TSTP Solution File: SWV652-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV652-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 21:14:17 EDT 2022
% Result : Timeout 300.03s 300.26s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV652-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 06:59:36 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.51/2.11 ============================== Prover9 ===============================
% 1.51/2.11 Prover9 (32) version 2009-11A, November 2009.
% 1.51/2.11 Process 2257 was started by sandbox2 on n011.cluster.edu,
% 1.51/2.11 Thu Jun 16 06:59:37 2022
% 1.51/2.11 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2098_n011.cluster.edu".
% 1.51/2.11 ============================== end of head ===========================
% 1.51/2.11
% 1.51/2.11 ============================== INPUT =================================
% 1.51/2.11
% 1.51/2.11 % Reading from file /tmp/Prover9_2098_n011.cluster.edu
% 1.51/2.11
% 1.51/2.11 set(prolog_style_variables).
% 1.51/2.11 set(auto2).
% 1.51/2.11 % set(auto2) -> set(auto).
% 1.51/2.11 % set(auto) -> set(auto_inference).
% 1.51/2.11 % set(auto) -> set(auto_setup).
% 1.51/2.11 % set(auto_setup) -> set(predicate_elim).
% 1.51/2.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.51/2.11 % set(auto) -> set(auto_limits).
% 1.51/2.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.51/2.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.51/2.11 % set(auto) -> set(auto_denials).
% 1.51/2.11 % set(auto) -> set(auto_process).
% 1.51/2.11 % set(auto2) -> assign(new_constants, 1).
% 1.51/2.11 % set(auto2) -> assign(fold_denial_max, 3).
% 1.51/2.11 % set(auto2) -> assign(max_weight, "200.000").
% 1.51/2.11 % set(auto2) -> assign(max_hours, 1).
% 1.51/2.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.51/2.11 % set(auto2) -> assign(max_seconds, 0).
% 1.51/2.11 % set(auto2) -> assign(max_minutes, 5).
% 1.51/2.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.51/2.11 % set(auto2) -> set(sort_initial_sos).
% 1.51/2.11 % set(auto2) -> assign(sos_limit, -1).
% 1.51/2.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.51/2.11 % set(auto2) -> assign(max_megs, 400).
% 1.51/2.11 % set(auto2) -> assign(stats, some).
% 1.51/2.11 % set(auto2) -> clear(echo_input).
% 1.51/2.11 % set(auto2) -> set(quiet).
% 1.51/2.11 % set(auto2) -> clear(print_initial_clauses).
% 1.51/2.11 % set(auto2) -> clear(print_given).
% 1.51/2.11 assign(lrs_ticks,-1).
% 1.51/2.11 assign(sos_limit,10000).
% 1.51/2.11 assign(order,kbo).
% 1.51/2.11 set(lex_order_vars).
% 1.51/2.11 clear(print_given).
% 1.51/2.11
% 1.51/2.11 % formulas(sos). % not echoed (2087 formulas)
% 1.51/2.11
% 1.51/2.11 ============================== end of input ==========================
% 1.51/2.11
% 1.51/2.11 % From the command line: assign(max_seconds, 300).
% 1.51/2.11
% 1.51/2.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.51/2.11
% 1.51/2.11 % Formulas that are not ordinary clauses:
% 1.51/2.11
% 1.51/2.11 ============================== end of process non-clausal formulas ===
% 1.51/2.11
% 1.51/2.11 ============================== PROCESS INITIAL CLAUSES ===============
% 1.51/2.11
% 1.51/2.11 ============================== PREDICATE ELIMINATION =================
% 1.51/2.11 1 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.51/2.11 2 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.51/2.11 3 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.51/2.11 4 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 1.51/2.11 5 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 1.51/2.11 6 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_lessequals(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 1.51/2.11 7 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 1.51/2.11 8 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) | -c_lessequals(C,D,tc_nat) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 1.51/2.11 9 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 1.51/2.11 10 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.51/2.11 11 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(D,C,tc_nat) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 1.51/2.11 12 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.51/2.11 13 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 1.51/2.11 14 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 1.51/2.11 15 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.51/2.11 16 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.51/2.11 17 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.51/2.11 18 -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) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.51/2.11 19 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.51/2.11 20 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.51/2.11 21 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.51/2.11 22 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.51/2.11 23 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D),A) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 1.51/2.11 24 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 1.51/2.11 25 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 1.51/2.11 26 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 1.51/2.11 27 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(B,D,A) # label(cls_power__mono_0) # label(axiom). [assumption].
% 1.51/2.11 28 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 1.51/2.11 29 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.51/2.11 30 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.51/2.11 31 -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 | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 1.51/2.11 32 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Suc,D)),A) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 1.51/2.11 33 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) # label(cls_power2__less__imp__less_0) # label(axiom). [assumption].
% 1.51/2.11 34 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(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),C),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 1.51/2.11 35 -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 | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 1.51/2.11 36 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.51/2.11 37 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) | B = C | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power2__eq__imp__eq_0) # label(axiom). [assumption].
% 1.51/2.11 38 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) # label(cls_power2__le__imp__le_0) # label(axiom). [assumption].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(1,a,2,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(1,a,3,a)].
% 1.51/2.11 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(1,a,4,a)].
% 1.51/2.11 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_lessequals(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,6,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(1,a,7,a)].
% 1.51/2.11 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(1,a,8,a)].
% 1.51/2.11 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,9,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(1,a,10,a)].
% 1.51/2.11 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(1,a,11,a)].
% 1.51/2.11 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(1,a,12,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,13,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,14,a)].
% 1.51/2.11 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(1,a,15,a)].
% 1.51/2.11 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(1,a,16,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(1,a,17,a)].
% 1.51/2.11 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | B = C. [resolve(1,a,18,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(1,a,19,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(1,a,20,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C),tc_nat). [resolve(1,a,23,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,24,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,25,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,26,a)].
% 1.51/2.11 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(1,a,27,a)].
% 1.51/2.11 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,28,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,29,a)].
% 1.51/2.11 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,30,a)].
% 1.51/2.11 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 | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,31,a)].
% 1.51/2.12 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),hAPP(c_Suc,C)),tc_nat). [resolve(1,a,32,a)].
% 1.51/2.12 Derived: 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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,34,a)].
% 1.51/2.12 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 | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,35,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,36,a)].
% 1.51/2.12 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) | A = B | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,37,a)].
% 1.51/2.12 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat). [resolve(1,a,38,a)].
% 1.51/2.12 39 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(39,a,2,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)),tc_Int_Oint). [resolve(39,a,3,a)].
% 1.51/2.12 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),C,tc_Int_Oint). [resolve(39,a,4,a)].
% 1.51/2.12 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),tc_Int_Oint) | -c_lessequals(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,6,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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)),tc_Int_Oint). [resolve(39,a,7,a)].
% 1.51/2.12 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,C,tc_nat). [resolve(39,a,8,a)].
% 1.51/2.12 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,9,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(39,a,10,a)].
% 1.51/2.12 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),tc_Int_Oint) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(C,B,tc_nat). [resolve(39,a,11,a)].
% 1.51/2.12 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(39,a,12,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,13,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,14,a)].
% 1.51/2.12 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(39,a,15,a)].
% 1.51/2.12 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(39,a,16,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(39,a,17,a)].
% 1.51/2.12 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) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | B = C. [resolve(39,a,18,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),C,tc_Int_Oint). [resolve(39,a,19,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(39,a,20,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(39,a,23,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(39,a,24,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),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) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,25,a)].
% 1.51/2.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(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)),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,26,a)].
% 1.51/2.12 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(39,a,27,a)].
% 2.01/2.26 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,28,a)].
% 2.01/2.26 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,29,a)].
% 2.01/2.26 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,30,a)].
% 2.01/2.26 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 | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,31,a)].
% 2.01/2.26 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Suc,C)),tc_Int_Oint). [resolve(39,a,32,a)].
% 2.01/2.26 Derived: 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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,34,a)].
% 2.01/2.26 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 | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,35,a)].
% 2.01/2.26 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,36,a)].
% 2.01/2.26 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) | A = B | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(39,a,37,a)].
% 2.01/2.26 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_Int_Oint). [resolve(39,a,38,a)].
% 2.01/2.26 40 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 2.01/2.26 41 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_sup__eq__if_1) # label(axiom). [assumption].
% 2.01/2.26 42 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 2.01/2.26 43 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 2.01/2.26 44 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 2.01/2.26 45 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 2.01/2.26 46 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastAtMost(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I21_J_0) # label(axiom). [assumption].
% 2.01/2.26 47 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I17_J_0) # label(axiom). [assumption].
% 2.01/2.26 48 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 2.01/2.26 49 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 2.01/2.26 50 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_0) # label(axiom). [assumption].
% 2.01/2.26 51 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 2.01/2.26 52 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 2.01/2.26 53 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 2.01/2.26 54 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 2.01/2.26 55 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 2.01/2.26 56 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 2.01/2.26 57 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 2.01/2.26 58 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_sup__eq__if_0) # label(axiom). [assumption].
% 2.01/2.26 59 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 2.01/2.26 60 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | -c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 2.01/2.26 61 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 2.01/2.26 62 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_1) # label(axiom). [assumption].
% 2.01/2.27 63 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 2.01/2.27 64 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 2.01/2.27 Derived: -class_OrderedGroup_Olordered__ab__group__add(tc_nat) | c_Lattices_Oupper__semilattice__class_Osup(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_nat),A),tc_nat) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(40,a,41,a)].
% 2.01/2.27 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(40,a,42,a)].
% 2.01/2.27 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(40,a,46,a)].
% 2.01/2.27 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(40,a,47,a)].
% 2.01/2.27 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(40,a,48,a)].
% 2.01/2.27 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | hAPP(c_HOL_Oabs__class_Oabs(tc_nat),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_nat),A) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(40,a,50,a)].
% 2.01/2.27 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(40,a,51,a)].
% 2.01/2.27 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(40,a,52,a)].
% 2.01/2.27 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(40,a,54,a)].
% 2.01/2.27 Derived: -class_OrderedGroup_Olordered__ab__group__add(tc_nat) | c_Lattices_Oupper__semilattice__class_Osup(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_nat),A),tc_nat) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_nat),A) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(40,a,58,a)].
% 2.01/2.27 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(40,a,59,a)].
% 2.01/2.27 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | hAPP(c_HOL_Oabs__class_Oabs(tc_nat),A) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(40,a,62,a)].
% 2.01/2.27 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(40,a,63,a)].
% 2.01/2.27 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(40,a,64,a)].
% 2.01/2.27 65 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 2.01/2.27 Derived: -class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) | c_Lattices_Oupper__semilattice__class_Osup(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(65,a,41,a)].
% 2.01/2.27 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(65,a,42,a)].
% 2.01/2.27 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(65,a,46,a)].
% 2.01/2.27 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_Int_Oint),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(65,a,47,a)].
% 2.16/2.42 Derived: A = B | -c_lessequals(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(65,a,48,a)].
% 2.16/2.42 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(65,a,50,a)].
% 2.16/2.42 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(65,a,51,a)].
