,a,560,a)].
% 3.01/3.26 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(566,a,561,a)].
% 3.01/3.26 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))). [resolve(566,a,562,a)].
% 3.01/3.26 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(566,a,563,a)].
% 3.01/3.26 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))). [resolve(566,a,564,a)].
% 3.01/3.26 567 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.01/3.26 568 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 3.01/3.26 569 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.01/3.26 570 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.01/3.26 571 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.01/3.26 572 -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].
% 3.01/3.26 573 -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].
% 3.01/3.26 574 -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].
% 3.01/3.26 575 -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].
% 3.01/3.26 576 -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].
% 3.01/3.26 577 -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].
% 3.01/3.26 578 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osuminf(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,tc_nat),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Series_Osuminf(C,A)) | -c_Series_Osummable(C,A) # label(cls_suminf__mult_0) # label(axiom). [assumption].
% 3.01/3.26 579 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Series_Osuminf(C,A)) = c_Series_Osuminf(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,tc_nat),C),A) | -c_Series_Osummable(C,A) # label(cls_mult__right_Osuminf_0) # label(axiom). [assumption].
% 3.01/3.26 580 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Series_Osuminf(B,A)),C) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_mult__left_Osuminf_0) # label(axiom). [assumption].
% 3.01/3.26 581 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Series_Osuminf(B,A)),C) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_suminf__mult2_0) # label(axiom). [assumption].
% 3.01/3.26 582 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),C),A,A,B),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__mult__right__zero_0) # label(axiom). [assumption].
% 3.01/3.26 583 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),C),A,A,B),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__right_OLIM__zero_0) # label(axiom). [assumption].
% 3.01/3.26 584 -class_RealVector_Oreal__normed__algebra(A) | c_Limits_Otendsto(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E),F,C,A) | -c_Limits_Otendsto(D,E,F,C,A) # label(cls_mult__right_Otendsto_0) # label(axiom). [assumption].
% 3.01/3.26 585 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),C),A,A,B),D),E,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),F),B,A) | -c_Lim_OLIM(D,E,F,B,A) # label(cls_mult__right_OLIM_0) # label(axiom). [assumption].
% 3.01/3.26 586 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))) # label(cls_mult_Oprod__diff__prod_0) # label(axiom). [assumption].
% 3.01/3.26 587 -class_RealVector_Oreal__normed__algebra(A) | c_Limits_Otendsto(hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),B),C)),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),D),F,B,A) | -c_Limits_Otendsto(C,E,F,B,A) # label(cls_mult__left_Otendsto_0) # label(axiom). [assumption].
% 3.01/3.26 588 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),B),C)),D),E,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),D),B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_mult__left_OLIM_0) # label(axiom). [assumption].
% 3.01/3.26 589 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),B),C),D,B,A,A),E,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),V6),B,A) | -c_Lim_OLIM(D,E,V6,B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__mult_0) # label(axiom). [assumption].
% 3.01/3.26 590 -class_RealVector_Oreal__normed__algebra(A) | c_Limits_Otendsto(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),B),C),D,B,A,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),F),V6,B,A) | -c_Limits_Otendsto(D,F,V6,B,A) | -c_Limits_Otendsto(C,E,V6,B,A) # label(cls_mult_Otendsto_0) # label(axiom). [assumption].
% 3.01/3.26 591 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__algebra(B) | c_Lim_OisCont(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(B),B,tc_fun(B,B),A),C),D,A,B,B),E,A,B) | -c_Lim_OisCont(D,E,A,B) | -c_Lim_OisCont(C,E,A,B) # label(cls_isCont__mult_0) # label(axiom). [assumption].
% 3.01/3.26 592 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__mult_0) # label(axiom). [assumption].
% 3.01/3.26 593 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B),C,tc_nat,A,A),A) | -c_SEQ_OZseq(C,A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__mult_0) # label(axiom). [assumption].
% 3.01/3.26 594 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_sums__mult2_0) # label(axiom). [assumption].
% 3.01/3.26 595 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_mult__left_Osums_0) # label(axiom). [assumption].
% 3.01/3.26 596 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_summable__mult2_0) # label(axiom). [assumption].
% 3.01/3.26 597 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_mult__left_Osummable_0) # label(axiom). [assumption].
% 3.01/3.26 598 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OCauchy(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_SEQ_OCauchy(B,A) # label(cls_mult__left_OCauchy_0) # label(axiom). [assumption].
% 3.01/3.26 599 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_mult__left_OLIMSEQ_0) # label(axiom). [assumption].
% 3.01/3.26 600 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__mult__left_0) # label(axiom). [assumption].
% 3.01/3.26 601 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OisCont(hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Otimes__class_Otimes(A)),B),C,A,A) # label(cls_mult__left_OisCont_0) # label(axiom). [assumption].
% 3.01/3.26 602 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Otimes__class_Otimes(A)),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A,A) # label(cls_mult__left_Ocont_0) # label(axiom). [assumption].
% 3.01/3.26 603 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OCauchy(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,tc_nat),C),A) | -c_SEQ_OCauchy(C,A) # label(cls_mult__right_OCauchy_0) # label(axiom). [assumption].
% 3.01/3.26 604 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_SEQ_OLIMSEQ(C,D,A) # label(cls_mult__right_OLIMSEQ_0) # label(axiom). [assumption].
% 3.01/3.26 605 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,tc_nat),C),A) | -c_SEQ_OZseq(C,A) # label(cls_mult__right_OZseq_0) # label(axiom). [assumption].
% 3.01/3.26 606 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,tc_nat),C),A) | -c_SEQ_OZseq(C,A) # label(cls_Zseq__mult__right_0) # label(axiom). [assumption].
% 3.01/3.26 607 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,tc_nat),C),A) | -c_Series_Osummable(C,A) # label(cls_summable__mult_0) # label(axiom). [assumption].
% 3.01/3.26 608 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,tc_nat),C),A) | -c_Series_Osummable(C,A) # label(cls_mult__right_Osummable_0) # label(axiom). [assumption].
% 3.01/3.26 609 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_Series_Osums(C,D,A) # label(cls_mult__right_Osums_0) # label(axiom). [assumption].
% 3.01/3.26 610 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_Series_Osums(C,D,A) # label(cls_sums__mult_0) # label(axiom). [assumption].