% 2.16/2.42 Derived: -c_lessequals(A,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(65,a,52,a)].
% 2.16/2.42 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(65,a,54,a)].
% 2.16/2.42 Derived: -class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) | c_Lattices_Oupper__semilattice__class_Osup(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(65,a,58,a)].
% 2.16/2.42 Derived: -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(65,a,59,a)].
% 2.16/2.42 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(65,a,62,a)].
% 2.16/2.42 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(65,a,63,a)].
% 2.16/2.42 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(65,a,64,a)].
% 2.16/2.42 66 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 2.16/2.42 67 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 2.16/2.42 68 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 2.16/2.42 69 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 2.16/2.42 70 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 2.16/2.42 71 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 2.16/2.42 72 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 2.16/2.42 73 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 2.16/2.42 74 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 2.16/2.42 75 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 2.16/2.42 76 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 2.16/2.42 77 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 2.16/2.42 78 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 2.16/2.42 79 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 2.16/2.42 80 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 2.16/2.42 81 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 2.16/2.42 82 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 2.16/2.42 83 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 2.16/2.42 84 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 2.16/2.42 85 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 2.16/2.42 86 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 2.16/2.42 87 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(66,a,67,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(66,a,68,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(66,a,69,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)). [resolve(66,a,70,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,C,tc_fun(E,A)). [resolve(66,a,73,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,D,tc_fun(E,A)). [resolve(66,a,74,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(66,a,75,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(66,a,76,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)),tc_fun(D,A)). [resolve(66,a,77,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(66,a,80,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(66,a,81,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(66,a,82,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)). [resolve(66,a,83,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)). [resolve(66,a,84,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -c_lessequals(B,C,tc_fun(D,A)). [resolve(66,a,85,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | c_lessequals(B,C,tc_fun(D,A)). [resolve(66,a,86,a)].
% 2.16/2.42 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -c_lessequals(C,B,tc_fun(D,A)). [resolve(66,a,87,a)].
% 2.16/2.42 88 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 2.16/2.42 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),B,tc_nat). [resolve(88,a,67,a)].
% 2.16/2.42 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),B,tc_nat). [resolve(88,a,68,a)].
% 2.16/2.42 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(88,a,69,a)].
% 2.16/2.42 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(88,a,70,a)].
% 2.16/2.42 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(88,a,73,a)].
% 2.16/2.42 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(88,a,74,a)].
% 2.16/2.42 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(88,a,75,a)].
% 2.16/2.42 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(88,a,76,a)].
% 2.16/2.42 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(88,a,77,a)].
% 2.16/2.42 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(88,a,80,a)].
% 2.16/2.42 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat). [resolve(88,a,81,a)].
% 2.16/2.42 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat). [resolve(88,a,82,a)].
% 2.16/2.42 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(88,a,83,a)].
% 2.16/2.42 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat). [resolve(88,a,84,a)].
% 2.16/2.42 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(88,a,85,a)].
% 2.16/2.42 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(88,a,86,a)].
% 2.16/2.42 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(88,a,87,a)].
% 2.16/2.42 89 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 2.16/2.42 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(89,a,67,a)].
% 2.16/2.43 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(89,a,68,a)].
% 2.16/2.43 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(89,a,69,a)].
% 2.16/2.43 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(89,a,70,a)].
% 2.16/2.43 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,B,tc_bool). [resolve(89,a,73,a)].
% 2.16/2.43 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(89,a,74,a)].
% 2.16/2.43 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(89,a,75,a)].
% 2.16/2.43 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(89,a,76,a)].
% 2.16/2.43 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(89,a,77,a)].
% 2.16/2.43 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(89,a,80,a)].
% 2.16/2.43 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [resolve(89,a,81,a)].
% 2.16/2.43 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(89,a,82,a)].
% 2.16/2.43 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(89,a,83,a)].
% 2.16/2.43 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool). [resolve(89,a,84,a)].
% 2.16/2.43 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(89,a,85,a)].
% 2.16/2.43 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(89,a,86,a)].
% 2.16/2.43 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(89,a,87,a)].
% 2.16/2.43 90 class_Lattices_Oupper__semilattice(tc_Int_Oint) # label(clsarity_Int__Oint__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 2.16/2.43 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(90,a,67,a)].
% 2.16/2.43 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_Int_Oint),B,tc_Int_Oint). [resolve(90,a,68,a)].
% 2.16/2.43 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(90,a,69,a)].
% 2.16/2.43 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(90,a,70,a)].
% 2.16/2.43 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(90,a,73,a)].
% 2.16/2.43 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(90,a,74,a)].
% 2.16/2.43 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(90,a,75,a)].
% 2.16/2.43 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(90,a,76,a)].
% 2.16/2.43 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(90,a,77,a)].
% 2.31/2.56 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_Int_Oint) = A. [resolve(90,a,80,a)].
% 2.31/2.56 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint),tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(90,a,81,a)].
% 2.31/2.56 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(90,a,82,a)].
% 2.31/2.56 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_Int_Oint). [resolve(90,a,83,a)].
% 2.31/2.56 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint),tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint). [resolve(90,a,84,a)].
% 2.31/2.56 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) = B | -c_lessequals(A,B,tc_Int_Oint). [resolve(90,a,85,a)].
% 2.31/2.56 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) != B | c_lessequals(A,B,tc_Int_Oint). [resolve(90,a,86,a)].
% 2.31/2.56 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) = A | -c_lessequals(B,A,tc_Int_Oint). [resolve(90,a,87,a)].
% 2.31/2.56 91 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 2.31/2.56 92 -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(c_Int_OMin,A)) = c_HOL_Oone__class_Oone(A) # label(cls_abs__minus__one_0) # label(axiom). [assumption].
% 2.31/2.56 93 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_abs__less__iff_2) # label(axiom). [assumption].
% 2.31/2.56 94 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),D),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__even_0) # label(axiom). [assumption].
% 2.31/2.56 95 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 2.31/2.56 96 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_lessequals(B,C,tc_Int_Oint) | -c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) # label(cls_le__number__of_0) # label(axiom). [assumption].
% 2.31/2.56 97 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | -c_lessequals(B,C,tc_Int_Oint) # label(cls_le__number__of_1) # label(axiom). [assumption].
% 2.31/2.56 98 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_lessequals(B,D,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__odd_0) # label(axiom). [assumption].
% 2.31/2.56 99 -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].
% 2.31/2.56 100 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__less__iff_1) # label(axiom). [assumption].
% 2.31/2.56 101 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__less__0__iff_0) # label(axiom). [assumption].
% 2.31/2.56 102 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__less__0__iff_1) # label(axiom). [assumption].
% 2.31/2.56 103 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) # label(cls_less__number__of_1) # label(axiom). [assumption].
% 2.31/2.56 104 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) # label(cls_less__number__of_0) # label(axiom). [assumption].
% 2.31/2.56 105 -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)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Int_Onumber__class_Onumber__of(B,A)) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__number__of_0) # label(axiom). [assumption].
% 2.31/2.56 106 -class_Ring__and__Field_Oordered__idom(A) | 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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),C),E,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),D,A) # label(cls_abs__mult__less_0) # label(axiom). [assumption].
% 2.31/2.56 107 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__less__iff_0) # label(axiom). [assumption].
% 2.31/2.56 108 -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].
% 2.31/2.56 109 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B)),C,A) # label(cls_abs__diff__less__iff_0) # label(axiom). [assumption].
% 2.31/2.56 110 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)),B)) = c_HOL_Oone__class_Oone(A) # label(cls_abs__power__minus__one_0) # label(axiom). [assumption].
% 2.31/2.56 111 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D),B,A) # label(cls_abs__diff__less__iff_2) # label(axiom). [assumption].
% 2.31/2.56 112 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)) = hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_abs__power__minus_0) # label(axiom). [assumption].
% 2.31/2.56 113 -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)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_abs__mult__pos_0) # label(axiom). [assumption].
% 2.31/2.56 114 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A) | -c_lessequals(C,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__right__le__one__le_0) # label(axiom). [assumption].
% 2.31/2.56 115 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) | -c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__left__le__one__le_0) # label(axiom). [assumption].
% 2.31/2.56 116 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D,A) # label(cls_abs__diff__less__iff_1) # label(axiom). [assumption].
% 2.31/2.56 117 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__minus__self__iff_0) # label(axiom). [assumption].
% 2.31/2.56 118 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__minus__self__iff_1) # label(axiom). [assumption].
% 2.31/2.56 119 -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_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_2) # label(axiom). [assumption].
% 2.31/2.56 120 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),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].
% 2.31/2.56 121 -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) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__number__of_1) # label(axiom). [assumption].
% 2.31/2.56 122 -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].
% 2.31/2.56 123 -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].
% 2.31/2.56 124 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A) # label(cls_zero__le__power__eq__number__of_0) # label(axiom). [assumption].
% 2.31/2.56 125 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | 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].
% 2.31/2.56 126 -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_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq__number__of_0) # label(axiom). [assumption].
% 2.31/2.56 127 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A) | -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].
% 2.31/2.56 128 -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) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_1) # label(axiom). [assumption].
% 2.31/2.56 129 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,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_5) # label(axiom). [assumption].
% 2.31/2.56 130 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),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) # label(cls_zero__less__power__eq__number__of_4) # label(axiom). [assumption].
% 2.31/2.56 131 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) # label(cls_zero__le__power__eq_0) # label(axiom). [assumption].
% 2.31/2.56 132 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_2) # label(axiom). [assumption].
% 2.31/2.56 133 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_0) # label(axiom). [assumption].
% 2.31/2.56 134 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_1) # label(axiom). [assumption].
% 2.31/2.56 135 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B),A) # label(cls_zero__le__power__iff_0) # label(axiom). [assumption].
% 2.31/2.56 136 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_2) # label(axiom). [assumption].
% 2.31/2.56 137 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),C),A) # label(cls_zero__le__power__abs_0) # label(axiom). [assumption].
% 2.31/2.56 138 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | 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].
% 2.31/2.56 139 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_5) # label(axiom). [assumption].
% 2.31/2.56 140 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_1) # label(axiom). [assumption].
% 2.31/2.56 141 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__less__zero__eq_2) # label(axiom). [assumption].
% 2.31/2.56 142 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq_0) # label(axiom). [assumption].
% 2.31/2.56 143 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_1) # label(axiom). [assumption].
% 2.31/2.56 144 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__iff_2) # label(axiom). [assumption].
% 2.31/2.56 145 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_Int_OBit1(c_Int_OPls),tc_Int_Oint) # label(cls_less__special_I4_J_1) # label(axiom). [assumption].
% 2.31/2.56 146 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(B,c_Int_OBit1(c_Int_OPls),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oone__class_Oone(A),A) # label(cls_less__special_I4_J_0) # label(axiom). [assumption].
% 2.31/2.56 147 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oone__class_Oone(A),A) | -c_lessequals(B,c_Int_OBit1(c_Int_OPls),tc_Int_Oint) # label(cls_le__special_I4_J_1) # label(axiom). [assumption].
% 2.31/2.56 148 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_lessequals(B,c_Int_OBit1(c_Int_OPls),tc_Int_Oint) | -c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oone__class_Oone(A),A) # label(cls_le__special_I4_J_0) # label(axiom). [assumption].
% 2.31/2.56 149 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(B,A),A) | -c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),B,tc_Int_Oint) # label(cls_less__special_I2_J_1) # label(axiom). [assumption].
% 2.31/2.56 150 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_less__special_I2_J_0) # label(axiom). [assumption].
% 2.31/2.56 151 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_lessequals(c_HOL_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(B,A),A) | -c_lessequals(c_Int_OBit1(c_Int_OPls),B,tc_Int_Oint) # label(cls_le__special_I2_J_1) # label(axiom). [assumption].
% 2.31/2.56 152 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_lessequals(c_Int_OBit1(c_Int_OPls),B,tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__special_I2_J_0) # label(axiom). [assumption].
% 2.31/2.56 153 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_3) # label(axiom). [assumption].
% 2.31/2.56 154 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq_1) # label(axiom). [assumption].
% 2.31/2.56 155 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power__iff_1) # label(axiom). [assumption].
% 2.31/2.56 156 -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) | 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)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_5) # label(axiom). [assumption].
% 2.31/2.56 157 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),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].
% 2.31/2.56 158 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,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) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A) # label(cls_zero__less__power__eq__number__of_0) # label(axiom). [assumption].
% 2.31/2.56 159 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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_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].
% 2.31/2.56 160 -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].
% 2.31/2.56 161 -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].
% 2.31/2.56 162 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__less__power__eq_2) # label(axiom). [assumption].
% 2.31/2.56 163 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)),A) # label(cls_zero__less__power__eq_3) # label(axiom). [assumption].
% 2.31/2.56 164 -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_0) # label(axiom). [assumption].
% 2.31/2.56 165 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq__number__of_1) # label(axiom). [assumption].
% 2.31/2.56 166 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_3) # label(axiom). [assumption].
% 2.31/2.56 167 -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__sum__power2__lt__zero_0) # label(axiom). [assumption].
% 2.31/2.56 168 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A) # label(cls_sum__power2__ge__zero_0) # label(axiom). [assumption].
% 2.31/2.56 169 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__gt__zero__iff_1) # label(axiom). [assumption].
% 2.31/2.56 170 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__gt__zero__iff_2) # label(axiom). [assumption].
% 2.31/2.56 171 -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A) # label(cls_sum__power2__gt__zero__iff_0) # label(axiom). [assumption].
% 2.31/2.56 172 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__power2__le__zero__iff_2) # label(axiom). [assumption].
% 2.31/2.56 173 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__power2__le__zero__iff_0) # label(axiom). [assumption].
% 2.31/2.56 174 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__power2__le__zero__iff_1) # label(axiom). [assumption].
% 2.31/2.56 175 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_Int_OPls,tc_Int_Oint) # label(cls_less__special_I3_J_1) # label(axiom). [assumption].
% 2.31/2.56 176 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(B,c_Int_OPls,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__special_I3_J_0) # label(axiom). [assumption].
% 2.31/2.56 177 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_Int_OPls,tc_Int_Oint) # label(cls_le__special_I3_J_1) # label(axiom). [assumption].
% 2.31/2.56 178 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_lessequals(B,c_Int_OPls,tc_Int_Oint) | -c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__special_I3_J_0) # label(axiom). [assumption].
% 2.31/2.56 179 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A) | -c_HOL_Oord__class_Oless(c_Int_OPls,B,tc_Int_Oint) # label(cls_less__special_I1_J_1) # label(axiom). [assumption].
% 2.31/2.56 180 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_Int_OPls,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_less__special_I1_J_0) # label(axiom). [assumption].
% 2.31/2.56 181 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A) | -c_lessequals(c_Int_OPls,B,tc_Int_Oint) # label(cls_le__special_I1_J_1) # label(axiom). [assumption].
% 2.31/2.56 182 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_lessequals(c_Int_OPls,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__special_I1_J_0) # label(axiom). [assumption].
% 2.31/2.56 183 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B),A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_zero__less__power__eq_1) # label(axiom). [assumption].
% 2.31/2.56 184 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),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].
% 2.31/2.56 185 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) # label(cls_zero__less__power__eq_0) # label(axiom). [assumption].
% 2.31/2.56 186 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_5) # label(axiom). [assumption].
% 2.31/2.56 187 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_0) # label(axiom). [assumption].
% 2.31/2.56 188 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A) # label(cls_zero__less__power__eq__number__of_3) # label(axiom). [assumption].
% 2.31/2.56 189 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__less__power__eq__number__of_2) # label(axiom). [assumption].
% 2.31/2.56 190 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_abs__power2_0) # label(axiom). [assumption].
% 2.31/2.56 191 -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_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_power2__abs_0) # label(axiom). [assumption].
% 2.31/2.56 192 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__power2_1) # label(axiom). [assumption].
% 2.31/2.56 193 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) # label(cls_zero__le__power2_0) # label(axiom). [assumption].
% 2.31/2.56 194 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__eq__zero__iff_0) # label(axiom). [assumption].
% 2.31/2.56 195 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__eq__zero__iff_1) # label(axiom). [assumption].
% 2.31/2.56 196 -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) # label(cls_zero__less__power2_0) # label(axiom). [assumption].
% 2.31/2.56 197 -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power2__less__0_0) # label(axiom). [assumption].
% 2.31/2.56 198 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__eq__zero__iff_2) # label(axiom). [assumption].
% 2.31/2.57 199 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__power__le__0__imp__0_0) # label(axiom). [assumption].
% 2.31/2.57 200 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)),A) # label(cls_zero__le__even__power_H_0) # label(axiom). [assumption].
% 2.31/2.57 201 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))),A) # label(cls_odd__0__le__power__imp__0__le_0) # label(axiom). [assumption].
% 2.31/2.57 202 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_odd__power__less__zero_0) # label(axiom). [assumption].
% 2.31/2.57 203 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__eq__power2_1) # label(axiom). [assumption].
% 2.31/2.57 204 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__eq__power2_0) # label(axiom). [assumption].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(91,a,92,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(91,a,93,a)].
% 2.31/2.57 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),C),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(91,a,94,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint). [resolve(91,a,96,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(91,a,97,a)].
% 2.31/2.57 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(91,a,98,a)].
% 2.31/2.57 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(91,a,99,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint). [resolve(91,a,100,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,101,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,102,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(91,a,103,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint). [resolve(91,a,104,a)].
% 2.31/2.57 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)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,105,a)].
% 2.31/2.57 Derived: 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)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),C,tc_Int_Oint). [resolve(91,a,106,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint). [resolve(91,a,107,a)].
% 2.31/2.57 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(91,a,108,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) | -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)),B,tc_Int_Oint). [resolve(91,a,109,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)),A)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(91,a,110,a)].
% 2.31/2.57 Derived: 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)),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C),A,tc_Int_Oint). [resolve(91,a,111,a)].
% 2.31/2.57 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(91,a,112,a)].
% 2.31/2.57 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)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(91,a,113,a)].
% 2.31/2.57 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),A,tc_Int_Oint) | -c_lessequals(B,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(91,a,114,a)].
% 2.31/2.57 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),B,tc_Int_Oint) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(91,a,115,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -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)),C,tc_Int_Oint). [resolve(91,a,116,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(91,a,117,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,118,a)].
% 2.31/2.57 Derived: c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(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),tc_Int_Oint). [resolve(91,a,119,a)].
% 2.31/2.57 Derived: 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)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(91,a,120,a)].
% 2.31/2.57 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) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,121,a)].
% 2.31/2.57 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(91,a,122,a)].
% 2.31/2.57 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(91,a,123,a)].
% 2.31/2.57 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint). [resolve(91,a,124,a)].
% 2.31/2.57 Derived: -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(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),tc_Int_Oint). [resolve(91,a,126,a)].
% 2.31/2.57 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(91,a,127,a)].
% 2.31/2.57 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) | -c_lessequals(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),tc_Int_Oint). [resolve(91,a,128,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint) | 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). [resolve(91,a,130,a)].
% 2.31/2.57 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint). [resolve(91,a,131,a)].
% 2.31/2.57 Derived: c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,136,a)].
% 2.31/2.57 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),B),tc_Int_Oint). [resolve(91,a,137,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(91,a,138,a)].
% 2.31/2.57 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,140,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(91,a,141,a)].
% 2.31/2.57 Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,142,a)].
% 2.31/2.57 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(91,a,143,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_Int_OBit1(c_Int_OPls),tc_Int_Oint). [resolve(91,a,145,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_Int_OBit1(c_Int_OPls),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,146,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_Int_OBit1(c_Int_OPls),tc_Int_Oint). [resolve(91,a,147,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_lessequals(A,c_Int_OBit1(c_Int_OPls),tc_Int_Oint) | -c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,148,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),A,tc_Int_Oint). [resolve(91,a,149,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint). [resolve(91,a,150,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_Int_OBit1(c_Int_OPls),A,tc_Int_Oint). [resolve(91,a,151,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_lessequals(c_Int_OBit1(c_Int_OPls),A,tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint). [resolve(91,a,152,a)].
% 2.31/2.57 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,153,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,154,a)].
% 2.31/2.57 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) | 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)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,156,a)].
% 2.31/2.57 Derived: c_lessequals(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),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),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(91,a,157,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,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) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint). [resolve(91,a,158,a)].
% 2.31/2.57 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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)),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat). [resolve(91,a,159,a)].
% 2.31/2.57 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(91,a,160,a)].
% 2.31/2.57 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,162,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)),tc_Int_Oint). [resolve(91,a,163,a)].
% 2.31/2.57 Derived: -c_lessequals(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),tc_Int_Oint). [resolve(91,a,164,a)].
% 2.31/2.57 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,167,a)].
% 2.31/2.57 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint). [resolve(91,a,168,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,169,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,170,a)].
% 2.31/2.57 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(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(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),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(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint). [resolve(91,a,171,a)].
% 2.31/2.57 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(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(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),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(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,172,a)].
% 2.31/2.57 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,173,a)].
% 2.31/2.57 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,174,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_Int_OPls,tc_Int_Oint). [resolve(91,a,175,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_Int_OPls,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,176,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_Int_OPls,tc_Int_Oint). [resolve(91,a,177,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_lessequals(A,c_Int_OPls,tc_Int_Oint) | -c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,178,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_OPls,A,tc_Int_Oint). [resolve(91,a,179,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_OPls,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint). [resolve(91,a,180,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_Int_OPls,A,tc_Int_Oint). [resolve(91,a,181,a)].
% 2.31/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_lessequals(c_Int_OPls,A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint). [resolve(91,a,182,a)].
% 2.31/2.57 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(91,a,183,a)].
% 2.31/2.57 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(91,a,184,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint). [resolve(91,a,185,a)].
% 2.31/2.57 Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat) | c_lessequals(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),tc_Int_Oint). [resolve(91,a,186,a)].
% 2.31/2.57 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(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),tc_Int_Oint). [resolve(91,a,187,a)].
% 2.31/2.57 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint). [resolve(91,a,188,a)].
% 2.31/2.57 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(91,a,190,a)].