% 3.01/3.26 611 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B)),C),A) | -c_SEQ_OZseq(B,A) # label(cls_mult__left_OZseq_0) # label(axiom). [assumption].
% 3.01/3.26 612 -class_RealVector_Oreal__normed__algebra(A) | -class_Power_Opower(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,tc_nat,A),hAPP(c_COMBB(c_Power_Opower__class_Opower(A),A,tc_fun(tc_nat,A),B),C)),D),E,hAPP(hAPP(c_Power_Opower__class_Opower(A),F),D),B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__power_0) # label(axiom). [assumption].
% 3.01/3.26 613 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__algebra(B) | -class_Power_Opower(B) | c_Lim_OisCont(hAPP(hAPP(c_COMBC(A,tc_nat,B),hAPP(c_COMBB(c_Power_Opower__class_Opower(B),B,tc_fun(tc_nat,B),A),C)),D),E,A,B) | -c_Lim_OisCont(C,E,A,B) # label(cls_isCont__power_0) # label(axiom). [assumption].
% 3.01/3.26 614 -class_RealVector_Oreal__normed__algebra(A) | -class_Power_Opower(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_nat,A),hAPP(c_COMBB(c_Power_Opower__class_Opower(A),A,tc_fun(tc_nat,A),tc_nat),B)),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__pow_0) # label(axiom). [assumption].
% 3.01/3.26 615 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),B),C)),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__mult__left__zero_0) # label(axiom). [assumption].
% 3.01/3.26 616 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),B),C)),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__left_OLIM__zero_0) # label(axiom). [assumption].
% 3.01/3.26 617 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),B),C),D,B,A,A),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__mult__zero_0) # label(axiom). [assumption].
% 3.01/3.26 618 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),B),C)),E)),D) # label(cls_mult__left_Osetsum_0) # label(axiom). [assumption].
% 3.01/3.26 619 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Finite__Set_Osetsum(C,A),D),E)) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,C),D)),E) # label(cls_mult__right_Osetsum_0) # label(axiom). [assumption].
% 3.01/3.26 620 -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].
% 3.01/3.26 621 -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].
% 3.01/3.26 622 -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].
% 3.01/3.26 623 -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].
% 3.01/3.26 624 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult__right_Odiff_0) # label(axiom). [assumption].
% 3.01/3.26 625 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult_Odiff__right_0) # label(axiom). [assumption].
% 3.01/3.26 626 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult_Odiff__left_0) # label(axiom). [assumption].
% 3.01/3.26 627 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Odiff_0) # label(axiom). [assumption].
% 3.01/3.26 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(571,a,576,a)].
% 3.01/3.26 Derived: c_Lim_OisCont(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(571,a,577,a)].
% 3.01/3.26 Derived: c_Series_Osuminf(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Series_Osuminf(B,tc_Complex_Ocomplex)) | -c_Series_Osummable(B,tc_Complex_Ocomplex). [resolve(571,a,578,a)].
% 3.01/3.26 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Series_Osuminf(B,tc_Complex_Ocomplex)) = c_Series_Osuminf(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),B),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex). [resolve(571,a,579,a)].
% 3.01/3.26 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),B) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(571,a,580,a)].
% 3.01/3.26 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),C),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(571,a,582,a)].
% 3.01/3.26 Derived: c_Limits_Otendsto(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex,B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D),E,B,tc_Complex_Ocomplex) | -c_Limits_Otendsto(C,D,E,B,tc_Complex_Ocomplex). [resolve(571,a,584,a)].
% 3.01/3.26 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),E),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,E,A,tc_Complex_Ocomplex). [resolve(571,a,585,a)].
% 3.01/3.26 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D))). [resolve(571,a,586,a)].
% 3.01/3.26 Derived: c_Limits_Otendsto(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),C),E,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,E,A,tc_Complex_Ocomplex). [resolve(571,a,587,a)].
% 3.01/3.26 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B)),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),C),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(571,a,588,a)].
% 3.01/3.26 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),F),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,F,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(571,a,589,a)].
% 3.01/3.26 Derived: c_Limits_Otendsto(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),E),F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(C,E,F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,F,A,tc_Complex_Ocomplex). [resolve(571,a,590,a)].
% 3.01/3.26 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OisCont(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,A,tc_Complex_Ocomplex) | -c_Lim_OisCont(C,D,A,tc_Complex_Ocomplex) | -c_Lim_OisCont(B,D,A,tc_Complex_Ocomplex). [resolve(571,a,591,b)].
% 3.01/3.26 Derived: c_SEQ_OLIMSEQ(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(571,a,592,a)].
% 3.01/3.26 Derived: c_SEQ_OZseq(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(571,a,593,a)].
% 3.01/3.26 Derived: c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(571,a,594,a)].
% 3.01/3.26 Derived: c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(571,a,596,a)].
% 3.01/3.26 Derived: c_SEQ_OCauchy(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(A,tc_Complex_Ocomplex). [resolve(571,a,598,a)].
% 3.01/3.26 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(571,a,599,a)].
% 3.01/3.26 Derived: c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(571,a,600,a)].
% 3.01/3.26 Derived: c_Lim_OisCont(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(571,a,601,a)].
% 3.01/3.26 Derived: c_Lim_OLIM(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A),B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(571,a,602,a)].
% 3.01/3.27 Derived: c_SEQ_OCauchy(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),B),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(B,tc_Complex_Ocomplex). [resolve(571,a,603,a)].
% 3.01/3.27 Derived: c_SEQ_OLIMSEQ(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,C,tc_Complex_Ocomplex). [resolve(571,a,604,a)].
% 3.01/3.27 Derived: c_SEQ_OZseq(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),B),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex). [resolve(571,a,605,a)].
% 3.01/3.27 Derived: c_Series_Osummable(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),B),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex). [resolve(571,a,607,a)].
% 3.01/3.27 Derived: c_Series_Osums(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_Series_Osums(B,C,tc_Complex_Ocomplex). [resolve(571,a,609,a)].
% 3.01/3.27 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),A),B)),C),D,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),E),C),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(571,a,612,a)].