% 2.31/2.57 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(91,a,191,a)].
% 2.31/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,192,a)].
% 2.31/2.57 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_Int_Oint). [resolve(91,a,193,a)].
% 2.31/2.57 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,194,a)].
% 2.31/2.57 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,195,a)].
% 2.53/2.85 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_Int_Oint). [resolve(91,a,196,a)].
% 2.53/2.85 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,197,a)].
% 2.53/2.85 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(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(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),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(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,198,a)].
% 2.53/2.85 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,199,a)].
% 2.53/2.85 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)),tc_Int_Oint). [resolve(91,a,200,a)].
% 2.53/2.85 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))),tc_Int_Oint). [resolve(91,a,201,a)].
% 2.53/2.85 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,202,a)].
% 2.53/2.85 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,203,a)].
% 2.53/2.85 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,204,a)].
% 2.53/2.85 205 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 2.53/2.85 206 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(C,D,E,B,A) | -c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),C,A,tc_fun(A,A),B),E,B,A,A),D,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__zero__iff_0) # label(axiom). [assumption].
% 2.53/2.85 207 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(c_COMBB(C,c_COMBC(c_HOL_Oplus__class_Oplus(B),D,B,B,B),B,A,B),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].
% 2.53/2.85 208 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),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].
% 2.53/2.85 209 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__minus_0) # label(axiom). [assumption].
% 2.53/2.85 210 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),C,A,tc_fun(A,A),B),D,B,A,A),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].
% 2.53/2.85 211 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),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].
% 2.53/2.85 212 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),C,A,A,B),D,hAPP(c_HOL_Ouminus__class_Ouminus(A),E),B,A) | -c_Lim_OLIM(C,D,E,B,A) # label(cls_LIM__minus_0) # label(axiom). [assumption].
% 2.53/2.85 213 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_LIMSEQ__Zseq__iff_0) # label(axiom). [assumption].
% 2.53/2.85 214 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) # label(cls_LIMSEQ__Zseq__iff_1) # label(axiom). [assumption].
% 2.53/2.85 215 -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].
% 2.53/2.85 216 -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].
% 2.53/2.85 217 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_Series_Osums(B,C,A) # label(cls_sums__minus_0) # label(axiom). [assumption].
% 2.53/2.85 218 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) # label(cls_LIMSEQ__minus__cancel_0) # label(axiom). [assumption].
% 2.53/2.85 219 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_LIMSEQ__minus_0) # label(axiom). [assumption].
% 2.53/2.85 220 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(C,hAPP(c_HOL_Oplus__class_Oplus(A),D),A,B,A),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].
% 2.53/2.85 221 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(C,D,hAPP(C,D),A,B) | -c_Lim_OLIM(c_COMBB(C,hAPP(c_HOL_Oplus__class_Oplus(A),D),A,B,A),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) # label(cls_LIM__isCont__iff_1) # label(axiom). [assumption].
% 2.53/2.85 222 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(c_COMBB(C,hAPP(c_HOL_Oplus__class_Oplus(B),D),B,A,B),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].
% 2.53/2.85 223 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(C,D,E,B,A) | -c_Lim_OLIM(c_COMBB(C,hAPP(c_HOL_Oplus__class_Oplus(B),D),B,A,B),c_HOL_Ozero__class_Ozero(B),E,B,A) # label(cls_LIM__offset__zero__cancel_0) # label(axiom). [assumption].
% 2.53/2.85 224 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),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].
% 2.53/2.85 225 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),D,A,tc_fun(A,A),tc_nat),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].
% 2.53/2.85 226 -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(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),C,A) # label(cls_sums__Suc_0) # label(axiom). [assumption].
% 2.53/2.85 227 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),C,A,tc_fun(A,A),B),c_COMBB(c_HOL_Ouminus__class_Ouminus(A),D,A,A,B),B,A,A),E,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),hAPP(c_HOL_Ouminus__class_Ouminus(A),V6)),B,A) | -c_Lim_OLIM(D,E,V6,B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__add__minus_0) # label(axiom). [assumption].
% 2.53/2.85 228 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),C,A,tc_fun(A,A),B),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].
% 2.53/2.85 229 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),C,A,tc_fun(A,A),B),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].
% 2.53/2.85 230 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),tc_nat),c_COMBB(c_HOL_Ouminus__class_Ouminus(A),C,A,A,tc_nat),tc_nat,A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),hAPP(c_HOL_Ouminus__class_Ouminus(A),E)),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__add__minus_0) # label(axiom). [assumption].
% 2.53/2.85 231 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),tc_nat),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].
% 2.53/2.85 232 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),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].
% 2.53/2.85 233 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),tc_nat),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].
% 2.53/2.85 234 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OZseq(C,A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__diff_0) # label(axiom). [assumption].
% 2.53/2.85 235 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),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].
% 2.53/2.85 236 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OZseq(C,A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__add_0) # label(axiom). [assumption].
% 2.53/2.85 237 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A)),A) | -c_Series_Osums(B,D,A) # label(cls_sums__split__initial__segment_0) # label(axiom). [assumption].
% 2.53/2.86 238 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(C,D,E,B,A) | -c_Lim_OLIM(F,D,E,B,A) | -c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),C,A,tc_fun(A,A),B),c_COMBB(c_HOL_Ouminus__class_Ouminus(A),F,A,A,B),B,A,A),D,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__trans_0) # label(axiom). [assumption].
% 2.53/2.86 239 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),C,A,tc_fun(A,A),B),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].
% 2.53/2.86 240 -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(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),C,A) # label(cls_sums__Suc__imp_0) # label(axiom). [assumption].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,D,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),D,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(205,a,206,a)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),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(205,a,207,b)].
% 2.53/2.86 Derived: c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(205,a,208,a)].
% 2.53/2.86 Derived: c_SEQ_OZseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(205,a,209,a)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,C,A,tc_Complex_Ocomplex). [resolve(205,a,210,a)].
% 2.53/2.86 Derived: c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(205,a,211,a)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),C,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),D),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,C,D,A,tc_Complex_Ocomplex). [resolve(205,a,212,a)].
% 2.53/2.86 Derived: c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex). [resolve(205,a,213,a)].
% 2.53/2.86 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(205,a,214,a)].
% 2.53/2.86 Derived: A = c_Series_Osuminf(B,tc_Complex_Ocomplex) | -c_Series_Osums(B,A,tc_Complex_Ocomplex). [resolve(205,a,215,a)].
% 2.53/2.86 Derived: c_Series_Osuminf(A,tc_Complex_Ocomplex) = B | -c_Series_Osums(A,B,tc_Complex_Ocomplex). [resolve(205,a,216,a)].
% 2.53/2.86 Derived: c_Series_Osums(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,B,tc_Complex_Ocomplex). [resolve(205,a,217,a)].
% 2.53/2.86 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex). [resolve(205,a,218,a)].
% 2.53/2.86 Derived: c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex). [resolve(205,a,219,a)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(B,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),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(205,a,220,a)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,hAPP(B,C),tc_Complex_Ocomplex,A) | -c_Lim_OLIM(c_COMBB(B,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(B,C),tc_Complex_Ocomplex,A). [resolve(205,a,221,a)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(B,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),D,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(B,C,D,tc_Complex_Ocomplex,A). [resolve(205,a,222,b)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,D,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(c_COMBB(B,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),D,tc_Complex_Ocomplex,A). [resolve(205,a,223,b)].
% 2.53/2.86 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(205,a,224,a)].
% 2.53/2.86 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(205,a,225,a)].
% 2.53/2.86 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(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex). [resolve(205,a,226,a)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),E),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),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(205,a,227,a)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),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(205,a,228,a)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),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(205,a,229,a)].
% 2.53/2.86 Derived: c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),D)),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(205,a,230,a)].
% 2.53/2.86 Derived: c_Series_Osums(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(205,a,231,a)].
% 2.53/2.86 Derived: c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(205,a,232,a)].
% 2.53/2.86 Derived: c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(205,a,233,a)].
% 2.53/2.86 Derived: c_SEQ_OZseq(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(205,a,234,a)].
% 2.53/2.86 Derived: c_Series_Osums(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(205,a,235,a)].
% 2.53/2.86 Derived: c_SEQ_OZseq(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(205,a,236,a)].
% 2.53/2.86 Derived: c_Series_Osums(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),B,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(205,a,237,a)].
% 2.53/2.86 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,D,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(E,C,D,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),E,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(205,a,238,a)].
% 2.69/3.00 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),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(205,a,239,a)].
% 2.69/3.00 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(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex). [resolve(205,a,240,a)].
% 2.69/3.00 241 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.69/3.00 242 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)) = C # label(cls_add__minus__cancel_0) # label(axiom). [assumption].
% 2.69/3.00 243 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom). [assumption].
% 2.69/3.00 244 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Ozero__class_Ozero(A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) # label(cls_group__add__class_Odiff__0_0) # label(axiom). [assumption].
% 2.69/3.00 245 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_diff__minus_0) # label(axiom). [assumption].
% 2.69/3.00 246 -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].
% 2.69/3.00 247 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) = C # label(cls_minus__unique_0) # label(axiom). [assumption].
% 2.69/3.00 248 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),C) # label(cls_eq__neg__iff__add__eq__0_1) # label(axiom). [assumption].
% 2.69/3.00 249 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__neg__iff__add__eq__0_0) # label(axiom). [assumption].
% 2.69/3.00 250 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus_0) # label(axiom). [assumption].
% 2.69/3.00 251 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_left__minus_0) # label(axiom). [assumption].
% 2.69/3.00 252 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) # label(cls_diff__minus__eq__add_0) # label(axiom). [assumption].
% 2.69/3.00 253 -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].
% 2.69/3.00 254 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_minus__equation__iff_1) # label(axiom). [assumption].
% 2.69/3.00 255 -class_OrderedGroup_Ogroup__add(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_equation__minus__iff_1) # label(axiom). [assumption].
% 2.69/3.00 256 -class_OrderedGroup_Ogroup__add(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_equation__minus__iff_0) # label(axiom). [assumption].
% 2.69/3.00 257 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_minus__minus_0) # label(axiom). [assumption].
% 2.69/3.00 258 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = C # label(cls_minus__add__cancel_0) # label(axiom). [assumption].
% 2.69/3.00 259 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom). [assumption].
% 2.69/3.00 260 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) # label(cls_neg__0__equal__iff__equal_1) # label(axiom). [assumption].
% 2.69/3.00 261 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom). [assumption].
% 2.69/3.00 262 -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].
% 2.69/3.00 263 -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].
% 2.69/3.00 264 -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].
% 2.69/3.00 265 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom). [assumption].
% 2.69/3.00 266 -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].
% 2.69/3.00 267 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_minus__add_0) # label(axiom). [assumption].
% 2.69/3.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) = B. [resolve(241,a,242,a)].
% 2.69/3.00 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B) | A = B. [resolve(241,a,243,a)].
% 2.69/3.00 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A). [resolve(241,a,244,a)].
% 2.69/3.00 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(241,a,245,a)].
% 2.69/3.00 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(241,a,246,a)].