% 3.01/3.27 Derived: -class_RealVector_Ometric__space(A) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Lim_OisCont(hAPP(hAPP(c_COMBC(A,tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),A),B)),C),D,A,tc_Complex_Ocomplex) | -c_Lim_OisCont(B,D,A,tc_Complex_Ocomplex). [resolve(571,a,613,b)].
% 3.01/3.27 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_Complex_Ocomplex),hAPP(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(571,a,614,a)].
% 3.01/3.27 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B)),C),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(571,a,615,a)].
% 3.01/3.27 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(571,a,617,a)].
% 3.01/3.27 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B)),D)),C). [resolve(571,a,618,a)].
% 3.01/3.27 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex,B),C)),D). [resolve(571,a,619,a)].
% 3.08/3.31 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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(571,a,624,a)].
% 3.08/3.31 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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(571,a,626,a)].
% 3.08/3.31 628 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 3.08/3.31 629 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F))) # label(cls_less__add__iff2_1) # label(axiom). [assumption].
% 3.08/3.31 630 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)),E)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F))) # label(cls_less__add__iff2_0) # label(axiom). [assumption].
% 3.08/3.31 631 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D),A),F)) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 3.08/3.31 632 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)),E),A),F)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F))) # label(cls_less__add__iff1_0) # label(axiom). [assumption].
% 3.08/3.31 633 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_lessequals(D,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F))) # label(cls_le__add__iff2_1) # label(axiom). [assumption].
% 3.08/3.31 634 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)),E)),F))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F))) # label(cls_le__add__iff2_0) # label(axiom). [assumption].
% 3.08/3.31 635 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D),A),F)) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 3.08/3.31 636 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)),E),A),F)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F))) # label(cls_le__add__iff1_0) # label(axiom). [assumption].
% 3.08/3.31 637 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),B)) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 3.08/3.31 638 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),C)) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 3.08/3.31 639 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 3.08/3.31 640 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 3.08/3.31 641 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 3.08/3.31 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(628,a,629,a)].
% 3.08/3.31 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C)),D)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)),E))). [resolve(628,a,630,a)].
% 3.08/3.31 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C),tc_Int_Oint),E)). [resolve(628,a,631,a)].
% 3.08/3.35 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),C)),D),tc_Int_Oint),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),D),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),E))). [resolve(628,a,632,a)].
% 3.08/3.35 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(628,a,633,a)].
% 3.08/3.35 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C)),D)),E))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)),E))). [resolve(628,a,634,a)].
% 3.08/3.35 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C),tc_Int_Oint),E)). [resolve(628,a,635,a)].
% 3.08/3.35 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),C)),D),tc_Int_Oint),E)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),D),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),E))). [resolve(628,a,636,a)].
% 3.08/3.35 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),A)). [resolve(628,a,637,a)].
% 3.08/3.35 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),B)). [resolve(628,a,638,a)].
% 3.08/3.35 642 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 3.08/3.35 643 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),C) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 3.08/3.35 644 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),C) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 3.08/3.35 645 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 3.08/3.35 646 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 3.08/3.35 647 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 3.20/3.42 648 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 3.20/3.42 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),B) = A. [resolve(642,a,643,a)].
% 3.20/3.42 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),B) = A. [resolve(642,a,644,a)].
% 3.20/3.42 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(642,a,646,a)].
% 3.20/3.42 649 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 3.20/3.42 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),B) = A. [resolve(649,a,643,a)].
% 3.20/3.42 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),B) = A. [resolve(649,a,644,a)].
% 3.20/3.42 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(649,a,646,a)].
% 3.20/3.42 650 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 3.20/3.42 651 -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].
% 3.20/3.42 652 -class_RealVector_Oreal__normed__algebra__1(A) | c_Series_Osuminf(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),B),hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),tc_nat,A,A),A) = hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) # label(cls_powser__zero_0) # label(axiom). [assumption].
% 3.20/3.42 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(650,a,651,b)].
% 3.20/3.42 Derived: c_Series_Osuminf(c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)). [resolve(650,a,652,a)].
% 3.20/3.42 653 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 3.20/3.42 654 -class_Ring__and__Field_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 3.20/3.42 655 -class_Ring__and__Field_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 3.20/3.42 656 -class_Ring__and__Field_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)) # label(cls_of__nat__mult_0) # label(axiom). [assumption].
% 3.20/3.42 657 -class_Ring__and__Field_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),C),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(A),tc_nat,A,B),C)),D) # label(cls_of__nat__setsum_0) # label(axiom). [assumption].
% 3.20/3.42 658 -class_Ring__and__Field_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),B)). [resolve(653,a,654,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),hAPP(c_Suc,A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A)). [resolve(653,a,655,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),B)). [resolve(653,a,656,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),tc_nat,tc_nat,A),B)),C). [resolve(653,a,657,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(653,a,658,a)].
% 3.20/3.43 659 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)). [resolve(659,a,654,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Suc,A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)). [resolve(659,a,655,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)). [resolve(659,a,656,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),tc_nat,tc_Int_Oint,A),B)),C). [resolve(659,a,657,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(659,a,658,a)].
% 3.20/3.43 660 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),B)). [resolve(660,a,654,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),hAPP(c_Suc,A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),A)). [resolve(660,a,655,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),B)). [resolve(660,a,656,a)].
% 3.20/3.43 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),tc_nat,tc_Complex_Ocomplex,A),B)),C). [resolve(660,a,657,a)].
% 3.31/3.55 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(660,a,658,a)].
% 3.31/3.55 661 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.31/3.55 662 -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].
% 3.31/3.55 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(661,a,662,a)].
% 3.31/3.55 663 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.31/3.55 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(663,a,662,a)].
% 3.31/3.55 664 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.31/3.55 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(664,a,662,a)].
% 3.31/3.55 665 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.31/3.55 666 -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].
% 3.31/3.55 667 -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].
% 3.31/3.55 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(665,a,667,a)].
% 3.31/3.55 668 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.31/3.55 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B) | A = C. [resolve(668,a,667,a)].
% 3.31/3.55 669 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.31/3.55 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(669,a,667,a)].
% 3.31/3.55 670 hBOOL(hAPP(A,B)) | -c_in(B,A,C) # label(cls_mem__def_0) # label(axiom). [assumption].
% 3.31/3.55 671 c_in(A,B,C) | -hBOOL(hAPP(B,A)) # label(cls_mem__def_1) # label(axiom). [assumption].