% 2.69/3.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) = B. [resolve(241,a,247,a)].
% 2.69/3.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B). [resolve(241,a,248,a)].
% 2.69/3.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(241,a,249,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(241,a,250,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B). [resolve(241,a,252,a)].
% 2.76/3.00 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(241,a,253,a)].
% 2.76/3.00 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)) = A. [resolve(241,a,254,a)].
% 2.76/3.00 Derived: A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(241,a,255,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)) = B. [resolve(241,a,258,a)].
% 2.76/3.00 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(241,a,259,a)].
% 2.76/3.00 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)). [resolve(241,a,260,a)].
% 2.76/3.00 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(241,a,261,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(241,a,262,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(241,a,263,a)].
% 2.76/3.00 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) | c_HOL_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(241,a,265,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(241,a,266,a)].
% 2.76/3.00 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(241,a,267,a)].
% 2.76/3.00 268 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B)) = B. [resolve(268,a,242,a)].
% 2.76/3.00 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B) | A = B. [resolve(268,a,243,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A). [resolve(268,a,244,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(268,a,245,a)].
% 2.76/3.00 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(268,a,246,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) = B. [resolve(268,a,247,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B). [resolve(268,a,248,a)].
% 2.76/3.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(268,a,249,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(268,a,250,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B). [resolve(268,a,252,a)].
% 2.83/3.13 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(268,a,253,a)].
% 2.83/3.13 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)) = A. [resolve(268,a,254,a)].
% 2.83/3.13 Derived: A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)). [resolve(268,a,255,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)) = B. [resolve(268,a,258,a)].
% 2.83/3.13 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(268,a,259,a)].
% 2.83/3.13 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(268,a,260,a)].
% 2.83/3.13 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(268,a,261,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(268,a,262,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(268,a,263,a)].
% 2.83/3.13 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(268,a,265,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(268,a,266,a)].
% 2.83/3.13 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)). [resolve(268,a,267,a)].
% 2.83/3.13 269 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.83/3.13 270 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)) # label(cls_comm__monoid__add_Opower__commutes_0) # label(axiom). [assumption].
% 2.83/3.13 271 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),E),D),tc_nat),tc_nat,A) = c_Finite__Set_Osetsum(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),D,tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(C,E,tc_nat),tc_nat,A) # label(cls_setsum__shift__bounds__cl__nat__ivl_0) # label(axiom). [assumption].
% 2.83/3.13 272 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(C,hAPP(c_Suc,D),tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(C,D,tc_nat),tc_nat,A)),hAPP(B,hAPP(c_Suc,D))) | c_HOL_Oord__class_Oless(hAPP(c_Suc,D),C,tc_nat) # label(cls_setsum__cl__ivl__Suc_1) # label(axiom). [assumption].
% 2.83/3.13 273 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 2.83/3.13 274 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 2.83/3.13 275 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_comm__monoid__add_Opower__one__right_0) # label(axiom). [assumption].
% 2.83/3.13 276 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 2.83/3.13 277 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 2.83/3.13 278 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 2.83/3.13 279 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),D)) # label(cls_comm__monoid__add_Opower__add_0) # label(axiom). [assumption].
% 2.83/3.13 280 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),D)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),C),D)) # label(cls_comm__monoid__add_Opower__mult__distrib_0) # label(axiom). [assumption].
% 2.83/3.13 281 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 2.83/3.13 282 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 2.83/3.13 283 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),E),tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(C,D,tc_nat),tc_nat,A)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),E),tc_nat),tc_nat,A)) | -c_lessequals(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) # label(cls_setsum__ub__add__nat_0) # label(axiom). [assumption].
% 2.83/3.13 284 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(C,D,tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Suc,C),D,tc_nat),tc_nat,A)) | -c_lessequals(C,D,tc_nat) # label(cls_setsum__head__Suc_0) # label(axiom). [assumption].
% 2.83/3.13 285 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_comm__monoid__add_Opower__one_0) # label(axiom). [assumption].
% 2.83/3.13 286 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 2.83/3.13 287 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 2.83/3.13 288 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(C,hAPP(c_Suc,D),tc_nat),tc_nat,A) = c_HOL_Ozero__class_Ozero(A) | -c_HOL_Oord__class_Oless(hAPP(c_Suc,D),C,tc_nat) # label(cls_setsum__cl__ivl__Suc_0) # label(axiom). [assumption].
% 2.83/3.13 289 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,hAPP(c_Suc,D),tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A)),hAPP(B,D)) | c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_setsum__op__ivl__Suc_1) # label(axiom). [assumption].
% 2.83/3.13 290 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),D,tc_nat),tc_nat,A)) | -c_HOL_Oord__class_Oless(C,D,tc_nat) # label(cls_setsum__head__upt__Suc_0) # label(axiom). [assumption].
% 2.83/3.13 291 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(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),tc_nat,A) = c_Finite__Set_Osetsum(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),D,tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat),tc_nat,A) # label(cls_setsum__shift__bounds__nat__ivl_0) # label(axiom). [assumption].
% 2.83/3.13 292 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C),tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(c_COMBB(B,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A)),c_Finite__Set_Osetsum(c_COMBB(B,c_COMBC(c_COMBB(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A)) # label(cls_setsum__splice_0) # label(axiom). [assumption].
% 2.83/3.13 293 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(A) # label(cls_comm__monoid__add_Opower__0_0) # label(axiom). [assumption].
% 2.83/3.13 294 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)) # label(cls_comm__monoid__add_Opower__Suc_0) # label(axiom). [assumption].
% 2.83/3.13 295 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),B) # label(cls_comm__monoid__add_Opower__Suc2_0) # label(axiom). [assumption].
% 2.83/3.13 296 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),D) # label(cls_comm__monoid__add_Opower__mult_0) # label(axiom). [assumption].
% 2.83/3.13 297 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__empty_0) # label(axiom). [assumption].
% 2.83/3.13 298 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)),B) # label(cls_comm__monoid__add_Opower3__eq__cube_0) # label(axiom). [assumption].
% 2.83/3.13 299 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) # label(cls_comm__monoid__add_Opower2__eq__square_0) # label(axiom). [assumption].
% 2.83/3.13 300 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),C),D,C,A,A),E,C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,E,C,A)),c_Finite__Set_Osetsum(D,E,C,A)) # label(cls_setsum__addf_0) # label(axiom). [assumption].
% 2.83/3.13 301 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(C,hAPP(c_Suc,D),tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),c_Finite__Set_Osetsum(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(C,D,tc_nat),tc_nat,A)) | c_HOL_Oord__class_Oless(hAPP(c_Suc,D),C,tc_nat) # label(cls_setsum__cl__ivl__Suc2_1) # label(axiom). [assumption].
% 2.83/3.13 302 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(D,E,tc_nat),tc_nat,A)) = c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat),tc_nat,A) | -c_lessequals(D,E,tc_nat) | -c_lessequals(C,D,tc_nat) # label(cls_setsum__add__nat__ivl_0) # label(axiom). [assumption].
% 2.83/3.13 303 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(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),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),D,tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat),tc_nat,A)) # label(cls_sumr__offset3_0) # label(axiom). [assumption].
% 2.83/3.13 304 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_comm__monoid__add_Opower__even__eq_0) # label(axiom). [assumption].
% 2.83/3.13 305 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Suc,C),hAPP(c_Suc,D),tc_nat),tc_nat,A) = c_Finite__Set_Osetsum(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(C,D,tc_nat),tc_nat,A) # label(cls_setsum__shift__bounds__cl__Suc__ivl_0) # label(axiom). [assumption].
% 2.83/3.13 306 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) # label(cls_comm__monoid__add_Opower__odd__eq_0) # label(axiom). [assumption].
% 2.83/3.13 307 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(B,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat))) # label(cls_Sum4_0) # label(axiom). [assumption].
% 2.83/3.13 308 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,hAPP(c_Suc,D),tc_nat),tc_nat,A) = c_HOL_Ozero__class_Ozero(A) | -c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_setsum__op__ivl__Suc_0) # label(axiom). [assumption].
% 2.83/3.13 309 -class_Power_Opower(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(A),B),A,tc_fun(A,A),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat),tc_nat,A) = c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),A,tc_fun(A,A),tc_nat),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),tc_nat,A) # label(cls_lemma__realpow__rev__sumr_0) # label(axiom). [assumption].
% 2.83/3.13 310 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),hAPP(c_Suc,D),tc_nat),tc_nat,A) = c_Finite__Set_Osetsum(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A) # label(cls_setsum__shift__bounds__Suc__ivl_0) # label(axiom). [assumption].
% 2.83/3.13 311 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_nat),tc_nat,A) = c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A) # label(cls_setsum__shift__lb__Suc0__0__upt_0) # label(axiom). [assumption].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)). [resolve(269,a,270,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat),tc_nat,tc_nat) = c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,D,tc_nat),tc_nat,tc_nat). [resolve(269,a,271,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_nat)),hAPP(A,hAPP(c_Suc,C))) | c_HOL_Oord__class_Oless(hAPP(c_Suc,C),B,tc_nat). [resolve(269,a,272,a)].
% 2.83/3.13 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(269,a,273,b)].
% 2.83/3.13 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(269,a,274,b)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(269,a,275,a)].
% 2.83/3.13 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(269,a,276,a)].
% 2.83/3.13 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(269,a,277,a)].
% 2.83/3.13 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(269,a,278,b)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),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_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),C)). [resolve(269,a,279,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),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_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),C)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),B),C)). [resolve(269,a,280,a)].
% 2.83/3.13 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(269,a,281,b)].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(269,a,282,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_nat)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat),tc_nat,tc_nat)) | -c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(269,a,283,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Suc,B),C,tc_nat),tc_nat,tc_nat)) | -c_lessequals(B,C,tc_nat). [resolve(269,a,284,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(269,a,285,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(269,a,286,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(269,a,287,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(hAPP(c_Suc,C),B,tc_nat). [resolve(269,a,288,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_nat)),hAPP(A,C)) | c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(269,a,289,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat),tc_nat,tc_nat)) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(269,a,290,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(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),tc_nat,tc_nat) = c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_nat). [resolve(269,a,291,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B),tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(c_COMBB(A,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_nat)),c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_COMBB(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_nat)). [resolve(269,a,292,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(269,a,293,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)). [resolve(269,a,294,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),A). [resolve(269,a,295,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),C). [resolve(269,a,296,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(269,a,297,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A)),A). [resolve(269,a,298,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A). [resolve(269,a,299,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_nat),A,tc_nat,tc_fun(tc_nat,tc_nat),B),C,B,tc_nat,tc_nat),D,B,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,D,B,tc_nat)),c_Finite__Set_Osetsum(C,D,B,tc_nat)). [resolve(269,a,300,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_nat)) | c_HOL_Oord__class_Oless(hAPP(c_Suc,C),B,tc_nat). [resolve(269,a,301,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_nat)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,tc_nat)) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_nat) | -c_lessequals(C,D,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(269,a,302,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(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),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(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),B,tc_nat),tc_nat,tc_nat)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,tc_nat)). [resolve(269,a,303,a)].