% 3.31/3.55 672 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(B,D) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_in(D,C,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(316,b,317,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(B,D) = c_HOL_Ozero__class_Ozero(tc_nat) | -class_Finite__Set_Ofinite_Ofinite(A) | -hBOOL(hAPP(C,D)). [resolve(672,c,671,a)].
% 3.31/3.55 673 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),D),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(D,E) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_in(E,C,A). [resolve(318,b,316,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),D),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(D,E) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(C,E)). [resolve(673,d,671,a)].
% 3.31/3.55 674 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(319,c,317,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | -class_Finite__Set_Ofinite_Ofinite(A) | hBOOL(hAPP(D,B)). [resolve(674,b,670,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(E,B) = c_HOL_Ozero__class_Ozero(tc_nat) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(674,b,672,c)].
% 3.31/3.55 675 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(319,c,318,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(D,B)). [resolve(675,b,670,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),F),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(V6,B) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(675,b,673,d)].
% 3.31/3.55 676 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(C,B) | -c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(320,c,317,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(C,B) | -class_Finite__Set_Ofinite_Ofinite(A) | -hBOOL(hAPP(D,B)). [resolve(676,b,671,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(C,B) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(676,b,674,b)].
% 3.31/3.55 677 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(320,c,318,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(D,B)). [resolve(677,b,671,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),C,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),F,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(677,b,675,b)].
% 3.31/3.55 678 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),D),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(D,E) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_in(E,C,A). [resolve(321,b,316,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),D),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(D,E) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(C,E)). [resolve(678,d,671,a)].
% 3.31/3.55 679 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(D,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),C) = hAPP(E,D) | -c_in(D,C,A). [resolve(321,b,320,c)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(D,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),C) = hAPP(E,D) | -hBOOL(hAPP(C,D)). [resolve(679,c,671,a)].
% 3.31/3.55 680 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(322,c,317,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -class_Finite__Set_Ofinite_Ofinite(A) | hBOOL(hAPP(D,B)). [resolve(680,b,670,b)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(E,B) = c_HOL_Ozero__class_Ozero(tc_nat) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(680,b,672,c)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(E,B) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(680,b,676,b)].
% 3.31/3.56 681 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(322,c,318,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(D,B)). [resolve(681,b,670,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),F),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(V6,B) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(681,b,673,d)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),F,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(F,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(681,b,677,b)].
% 3.31/3.56 682 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(322,c,321,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(D,B)). [resolve(682,b,670,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),F),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(V6,B) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(682,b,678,d)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),F),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),V6,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(V6,B). [resolve(682,b,679,c)].
% 3.31/3.56 683 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(323,c,317,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -class_Finite__Set_Ofinite_Ofinite(A) | -hBOOL(hAPP(D,B)). [resolve(683,b,671,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(683,b,674,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),E,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(683,b,680,b)].
% 3.31/3.56 684 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(323,c,318,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(D,B)). [resolve(684,b,671,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),F,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(684,b,675,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),F,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(684,b,681,b)].
% 3.31/3.56 685 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(323,c,321,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(D,B)). [resolve(685,b,671,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),C,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),F,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),V6),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(685,b,682,b)].
% 3.31/3.56 686 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),D),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(D,E) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_in(E,C,A). [resolve(324,b,316,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),D),C) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(D,E) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(C,E)). [resolve(686,d,671,a)].
% 3.31/3.56 687 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(D,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),C) = hAPP(E,D) | -c_in(D,C,A). [resolve(324,b,320,c)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(D,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),C) = hAPP(E,D) | -hBOOL(hAPP(C,D)). [resolve(687,c,671,a)].
% 3.31/3.56 688 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(D,A)),E,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),C) = hAPP(E,D) | -c_in(D,C,A). [resolve(324,b,323,c)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(D,A)),E,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),C) = hAPP(E,D) | -hBOOL(hAPP(C,D)). [resolve(688,c,671,a)].
% 3.31/3.56 689 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(325,c,317,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -class_Finite__Set_Ofinite_Ofinite(A) | hBOOL(hAPP(D,B)). [resolve(689,b,670,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(E,B) = c_HOL_Ozero__class_Ozero(tc_nat) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(689,b,672,c)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(E,B) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(689,b,676,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),E,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(E,B) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(689,b,683,b)].
% 3.31/3.56 690 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(325,c,318,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(D,B)). [resolve(690,b,670,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),F),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(V6,B) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(690,b,673,d)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),F,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(F,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(690,b,677,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),F,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(F,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(690,b,684,b)].
% 3.31/3.56 691 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(325,c,321,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(D,B)). [resolve(691,b,670,b)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),F),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(V6,B) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(691,b,678,d)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),F),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),V6,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(V6,B). [resolve(691,b,679,c)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),F,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(F,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),V6),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(691,b,685,b)].
% 3.31/3.57 692 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(325,c,324,b)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hBOOL(hAPP(D,B)). [resolve(692,b,670,b)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),F),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(V6,B) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(692,b,686,d)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),F),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),V6,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = hAPP(V6,B). [resolve(692,b,687,c)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),F),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),V6,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = hAPP(V6,B). [resolve(692,b,688,c)].
% 3.31/3.57 693 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -c_in(B,D,A) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(326,c,317,b)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -class_Finite__Set_Ofinite_Ofinite(A) | -hBOOL(hAPP(D,B)). [resolve(693,b,671,a)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),E,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(693,b,674,b)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),E,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(693,b,680,b)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -class_Finite__Set_Ofinite_Ofinite(A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),E,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -class_Finite__Set_Ofinite_Ofinite(A). [resolve(693,b,689,b)].
% 3.31/3.57 694 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(326,c,318,b)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(D,B)). [resolve(694,b,671,a)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_nat),tc_bool,tc_fun(tc_nat,tc_fun(tc_nat,tc_nat)),A),c_fequal(B,A)),F,A,tc_nat,tc_fun(tc_nat,tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(694,b,675,b)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),F,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(694,b,681,b)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),E),D) = c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),F,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),V6),D) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(694,b,690,b)].
% 3.31/3.57 695 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(326,c,321,b)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(D,B)). [resolve(695,b,671,a)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Int_Oint),tc_bool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_fequal(B,A)),F,A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),V6),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(695,b,682,b)].