% 2.83/3.13 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(269,a,304,a)].
% 2.83/3.13 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_nat). [resolve(269,a,305,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(269,a,306,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(A,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(269,a,307,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(269,a,308,a)].
% 2.83/3.14 Derived: -class_Power_Opower(tc_nat) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),B),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),hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_nat,tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),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),tc_nat,tc_nat). [resolve(269,a,309,b)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_nat). [resolve(269,a,310,a)].
% 2.83/3.14 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat),tc_nat,tc_nat) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_nat). [resolve(269,a,311,a)].
% 2.83/3.14 312 class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.83/3.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)). [resolve(312,a,270,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat),tc_nat,tc_Int_Oint) = c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,D,tc_nat),tc_nat,tc_Int_Oint). [resolve(312,a,271,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Int_Oint)),hAPP(A,hAPP(c_Suc,C))) | c_HOL_Oord__class_Oless(hAPP(c_Suc,C),B,tc_nat). [resolve(312,a,272,a)].
% 2.83/3.14 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(312,a,273,b)].
% 2.83/3.14 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(312,a,274,b)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(312,a,275,a)].
% 2.83/3.14 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(312,a,276,a)].
% 2.83/3.14 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(312,a,277,a)].
% 2.83/3.14 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(312,a,278,b)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),C)). [resolve(312,a,279,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),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_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),B),C)). [resolve(312,a,280,a)].
% 2.83/3.14 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(312,a,281,b)].
% 2.83/3.14 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(312,a,282,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Int_Oint)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat),tc_nat,tc_Int_Oint)) | -c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(312,a,283,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(A,B)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Suc,B),C,tc_nat),tc_nat,tc_Int_Oint)) | -c_lessequals(B,C,tc_nat). [resolve(312,a,284,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(312,a,285,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(312,a,286,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(312,a,287,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_Suc,C),B,tc_nat). [resolve(312,a,288,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Int_Oint)),hAPP(A,C)) | c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(312,a,289,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(A,B)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat),tc_nat,tc_Int_Oint)) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(312,a,290,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(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),tc_nat,tc_Int_Oint) = c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_Int_Oint). [resolve(312,a,291,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B),tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Finite__Set_Osetsum(c_COMBB(A,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Int_Oint)),c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_COMBB(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Int_Oint)). [resolve(312,a,292,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(312,a,293,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)). [resolve(312,a,294,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),A). [resolve(312,a,295,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),C). [resolve(312,a,296,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(312,a,297,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A)),A). [resolve(312,a,298,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A). [resolve(312,a,299,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),B),C,B,tc_Int_Oint,tc_Int_Oint),D,B,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Finite__Set_Osetsum(A,D,B,tc_Int_Oint)),c_Finite__Set_Osetsum(C,D,B,tc_Int_Oint)). [resolve(312,a,300,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(A,B)),c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Int_Oint)) | c_HOL_Oord__class_Oless(hAPP(c_Suc,C),B,tc_nat). [resolve(312,a,301,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Int_Oint)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,tc_Int_Oint)) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_Int_Oint) | -c_lessequals(C,D,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(312,a,302,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(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),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Int_Oint)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,tc_Int_Oint)). [resolve(312,a,303,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(312,a,304,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat),tc_nat,tc_Int_Oint) = c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Int_Oint). [resolve(312,a,305,a)].
% 2.83/3.14 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(312,a,306,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(A,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(312,a,307,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(312,a,308,a)].
% 2.83/3.14 Derived: -class_Power_Opower(tc_Int_Oint) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Int_Oint,tc_nat),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),tc_nat,tc_Int_Oint) = c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Int_Oint,tc_nat),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),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),tc_nat,tc_Int_Oint). [resolve(312,a,309,b)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat),tc_nat,tc_Int_Oint) = c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Int_Oint). [resolve(312,a,310,a)].
% 2.83/3.14 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat),tc_nat,tc_Int_Oint) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Int_Oint). [resolve(312,a,311,a)].
% 2.83/3.14 313 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.83/3.14 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B)). [resolve(313,a,270,a)].
% 2.83/3.14 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat),tc_nat,tc_Complex_Ocomplex) = c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,D,tc_nat),tc_nat,tc_Complex_Ocomplex). [resolve(313,a,271,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex)),hAPP(A,hAPP(c_Suc,C))) | c_HOL_Oord__class_Oless(hAPP(c_Suc,C),B,tc_nat). [resolve(313,a,272,a)].
% 2.83/3.15 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) | -c_lessequals(A,B,tc_Complex_Ocomplex) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),C,tc_Complex_Ocomplex). [resolve(313,a,273,b)].
% 2.83/3.15 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) | -c_lessequals(A,C,tc_Complex_Ocomplex) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(313,a,274,b)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(313,a,275,a)].
% 2.83/3.15 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(313,a,276,a)].
% 2.83/3.15 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(313,a,277,a)].
% 2.83/3.15 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) | -c_HOL_Oord__class_Oless(A,C,tc_Complex_Ocomplex) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(313,a,278,b)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),C)). [resolve(313,a,279,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),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_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B),C)). [resolve(313,a,280,a)].
% 2.83/3.15 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Complex_Ocomplex) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) | -c_lessequals(A,C,tc_Complex_Ocomplex) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(313,a,281,b)].
% 2.83/3.15 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(313,a,282,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat),tc_nat,tc_Complex_Ocomplex)) | -c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(313,a,283,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(A,B)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Suc,B),C,tc_nat),tc_nat,tc_Complex_Ocomplex)) | -c_lessequals(B,C,tc_nat). [resolve(313,a,284,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(313,a,285,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(313,a,286,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(313,a,287,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_HOL_Oord__class_Oless(hAPP(c_Suc,C),B,tc_nat). [resolve(313,a,288,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex)),hAPP(A,C)) | c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(313,a,289,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(A,B)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat),tc_nat,tc_Complex_Ocomplex)) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(313,a,290,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(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),tc_nat,tc_Complex_Ocomplex) = c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_Complex_Ocomplex). [resolve(313,a,291,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B),tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(c_COMBB(A,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_Complex_Ocomplex,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex)),c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_COMBB(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex)). [resolve(313,a,292,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(313,a,293,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B)). [resolve(313,a,294,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B)),A). [resolve(313,a,295,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B)),C). [resolve(313,a,296,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(313,a,297,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),A)),A). [resolve(313,a,298,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),A). [resolve(313,a,299,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),B),C,B,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,B,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,D,B,tc_Complex_Ocomplex)),c_Finite__Set_Osetsum(C,D,B,tc_Complex_Ocomplex)). [resolve(313,a,300,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(A,B)),c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex)) | c_HOL_Oord__class_Oless(hAPP(c_Suc,C),B,tc_nat). [resolve(313,a,301,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_Complex_Ocomplex) | -c_lessequals(C,D,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(313,a,302,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(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),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,tc_Complex_Ocomplex)). [resolve(313,a,303,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(313,a,304,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat),tc_nat,tc_Complex_Ocomplex) = c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex). [resolve(313,a,305,a)].
% 2.83/3.15 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(313,a,306,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(A,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(313,a,307,a)].
% 2.83/3.15 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(313,a,308,a)].
% 2.83/3.15 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),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),tc_nat,tc_Complex_Ocomplex) = c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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),tc_nat,tc_Complex_Ocomplex). [resolve(313,a,309,b)].
% 2.99/3.30 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat),tc_nat,tc_Complex_Ocomplex) = c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex). [resolve(313,a,310,a)].
% 2.99/3.30 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat),tc_nat,tc_Complex_Ocomplex) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex). [resolve(313,a,311,a)].
% 2.99/3.30 314 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 2.99/3.30 315 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__le__D2_0) # label(axiom). [assumption].
% 2.99/3.30 316 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__nonneg_0) # label(axiom). [assumption].
% 2.99/3.30 317 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_0) # label(axiom). [assumption].
% 2.99/3.30 318 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | 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)),hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),A) # label(cls_abs__triangle__ineq2_0) # label(axiom). [assumption].
% 2.99/3.30 319 -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].
% 2.99/3.30 320 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__neg_0) # label(axiom). [assumption].
% 2.99/3.30 321 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__minus__le__zero_0) # label(axiom). [assumption].
% 2.99/3.30 322 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__le__D1_0) # label(axiom). [assumption].
% 2.99/3.30 323 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(B,C,A) # label(cls_abs__leI_0) # label(axiom). [assumption].
% 2.99/3.30 324 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(B,C,A) # label(cls_abs__le__iff_2) # label(axiom). [assumption].
% 2.99/3.30 325 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = hAPP(c_HOL_Oabs__class_Oabs(A),B) # label(cls_abs__minus__cancel_0) # label(axiom). [assumption].
% 2.99/3.30 326 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_1) # label(axiom). [assumption].
% 2.99/3.30 327 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | 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))),hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),A) # label(cls_abs__triangle__ineq3_0) # label(axiom). [assumption].
% 2.99/3.30 328 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),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)),A) # label(cls_abs__triangle__ineq_0) # label(axiom). [assumption].
% 2.99/3.30 329 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | 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))),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))),A) # label(cls_abs__diff__triangle__ineq_0) # label(axiom). [assumption].
% 2.99/3.30 330 -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].
% 2.99/3.30 331 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oabs__class_Oabs(A),B),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__abs__iff_1) # label(axiom). [assumption].
% 2.99/3.30 332 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),B),A) # label(cls_abs__ge__minus__self_0) # label(axiom). [assumption].
% 2.99/3.30 333 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,hAPP(c_HOL_Oabs__class_Oabs(A),B),A) # label(cls_abs__ge__self_0) # label(axiom). [assumption].
% 2.99/3.30 334 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__pos_0) # label(axiom). [assumption].
% 2.99/3.30 335 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__nonpos_0) # label(axiom). [assumption].
% 2.99/3.30 336 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__not__less__zero_0) # label(axiom). [assumption].
% 2.99/3.30 337 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),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)),A) # label(cls_abs__triangle__ineq4_0) # label(axiom). [assumption].
% 2.99/3.30 338 -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].
% 2.99/3.30 339 -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].
% 2.99/3.30 340 -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].
% 2.99/3.30 341 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)),A) # label(cls_zero__less__abs__iff_0) # label(axiom). [assumption].
% 2.99/3.30 342 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oabs__class_Oabs(A),B),A) # label(cls_abs__ge__zero_0) # label(axiom). [assumption].
% 2.99/3.30 343 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_Finite__Set_Osetsum(B,C,D,A)),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,D),C,D,A),A) # label(cls_setsum__abs_0) # label(axiom). [assumption].
% 2.99/3.30 344 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),D,C,A)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),D,C,A) # label(cls_abs__setsum__abs_0) # label(axiom). [assumption].
% 2.99/3.30 345 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),D,C,A),A) # label(cls_setsum__abs__ge__zero_0) # label(axiom). [assumption].
% 2.99/3.30 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint). [resolve(314,a,315,a)].
% 2.99/3.30 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(314,a,316,a)].
% 2.99/3.30 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(314,a,317,a)].
% 2.99/3.30 Derived: 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)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),tc_Int_Oint). [resolve(314,a,318,a)].
% 2.99/3.30 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(314,a,319,a)].
% 2.99/3.30 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(314,a,320,a)].
% 2.99/3.30 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(314,a,321,a)].
% 2.99/3.30 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint). [resolve(314,a,322,a)].
% 2.99/3.30 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(314,a,323,a)].
% 2.99/3.30 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A). [resolve(314,a,325,a)].
% 2.99/3.30 Derived: c_lessequals(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),tc_Int_Oint). [resolve(314,a,326,a)].
% 2.99/3.30 Derived: 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))),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),tc_Int_Oint). [resolve(314,a,327,a)].
% 2.99/3.30 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(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),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)),tc_Int_Oint). [resolve(314,a,328,a)].
% 2.99/3.30 Derived: 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))),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))),tc_Int_Oint). [resolve(314,a,329,a)].
% 3.18/3.44 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(314,a,330,a)].
% 3.18/3.44 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(314,a,331,a)].
% 3.18/3.44 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint). [resolve(314,a,332,a)].
% 3.18/3.44 Derived: c_lessequals(A,hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint). [resolve(314,a,333,a)].
% 3.18/3.44 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(314,a,334,a)].
% 3.18/3.44 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(314,a,335,a)].
% 3.18/3.44 Derived: -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(314,a,336,a)].
% 3.18/3.44 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),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)),tc_Int_Oint). [resolve(314,a,337,a)].
% 3.18/3.44 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(314,a,338,a)].
% 3.18/3.44 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(314,a,339,a)].
% 3.18/3.44 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(314,a,340,a)].
% 3.18/3.44 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),tc_Int_Oint). [resolve(314,a,341,a)].
% 3.18/3.44 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint). [resolve(314,a,342,a)].
% 3.18/3.44 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Finite__Set_Osetsum(A,B,C,tc_Int_Oint)),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,C),B,C,tc_Int_Oint),tc_Int_Oint). [resolve(314,a,343,a)].
% 3.18/3.44 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),C,B,tc_Int_Oint)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),C,B,tc_Int_Oint). [resolve(314,a,344,a)].
% 3.18/3.44 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),C,B,tc_Int_Oint),tc_Int_Oint). [resolve(314,a,345,a)].
% 3.18/3.44 346 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 3.18/3.44 347 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__add__self2_0) # label(axiom). [assumption].
% 3.18/3.44 348 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A) = c_Divides_Odiv__class_Omod(C,B,A) # label(cls_mod__add__self1_0) # label(axiom). [assumption].
% 3.18/3.44 349 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) # label(cls_zmod__simps_I2_J_0) # label(axiom). [assumption].
% 3.18/3.44 350 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A) # label(cls_zmod__simps_I1_J_0) # label(axiom). [assumption].
% 3.18/3.44 351 -class_Divides_Osemiring__div(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A)) # label(cls_mod__div__decomp_0) # label(axiom). [assumption].
% 3.18/3.44 352 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A)) = B # label(cls_mod__div__equality_0) # label(axiom). [assumption].
% 3.18/3.44 353 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(C,B,A))),c_Divides_Odiv__class_Omod(C,B,A)) = C # label(cls_mod__div__equality2_0) # label(axiom). [assumption].
% 3.18/3.44 354 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(C,B,A)),c_HOL_Oone__class_Oone(A)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self1_0) # label(axiom). [assumption].
% 3.18/3.44 355 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_HOL_Oone__class_Oone(A)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self2_0) # label(axiom). [assumption].
% 3.18/3.44 356 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__eq_0) # label(axiom). [assumption].
% 3.18/3.44 357 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__right__eq_0) # label(axiom). [assumption].
% 3.18/3.44 358 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__add__left__eq_0) # label(axiom). [assumption].
% 3.18/3.44 359 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mod__trivial_0) # label(axiom). [assumption].
% 3.18/3.44 360 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__self_0) # label(axiom). [assumption].
% 3.18/3.44 361 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A))),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) # label(cls_div__mod__equality_0) # label(axiom). [assumption].
% 3.18/3.44 362 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(C,B,A))),c_Divides_Odiv__class_Omod(C,B,A))),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D) # label(cls_div__mod__equality2_0) # label(axiom). [assumption].
% 3.18/3.44 363 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__div__trivial_0) # label(axiom). [assumption].
% 3.18/3.44 364 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),D),C,A) # label(cls_mod__add__cong_0) # label(axiom). [assumption].
% 3.18/3.44 365 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mult__self2_0) # label(axiom). [assumption].
% 3.18/3.44 366 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),D,A) = c_Divides_Odiv__class_Omod(B,D,A) # label(cls_mod__mult__self1_0) # label(axiom). [assumption].
% 3.18/3.44 367 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_div__by__1_0) # label(axiom). [assumption].
% 3.18/3.44 368 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__by__1_0) # label(axiom). [assumption].
% 3.18/3.44 369 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__self_0) # label(axiom). [assumption].
% 3.18/3.44 370 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_mod__by__0_0) # label(axiom). [assumption].
% 3.18/3.44 371 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__by__0_0) # label(axiom). [assumption].
% 3.18/3.44 372 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__0_0) # label(axiom). [assumption].
% 3.18/3.44 373 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__0_0) # label(axiom). [assumption].
% 3.18/3.44 374 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(B,C,A)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2_0) # label(axiom). [assumption].
% 3.18/3.44 375 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_Divides_Odiv__class_Odiv(B,D,A)) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1_0) # label(axiom). [assumption].
% 3.18/3.44 376 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)) = B # label(cls_semiring__div__class_Omod__div__equality_H_0) # label(axiom). [assumption].
% 3.18/3.44 377 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,D,A)),C) # label(cls_mod__mult__mult2_0) # label(axiom). [assumption].
% 3.18/3.44 378 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(C,D,A)) # label(cls_mod__mult__mult1_0) # label(axiom). [assumption].
% 3.18/3.44 379 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),D),C,A) # label(cls_mod__mult__cong_0) # label(axiom). [assumption].
% 3.18/3.44 380 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__mult__eq_0) # label(axiom). [assumption].
% 3.18/3.44 381 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) # label(cls_zmod__simps_I4_J_0) # label(axiom). [assumption].
% 3.18/3.44 382 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__mult__right__eq_0) # label(axiom). [assumption].
% 3.18/3.44 383 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__mult__left__eq_0) # label(axiom). [assumption].
% 3.18/3.44 384 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A) = C | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1__is__id_0) # label(axiom). [assumption].
% 3.18/3.44 385 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2__is__id_0) # label(axiom). [assumption].
% 3.18/3.44 386 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),C),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1__if_0) # label(axiom). [assumption].
% 3.18/3.44 387 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = c_Divides_Odiv__class_Odiv(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1_0) # label(axiom). [assumption].
% 3.18/3.44 388 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) = c_Divides_Odiv__class_Odiv(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult2_0) # label(axiom). [assumption].
% 3.18/3.44 389 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self1__is__0_0) # label(axiom). [assumption].
% 3.18/3.44 390 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self2__is__0_0) # label(axiom). [assumption].
% 3.18/3.44 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(346,a,347,a)].
% 3.18/3.44 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat) = c_Divides_Odiv__class_Omod(B,A,tc_nat). [resolve(346,a,348,a)].
% 3.18/3.44 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat). [resolve(346,a,349,a)].
% 3.18/3.44 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat). [resolve(346,a,350,a)].
% 3.18/3.44 Derived: A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)),c_Divides_Odiv__class_Omod(A,B,tc_nat)). [resolve(346,a,351,a)].
% 3.18/3.44 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)),c_Divides_Odiv__class_Omod(A,B,tc_nat)) = A. [resolve(346,a,352,a)].
% 3.18/3.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,A,tc_nat))),c_Divides_Odiv__class_Omod(B,A,tc_nat)) = B. [resolve(346,a,353,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(B,A,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,354,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,355,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(346,a,356,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(346,a,357,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B),C,tc_nat). [resolve(346,a,358,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(346,a,359,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,360,a)].
% 3.18/3.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)),c_Divides_Odiv__class_Omod(A,B,tc_nat))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C). [resolve(346,a,361,a)].
% 3.18/3.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,A,tc_nat))),c_Divides_Odiv__class_Omod(B,A,tc_nat))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C). [resolve(346,a,362,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,363,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),E),C),B,tc_nat). [resolve(346,a,364,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(346,a,365,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),C,tc_nat) = c_Divides_Odiv__class_Omod(A,C,tc_nat). [resolve(346,a,366,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(346,a,367,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,368,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,369,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(346,a,370,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,371,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,372,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,373,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),B,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_Divides_Odiv__class_Odiv(A,B,tc_nat)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,374,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),C,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_Divides_Odiv__class_Odiv(A,C,tc_nat)) | C = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,375,a)].
% 3.18/3.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)) = A. [resolve(346,a,376,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B). [resolve(346,a,377,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)). [resolve(346,a,378,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),E),C),B,tc_nat). [resolve(346,a,379,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(346,a,380,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),B,tc_nat). [resolve(346,a,381,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(346,a,382,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B),C,tc_nat). [resolve(346,a,383,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),A,tc_nat) = B | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,384,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),B,tc_nat) = A | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,385,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,386,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) = c_Divides_Odiv__class_Odiv(B,C,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,387,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) = c_Divides_Odiv__class_Odiv(A,C,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,388,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,389,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,390,a)].
% 3.18/3.45 391 class_Divides_Osemiring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(391,a,347,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),A,tc_Int_Oint) = c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint). [resolve(391,a,348,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint). [resolve(391,a,349,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)),C),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),B,tc_Int_Oint). [resolve(391,a,350,a)].
% 3.18/3.45 Derived: A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)). [resolve(391,a,351,a)].
% 3.18/3.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)) = A. [resolve(391,a,352,a)].
% 3.18/3.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint))),c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint)) = B. [resolve(391,a,353,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),A,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint)) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,354,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),B,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,355,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(391,a,356,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(391,a,357,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B),C,tc_Int_Oint). [resolve(391,a,358,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(391,a,359,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,360,a)].
% 3.18/3.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C). [resolve(391,a,361,a)].
% 3.18/3.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint))),c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C). [resolve(391,a,362,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,363,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),D),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),E),C),B,tc_Int_Oint). [resolve(391,a,364,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(391,a,365,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint). [resolve(391,a,366,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(391,a,367,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,368,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,369,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(391,a,370,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,371,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,372,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,373,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),B,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,374,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),C,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint)) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,375,a)].
% 3.18/3.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)) = A. [resolve(391,a,376,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B). [resolve(391,a,377,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)). [resolve(391,a,378,a)].
% 3.18/3.45 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),E),C),B,tc_Int_Oint). [resolve(391,a,379,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(391,a,380,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)),C),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),B,tc_Int_Oint). [resolve(391,a,381,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(391,a,382,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B),C,tc_Int_Oint). [resolve(391,a,383,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),A,tc_Int_Oint) = B | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,384,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),B,tc_Int_Oint) = A | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,385,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,386,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,387,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,388,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,389,a)].
% 3.34/3.60 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,390,a)].