% 3.31/3.57 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),E),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),F,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),V6),D) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(695,b,691,b)].
% 3.36/3.60 696 hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | -c_in(B,D,A) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(326,c,324,b)].
% 3.36/3.60 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -hBOOL(hAPP(D,B)). [resolve(696,b,671,a)].
% 3.36/3.60 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),C,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = hAPP(C,B) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),E),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_OIf(tc_Complex_Ocomplex),tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),A),c_fequal(B,A)),F,A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex))),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),V6),D) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(696,b,692,b)].
% 3.36/3.60 697 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 3.36/3.60 698 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) # label(cls_power__mult_0) # label(axiom). [assumption].
% 3.36/3.60 699 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(cls_power__add_0) # label(axiom). [assumption].
% 3.36/3.60 700 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(cls_power__Suc2_0) # label(axiom). [assumption].
% 3.36/3.60 701 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C)),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D))),B) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_lemma__realpow__diff_0) # label(axiom). [assumption].
% 3.36/3.60 702 -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),hAPP(c_Power_Opower__class_Opower(A),B)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(A),C),tc_nat,A,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,D))),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),hAPP(c_Power_Opower__class_Opower(A),B)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(A),C),tc_nat,A,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D)),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat))) # label(cls_lemma__realpow__diff__sumr_0) # label(axiom). [assumption].
% 3.36/3.60 703 -class_Ring__and__Field_Ocomm__ring(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Suc,C))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),hAPP(c_Power_Opower__class_Opower(A),B)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(A),D),tc_nat,A,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat))) # label(cls_lemma__realpow__diff__sumr2_0) # label(axiom). [assumption].
% 3.36/3.60 704 -class_Ring__and__Field_Ocomm__ring(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),tc_nat,A,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D))),hAPP(c_Power_Opower__class_Opower(A),B),tc_nat,A,A))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),tc_nat),hAPP(c_Power_Opower__class_Opower(A),B)),c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),tc_nat,A,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D))),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(A),B),tc_nat,A,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D)),tc_nat,A,A),tc_nat,A,A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat)) # label(cls_lemma__termdiff1_0) # label(axiom). [assumption].
% 3.36/3.60 705 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oone__class_Oone(A)),B) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 3.36/3.60 706 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_power__commutes_0) # label(axiom). [assumption].
% 3.36/3.60 707 -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].
% 3.36/3.60 708 -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].
% 3.36/3.60 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C). [resolve(697,a,698,a)].
% 3.36/3.60 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)). [resolve(697,a,699,a)].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A). [resolve(697,a,700,a)].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,B)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(697,a,701,a)].
% 3.36/3.61 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),B),tc_nat,tc_nat,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C))),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),B),tc_nat,tc_nat,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat))). [resolve(697,a,702,b)].
% 3.36/3.61 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),hAPP(c_Suc,B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),C)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),C),tc_nat,tc_nat,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B)),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,B),tc_nat))). [resolve(697,a,703,b)].
% 3.36/3.61 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),tc_nat,tc_nat,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_nat,tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),tc_nat,tc_nat,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_nat,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)). [resolve(697,a,704,b)].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = c_HOL_Oone__class_Oone(tc_nat). [resolve(697,a,705,a)].
% 3.36/3.61 709 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),C). [resolve(709,a,698,a)].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)). [resolve(709,a,699,a)].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A). [resolve(709,a,700,a)].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,B)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(709,a,701,a)].
% 3.36/3.61 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),tc_nat,tc_Int_Oint,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C))),tc_nat,tc_Int_Oint,tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),tc_nat,tc_Int_Oint,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)),tc_nat,tc_Int_Oint,tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat))). [resolve(709,a,702,b)].
% 3.36/3.61 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(c_Suc,B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),tc_nat,tc_Int_Oint,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B)),tc_nat,tc_Int_Oint,tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,B),tc_nat))). [resolve(709,a,703,b)].
% 3.36/3.61 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),hAPP(hAPP(c_COMBC(tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),tc_nat,tc_Int_Oint,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),tc_nat,tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),tc_nat,tc_Int_Oint,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),tc_nat,tc_Int_Oint,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)),tc_nat,tc_Int_Oint,tc_Int_Oint),tc_nat,tc_Int_Oint,tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)). [resolve(709,a,704,b)].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(709,a,705,a)].
% 3.36/3.61 710 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C). [resolve(710,a,698,a)].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)). [resolve(710,a,699,a)].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A). [resolve(710,a,700,a)].
% 3.36/3.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,B)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(710,a,701,a)].
% 3.36/3.61 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C))),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat))). [resolve(710,a,702,b)].
% 3.36/3.61 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),hAPP(c_Suc,B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,B),tc_nat))). [resolve(710,a,703,b)].
% 3.45/3.69 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)),c_COMBS(hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),hAPP(c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)). [resolve(710,a,704,b)].
% 3.45/3.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(710,a,705,a)].
% 3.45/3.69 711 class_Ring__and__Field_Oabs__if(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 3.45/3.69 712 -class_Ring__and__Field_Oabs__if(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__if_1) # label(axiom). [assumption].
% 3.45/3.69 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(711,a,712,a)].
% 3.45/3.69 713 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 3.45/3.69 714 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 3.45/3.69 715 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 3.45/3.69 716 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 3.45/3.69 717 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 3.45/3.69 718 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 3.45/3.69 719 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 3.45/3.69 720 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 3.45/3.69 721 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 3.45/3.69 722 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 3.45/3.69 723 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 3.45/3.69 724 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 3.45/3.69 725 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 3.45/3.69 726 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 3.45/3.69 727 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 3.45/3.69 728 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 3.45/3.69 729 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 3.45/3.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(713,a,714,a)].
% 3.45/3.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(713,a,715,a)].
% 3.45/3.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(713,a,716,a)].
% 3.45/3.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))). [resolve(713,a,717,a)].
% 3.45/3.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(713,a,718,a)].
% 3.45/3.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(713,a,719,a)].
% 3.45/3.69 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))). [resolve(713,a,720,a)].
% 3.45/3.70 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(713,a,721,a)].
% 3.45/3.70 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(713,a,722,a)].
% 3.45/3.70 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(713,a,723,a)].
% 3.45/3.70 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(713,a,724,a)].
% 3.45/3.70 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A))). [resolve(713,a,725,a)].
% 3.45/3.70 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))). [resolve(713,a,726,a)].
% 3.45/3.70 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(713,a,727,a)].
% 3.45/3.70 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(713,a,728,a)].
% 3.45/3.70 730 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 3.45/3.70 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(730,a,714,a)].
% 3.45/3.70 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(730,a,715,a)].
% 3.45/3.70 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(730,a,716,a)].
% 3.50/3.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C))). [resolve(730,a,717,a)].
% 3.50/3.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))). [resolve(730,a,718,a)].
% 3.50/3.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(730,a,719,a)].
% 3.50/3.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C))). [resolve(730,a,720,a)].
% 3.50/3.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(730,a,724,a)].
% 3.50/3.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A))). [resolve(730,a,725,a)].
% 3.50/3.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(730,a,726,a)].
% 3.50/3.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(730,a,727,a)].
% 3.50/3.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(730,a,728,a)].
% 3.50/3.74 731 class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 3.50/3.74 732 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__eq__mult_3) # label(axiom). [assumption].
% 3.66/3.90 733 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_abs__eq__mult_2) # label(axiom). [assumption].
% 3.66/3.90 734 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_abs__eq__mult_1) # label(axiom). [assumption].
% 3.66/3.90 735 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_abs__eq__mult_0) # label(axiom). [assumption].
% 3.66/3.90 736 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 3.66/3.90 737 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 3.66/3.90 738 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 3.66/3.90 739 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 3.66/3.90 740 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.66/3.90 741 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 3.66/3.90 742 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.66/3.90 743 class_Ring__and__Field_Olordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Olordered__ring) # label(axiom). [assumption].
% 3.66/3.90 744 -class_Ring__and__Field_Olordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)))) # label(cls_abs__le__mult_0) # label(axiom). [assumption].
% 3.66/3.90 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)))). [resolve(743,a,744,a)].
% 3.66/3.90 745 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 3.66/3.90 746 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B)),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E) # label(cls_eq__add__iff2_1) # label(axiom). [assumption].
% 3.66/3.91 747 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D)) # label(cls_right__diff__distrib__number__of_0) # label(axiom). [assumption].
% 3.66/3.91 748 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),c_Int_Onumber__class_Onumber__of(D,A)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Int_Onumber__class_Onumber__of(D,A))) # label(cls_left__diff__distrib__number__of_0) # label(axiom). [assumption].
% 3.66/3.91 749 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D)) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 3.66/3.91 750 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 3.66/3.91 751 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F) | D = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 3.66/3.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),A)),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)),D). [resolve(745,a,746,a)].
% 3.66/3.91 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),C)). [resolve(745,a,747,a)].
% 3.66/3.91 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint))). [resolve(745,a,748,a)].
% 3.66/3.91 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)). [resolve(745,a,749,a)].
% 3.66/3.95 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C) = E. [resolve(745,a,750,a)].
% 3.66/3.95 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | C = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E). [resolve(745,a,751,a)].
% 3.66/3.95 752 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 3.66/3.95 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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),A)),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(752,a,746,a)].
% 3.66/3.95 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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B)),C)). [resolve(752,a,749,a)].
% 3.66/3.95 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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B)),C) = E. [resolve(752,a,750,a)].
% 3.66/3.95 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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),A)),B)),E). [resolve(752,a,751,a)].
% 3.66/3.95 753 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 3.66/3.95 754 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff__number__of_2) # label(axiom). [assumption].
% 3.66/3.95 755 -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_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_1) # label(axiom). [assumption].
% 3.66/3.95 756 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_0) # label(axiom). [assumption].
% 3.66/3.95 757 -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].
% 3.66/3.95 758 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 3.66/3.95 759 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 3.66/3.95 760 -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].
% 3.66/3.95 761 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(753,a,754,a)].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(753,a,755,a)].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(753,a,756,a)].
% 3.66/3.95 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(753,a,757,a)].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(753,a,758,a)].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(753,a,759,a)].
% 3.66/3.95 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(753,a,760,a)].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(753,a,761,a)].
% 3.66/3.95 762 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(762,a,754,a)].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(762,a,755,a)].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(762,a,756,a)].
% 3.66/3.95 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(762,a,757,a)].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(762,a,758,a)].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(762,a,759,a)].
% 3.66/3.95 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(762,a,760,a)].
% 3.66/3.95 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(762,a,761,a)].
% 3.66/3.95 763 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 3.66/3.95 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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(763,a,754,a)].
% 3.66/3.95 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_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(763,a,755,a)].
% 3.66/3.95 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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(763,a,756,a)].
% 3.66/3.95 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(763,a,757,a)].
% 3.76/4.00 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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(763,a,758,a)].
% 3.76/4.00 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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(763,a,759,a)].
% 3.76/4.00 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(763,a,760,a)].
% 3.76/4.00 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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(763,a,761,a)].
% 3.76/4.00 764 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 3.76/4.00 765 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left__number__of_1) # label(axiom). [assumption].
% 3.76/4.00 766 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),hAPP(c_Suc,B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 3.76/4.00 767 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left__number__of_0) # label(axiom). [assumption].
% 3.76/4.00 768 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),B),C)),E)),D) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 3.76/4.00 769 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Finite__Set_Osetsum(C,A),D),E)) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,C),D)),E) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 3.76/4.00 770 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 3.76/4.00 771 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 3.76/4.00 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(764,a,765,a)].
% 3.76/4.00 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(764,a,766,a)].
% 3.76/4.00 Derived: -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(764,a,767,a)].
% 3.76/4.00 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),A),B)),D)),C). [resolve(764,a,768,a)].
% 3.76/4.00 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),C),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),tc_nat,tc_nat,B),C)),D). [resolve(764,a,769,a)].
% 3.76/4.00 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(764,a,771,a)].
% 3.76/4.00 772 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 3.76/4.00 Derived: -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(772,a,765,a)].
% 3.76/4.00 Derived: -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(772,a,766,a)].
% 3.76/4.00 Derived: -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(772,a,767,a)].
% 3.76/4.00 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),B)),D)),C). [resolve(772,a,768,a)].
% 3.76/4.00 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Int_Oint),C),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Int_Oint),hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),tc_Int_Oint,tc_Int_Oint,B),C)),D). [resolve(772,a,769,a)].
% 3.76/4.00 Derived: -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(772,a,771,a)].
% 3.76/4.00 773 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 3.76/4.00 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(773,a,765,a)].
% 3.76/4.00 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(773,a,766,a)].
% 3.76/4.00 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(773,a,767,a)].
% 3.76/4.00 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(773,a,771,a)].
% 3.94/4.17 774 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 3.94/4.17 775 -class_RealVector_Oreal__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))),F) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)),F))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),F)),E)) # label(cls_DERIV__mult__lemma_0) # label(axiom). [assumption].
% 3.94/4.17 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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))),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),E)),D)). [resolve(774,a,775,a)].
% 3.94/4.17 776 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 3.94/4.17 777 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 3.94/4.17 778 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 3.94/4.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(776,a,777,a)].
% 3.94/4.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(776,a,778,a)].
% 3.94/4.17 779 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 3.94/4.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(779,a,777,a)].
% 3.94/4.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)). [resolve(779,a,778,a)].
% 3.94/4.17 780 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 3.94/4.17 781 -class_Ring__and__Field_Omult__mono1(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 4.03/4.25 782 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 4.03/4.25 783 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.03/4.25 784 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 4.03/4.25 785 -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].
% 4.03/4.25 786 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.03/4.25 787 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.03/4.25 788 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 4.03/4.25 789 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 4.03/4.25 790 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 4.03/4.25 791 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 4.03/4.25 792 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 4.03/4.25 793 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 4.03/4.25 794 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 4.03/4.25 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(788,a,789,a)].
% 4.03/4.25 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(788,a,790,a)].
% 4.06/4.33 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(788,a,791,a)].
% 4.06/4.33 795 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 4.06/4.33 796 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.06/4.33 797 -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].
% 4.06/4.33 798 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.06/4.33 799 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 4.06/4.33 800 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 4.06/4.33 801 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 4.06/4.33 802 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 4.11/4.33 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(800,a,801,a)].
% 4.11/4.33 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(800,a,802,a)].
% 4.11/4.33 803 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 4.11/4.33 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(803,a,801,a)].
% 4.11/4.33 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(803,a,802,a)].
% 4.13/4.41 804 class_Ring__and__Field_Oring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 4.13/4.41 805 -class_Ring__and__Field_Oring__1(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(A),A,tc_fun(A,A),tc_nat),B)),D)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) # label(cls_sumr__diff__mult__const2_0) # label(axiom). [assumption].
% 4.13/4.41 806 -class_Ring__and__Field_Oring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) # label(cls_of__nat__diff_0) # label(axiom). [assumption].
% 4.13/4.41 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)),C)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Int_Oint),hAPP(hAPP(c_COMBC(tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),A)),C)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(804,a,805,a)].
% 4.13/4.41 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(804,a,806,a)].
% 4.13/4.41 807 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 4.13/4.41 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),B)),C)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),A)),C)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(807,a,805,a)].
% 4.13/4.41 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),B)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(807,a,806,a)].
% 4.13/4.41 808 class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 4.13/4.41 809 -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].
% 4.13/4.41 810 -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].
% 4.13/4.41 811 -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].
% 4.41/4.64 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(808,a,811,a)].
% 4.41/4.64 812 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].
% 4.41/4.64 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(812,a,811,a)].
% 4.41/4.64 813 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 4.41/4.64 814 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 4.41/4.64 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(813,a,814,a)].
% 4.41/4.64 815 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].
% 4.41/4.64 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(815,a,814,a)].
% 4.41/4.64 816 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 4.41/4.64 817 -class_Nat_Osemiring__char__0(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 4.41/4.64 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),A) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),B) | A = B. [resolve(816,a,817,a)].
% 4.41/4.64 818 class_Nat_Osemiring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 4.41/4.64 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B) | A = B. [resolve(818,a,817,a)].
% 4.41/4.64 819 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 4.41/4.64 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),A) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Complex_Ocomplex),B) | A = B. [resolve(819,a,817,a)].
% 4.41/4.64
% 4.41/4.64 ============================== end predicate elimination =============
% 4.41/4.64
% 4.41/4.64 Auto_denials: (non-Horn, no changes).
% 4.41/4.64
% 4.41/4.64 Term ordering decisions:
% 4.41/4.64 Function symbol KB weights: tc_nat=1. tc_Complex_Ocomplex=1. tc_Int_Oint=1. c_Suc=1. tc_bool=1. v_i=1. v_n=1. v_a=1. hAPP=1. c_HOL_Oord__class_Oless=1. c_lessequals=1. tc_fun=1. c_Finite__Set_Osetsum=1. c_Int_Onumber__class_Onumber__of=1. c_fequal=1. c_Series_Osuminf=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Oplus__class_Oplus=1. c_Power_Opower__class_Opower=1. c_HOL_Ominus__class_Ominus=1. c_HOL_Oinverse__class_Odivide=1. c_HOL_Oone__class_Oone=1. c_HOL_OIf=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_HOL_Oabs__class_Oabs=1. c_HOL_Oinverse__class_Oinverse=1. c_FFT__Mirabelle_Oroot=1. c_COMBC=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_FFT__Mirabelle_ODFT=1. c_FFT__Mirabelle_OIDFT=1. c_COMBB=1. c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1=1. c_COMBS=1. c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1=1.
% 4.41/4.64
% 4.41/4.64 ============================== end of process initial clauses ========
% 4.41/4.64
% 4.41/4.64 ============================== CLAUSES FOR SEARCH ====================
% 27.60/27.83
% 27.60/27.83 ============================== end of clauses for search =============
% 27.60/27.83
% 27.60/27.83 ============================== SEARCH ================================
% 27.60/27.83
% 27.60/27.83 % Starting search at 3.04 seconds.
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=110.000, iters=3677
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=102.000, iters=3657
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=84.000, iters=3597
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=80.000, iters=3586
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=74.000, iters=3516
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=66.000, iters=3385
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=65.000, iters=3523
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=61.000, iters=3380
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=60.000, iters=3380
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=58.000, iters=3352
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=57.000, iters=3419
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=56.000, iters=3374
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=55.000, iters=3379
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=54.000, iters=3350
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=53.000, iters=3448
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=51.000, iters=3391
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=50.000, iters=3333
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=47.000, iters=3344
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=46.000, iters=3347
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=45.000, iters=3333
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=44.000, iters=3500
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=43.000, iters=3443
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=42.000, iters=3353
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=41.000, iters=3364
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=40.000, iters=3335
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=38.000, iters=3342
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=37.000, iters=3367
% 27.60/27.83
% 27.60/27.83 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 31 (0.00 of 3.55 sec).
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=36.000, iters=3359
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=35.000, iters=3367
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=34.000, iters=3384
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=33.000, iters=3371
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=32.000, iters=3357
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=31.000, iters=3345
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=30.000, iters=3341
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=29.000, iters=3345
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=28.000, iters=3342
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=27.000, iters=3333
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=26.000, iters=3348
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=25.000, iters=3406
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=24.000, iters=3335
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=23.000, iters=3352
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=22.000, iters=3349
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=21.000, iters=3337
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=4905, wt=134.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=4946, wt=132.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=4951, wt=130.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=4906, wt=116.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=5110, wt=114.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=5156, wt=112.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=5168, wt=110.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=4847, wt=107.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=5111, wt=106.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=5159, wt=104.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=4963, wt=103.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=4950, wt=102.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=5023, wt=101.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=5014, wt=100.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=5143, wt=99.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=4122, wt=98.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=4964, wt=97.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=4125, wt=96.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=5026, wt=95.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=14068, wt=18.000
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=20.000, iters=3333
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=14421, wt=17.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=14792, wt=16.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=17147, wt=15.000
% 27.60/27.83
% 27.60/27.83 Low Water (displace): id=17212, wt=14.000
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=19.000, iters=3333
% 27.60/27.83
% 27.60/27.83 Low Water (keep): wt=18.000, iters=3334
% 27.60/27.83
% 27.60/27.83 ============================== PROOF =================================
% 27.60/27.83 % SZS status Unsatisfiable
% 27.60/27.83 % SZS output start Refutation
% 27.60/27.83
% 27.60/27.83 % Proof 1 at 25.73 (+ 0.51) seconds.
% 27.60/27.83 % Length of proof is 24.
% 27.60/27.83 % Level of proof is 7.
% 27.60/27.83 % Maximum clause weight is 25.000.
% 27.60/27.83 % Given clauses 9134.
% 27.60/27.83
% 27.60/27.83 48 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 27.60/27.83 85 -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].
% 27.60/27.83 753 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 27.60/27.83 757 -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].
% 27.60/27.83 893 hAPP(c_Suc,A) != c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_nat_Osimps_I3_J_0) # label(axiom). [assumption].
% 27.60/27.83 911 A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_natgb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 27.60/27.83 912 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != A | c_HOL_Ozero__class_Ozero(tc_nat) = B. [copy(911),flip(a),flip(b)].
% 27.60/27.83 962 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B)) # label(cls_add__Suc__shift_0) # label(axiom). [assumption].
% 27.60/27.83 1042 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),B) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) # label(cls_add__Suc_0) # label(axiom). [assumption].
% 27.60/27.83 1043 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)). [copy(1042),rewrite([962(6)])].
% 27.60/27.83 1048 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A) # label(cls_nat__add__commute_0) # label(axiom). [assumption].
% 27.60/27.83 1146 hAPP(hAPP(c_COMBB(A,B,C,D),E),F) = hAPP(A,hAPP(E,F)) # label(cls_COMBB__def_0) # label(axiom). [assumption].
% 27.60/27.83 1148 hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)) # label(cls_COMBS__def_0) # label(axiom). [assumption].
% 27.60/27.83 1358 hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(48,a,85,a)].
% 27.60/27.83 2217 c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(753,a,757,a)].
% 27.60/27.83 2218 c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [copy(2217),flip(a)].
% 27.60/27.83 2466 c_HOL_Oone__class_Oone(tc_nat) = c_0. [new_symbol(2218)].
% 27.60/27.83 2527 hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_0),A) = A. [back_rewrite(1358),rewrite([2466(4)])].
% 27.60/27.83 3561 hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) != A. [para(1043(a,1),912(a,1)),flip(b),unit_del(b,893)].
% 27.60/27.83 9512 hAPP(c_COMBS(A,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_0),B,C,D),E) = hAPP(hAPP(A,E),E). [para(2527(a,1),1148(a,2,2))].
% 27.60/27.83 9713 hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) != B. [para(1048(a,1),3561(a,1,2))].
% 27.60/27.83 9732 hAPP(c_Suc,hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),A,B,C,D),E)) != hAPP(A,E). [para(1148(a,2),9713(a,1,2))].
% 27.60/27.83 71141 hAPP(hAPP(A,B),B) != hAPP(c_Suc,hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),c_COMBS(A,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_0),C,D,E),F,V6,V7),B)). [para(9512(a,1),9732(a,2)),flip(a)].
% 27.60/27.83 71142 $F. [resolve(71141,a,1146,a)].
% 27.60/27.83
% 27.60/27.83 % SZS output end Refutation
% 27.60/27.83 ============================== end of proof ==========================
% 27.60/27.83
% 27.60/27.83 ============================== STATISTICS ============================
% 27.60/27.83
% 27.60/27.83 Given=9134. Generated=842621. Kept=69886. proofs=1.
% 27.60/27.83 Usable=9080. Sos=9989. Demods=1083. Limbo=23, Disabled=53103. Hints=0.
% 27.60/27.83 Megabytes=74.23.
% 27.60/27.83 User_CPU=25.73, System_CPU=0.51, Wall_clock=26.
% 27.60/27.83
% 27.60/27.83 ============================== end of statistics =====================
% 27.60/27.83
% 27.60/27.83 ============================== end of search =========================
% 27.60/27.83
% 27.60/27.83 THEOREM PROVED
% 27.60/27.83 % SZS status Unsatisfiable
% 27.60/27.83
% 27.60/27.83 Exiting with 1 proof.
% 27.60/27.83
% 27.60/27.83 Process 19210 exit (max_proofs) Wed Jun 15 21:24:38 2022
% 27.60/27.83 Prover9 interrupted
%------------------------------------------------------------------------------