% 3.34/3.60 392 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.34/3.60 393 -class_RealVector_Oreal__normed__algebra(A) | -class_Power_Opower(A) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(A),B,A,tc_fun(tc_nat,A),tc_nat),C,tc_nat,tc_nat,A),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].
% 3.34/3.60 394 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OLIM(c_COMBC(c_HOL_Otimes__class_Otimes(A),B,A,A,A),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A,A) # label(cls_mult__left_Ocont_0) # label(axiom). [assumption].
% 3.34/3.60 395 -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].
% 3.34/3.60 396 -class_RealVector_Oreal__normed__algebra(A) | -class_Power_Opower(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(A),C,A,tc_fun(tc_nat,A),B),D,B,tc_nat,A),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].
% 3.34/3.60 397 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 3.34/3.60 398 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 3.34/3.60 399 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 3.34/3.60 400 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 3.34/3.60 401 -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].
% 3.34/3.60 402 -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].
% 3.34/3.60 403 -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].
% 3.34/3.60 404 -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].
% 3.34/3.60 405 -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].
% 3.34/3.60 406 -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].
% 3.34/3.60 407 -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].
% 3.34/3.60 408 -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].
% 3.34/3.60 409 -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].
% 3.34/3.60 410 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),C,A,tc_fun(A,A),B),D,B,A,A),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].
% 3.34/3.60 411 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),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].
% 3.34/3.60 412 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),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].
% 3.34/3.60 413 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),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].
% 3.34/3.60 414 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__mult__left_0) # label(axiom). [assumption].
% 3.34/3.60 415 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OZseq(B,A) # label(cls_mult__left_OZseq_0) # label(axiom). [assumption].
% 3.34/3.60 416 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),C),D,A,A,B),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].
% 3.34/3.60 417 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),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].
% 3.34/3.60 418 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),A) | -c_SEQ_OZseq(C,A) # label(cls_mult__right_OZseq_0) # label(axiom). [assumption].
% 3.34/3.60 419 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),A) | -c_SEQ_OZseq(C,A) # label(cls_Zseq__mult__right_0) # label(axiom). [assumption].
% 3.34/3.60 420 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),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].
% 3.34/3.60 421 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),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].
% 3.34/3.60 422 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),C),D,A,A,B),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].
% 3.34/3.60 423 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),C),D,A,A,B),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].
% 3.34/3.60 424 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),C,A,tc_fun(A,A),B),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].
% 3.34/3.60 425 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A) # label(cls_mult__left_Osetsum_0) # label(axiom). [assumption].
% 3.34/3.60 426 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),C,A,tc_fun(A,A),B),D,B,A,A),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].
% 3.34/3.60 427 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),C,A,tc_fun(A,A),B),D,B,A,A),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].
% 3.34/3.60 428 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OZseq(C,A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__mult_0) # label(axiom). [assumption].
% 3.34/3.60 429 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),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].
% 3.34/3.60 430 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),C,A,tc_fun(A,A),B),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].
% 3.34/3.60 431 -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].
% 3.34/3.60 432 -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].
% 3.34/3.60 433 -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].
% 3.34/3.60 434 -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].
% 3.34/3.60 435 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,E),D,E,A) # label(cls_mult__right_Osetsum_0) # label(axiom). [assumption].
% 3.34/3.60 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(392,a,393,a)].
% 3.34/3.60 Derived: c_Lim_OLIM(c_COMBC(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(392,a,394,a)].
% 3.34/3.60 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(392,a,395,a)].
% 3.34/3.60 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),A),C,A,tc_nat,tc_Complex_Ocomplex),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(392,a,396,a)].
% 3.34/3.60 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)). [resolve(392,a,397,a)].
% 3.34/3.60 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)). [resolve(392,a,399,a)].
% 3.34/3.60 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(392,a,401,a)].
% 3.34/3.60 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(392,a,403,a)].
% 3.34/3.60 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(392,a,405,a)].
% 3.34/3.60 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(392,a,406,a)].
% 3.34/3.60 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(392,a,408,a)].
% 3.34/3.60 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),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(392,a,410,a)].
% 3.34/3.60 Derived: c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(392,a,411,a)].
% 3.34/3.61 Derived: c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(392,a,413,a)].
% 3.34/3.61 Derived: c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(392,a,414,a)].
% 3.34/3.61 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),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(392,a,416,a)].
% 3.34/3.61 Derived: c_SEQ_OLIMSEQ(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,C,tc_Complex_Ocomplex). [resolve(392,a,417,a)].
% 3.34/3.61 Derived: c_SEQ_OZseq(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex). [resolve(392,a,418,a)].
% 3.34/3.61 Derived: c_Series_Osums(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_Series_Osums(B,C,tc_Complex_Ocomplex). [resolve(392,a,420,a)].
% 3.34/3.61 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),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(392,a,422,a)].
% 3.34/3.61 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),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(392,a,424,a)].
% 3.34/3.61 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,B,C,tc_Complex_Ocomplex)),D) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),C),D,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex). [resolve(392,a,425,a)].
% 3.34/3.61 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),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(392,a,426,a)].
% 3.34/3.61 Derived: c_SEQ_OZseq(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(392,a,428,a)].
% 3.34/3.61 Derived: c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(392,a,429,a)].
% 3.47/3.75 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),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(392,a,430,a)].
% 3.47/3.75 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(392,a,431,a)].
% 3.47/3.75 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(392,a,433,a)].
% 3.47/3.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Finite__Set_Osetsum(B,C,D,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,D),C,D,tc_Complex_Ocomplex). [resolve(392,a,435,a)].
% 3.47/3.75 436 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 3.47/3.75 437 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 3.47/3.75 438 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 3.47/3.75 439 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 3.47/3.75 440 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 3.47/3.75 441 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 3.47/3.75 442 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 3.47/3.75 443 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 3.47/3.75 444 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 3.47/3.75 445 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 3.47/3.75 446 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 3.47/3.75 447 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 3.47/3.75 448 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 3.47/3.75 449 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 3.47/3.75 450 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 3.47/3.75 451 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 3.47/3.75 452 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 3.47/3.75 453 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 3.47/3.75 454 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 3.47/3.75 455 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 3.47/3.75 456 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 3.47/3.75 457 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(436,a,437,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(436,a,440,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),B,tc_fun(D,A)). [resolve(436,a,441,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(C,E,tc_fun(D,A)). [resolve(436,a,442,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(B,E,tc_fun(D,A)). [resolve(436,a,443,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(436,a,444,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(436,a,445,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(436,a,446,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(E,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(436,a,447,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(436,a,448,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)). [resolve(436,a,449,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)). [resolve(436,a,452,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | c_lessequals(B,C,tc_fun(D,A)). [resolve(436,a,453,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -c_lessequals(B,C,tc_fun(D,A)). [resolve(436,a,454,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(436,a,455,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(436,a,456,a)].
% 3.47/3.75 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(436,a,457,a)].
% 3.47/3.75 458 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 3.47/3.75 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(458,a,437,a)].
% 3.47/3.75 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(458,a,440,a)].
% 3.47/3.75 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(458,a,441,a)].
% 3.47/3.75 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(458,a,442,a)].
% 3.47/3.75 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(458,a,443,a)].
% 3.47/3.75 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(458,a,444,a)].
% 3.47/3.75 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(458,a,445,a)].
% 3.47/3.75 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(458,a,446,a)].
% 3.47/3.75 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat). [resolve(458,a,447,a)].
% 3.47/3.75 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(458,a,448,a)].
% 3.47/3.75 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(458,a,449,a)].
% 3.47/3.75 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(458,a,452,a)].
% 3.47/3.75 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(458,a,453,a)].
% 3.47/3.75 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(458,a,454,a)].
% 3.47/3.75 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(458,a,455,a)].
% 3.47/3.75 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat). [resolve(458,a,456,a)].
% 3.47/3.75 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(458,a,457,a)].
% 3.47/3.75 459 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 3.47/3.75 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(459,a,437,a)].
% 3.47/3.75 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(459,a,440,a)].
% 3.47/3.75 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(459,a,441,a)].
% 3.47/3.76 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(B,C,tc_bool). [resolve(459,a,442,a)].
% 3.47/3.76 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(459,a,443,a)].
% 3.47/3.76 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(459,a,444,a)].
% 3.47/3.76 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(459,a,445,a)].
% 3.47/3.76 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(459,a,446,a)].
% 3.47/3.76 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(459,a,447,a)].
% 3.47/3.76 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(459,a,448,a)].
% 3.47/3.76 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(459,a,449,a)].
% 3.47/3.76 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(459,a,452,a)].
% 3.47/3.76 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(459,a,453,a)].
% 3.47/3.76 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(459,a,454,a)].
% 3.47/3.76 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(459,a,455,a)].
% 3.47/3.76 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(459,a,456,a)].
% 3.47/3.76 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(459,a,457,a)].
% 3.47/3.76 460 class_Lattices_Olower__semilattice(tc_Int_Oint) # label(clsarity_Int__Oint__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 3.47/3.76 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(460,a,437,a)].
% 3.47/3.76 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),B,tc_Int_Oint). [resolve(460,a,440,a)].
% 3.47/3.76 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),A,tc_Int_Oint). [resolve(460,a,441,a)].
% 3.47/3.76 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(460,a,442,a)].
% 3.47/3.76 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(460,a,443,a)].
% 3.47/3.76 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint),tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(460,a,444,a)].
% 3.47/3.76 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(460,a,445,a)].
% 3.47/3.76 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(460,a,446,a)].
% 3.47/3.76 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(460,a,447,a)].
% 3.47/3.76 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(460,a,448,a)].
% 3.80/4.03 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(460,a,449,a)].
% 3.80/4.03 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = B | -c_lessequals(B,A,tc_Int_Oint). [resolve(460,a,452,a)].
% 3.80/4.03 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) != A | c_lessequals(A,B,tc_Int_Oint). [resolve(460,a,453,a)].
% 3.80/4.03 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = A | -c_lessequals(A,B,tc_Int_Oint). [resolve(460,a,454,a)].
% 3.80/4.03 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_Int_Oint). [resolve(460,a,455,a)].
% 3.80/4.03 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint). [resolve(460,a,456,a)].
% 3.80/4.03 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_Int_Oint) = A. [resolve(460,a,457,a)].
% 3.80/4.03 461 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 3.80/4.03 462 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__le__0__iff__le_1) # label(axiom). [assumption].
% 3.80/4.03 463 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__le__0__iff__le_0) # label(axiom). [assumption].
% 3.80/4.03 464 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_neg__less__iff__less_1) # label(axiom). [assumption].
% 3.80/4.03 465 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__less__iff__less_0) # label(axiom). [assumption].
% 3.80/4.03 466 -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) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,E,A) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 3.80/4.03 467 -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) | c_HOL_Oord__class_Oless(D,E,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 3.80/4.03 468 -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) | c_lessequals(C,B,A) | -c_lessequals(E,D,A) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 3.80/4.03 469 -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) | c_lessequals(E,D,A) | -c_lessequals(C,B,A) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 3.80/4.03 470 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__le__iff__le_0) # label(axiom). [assumption].
% 3.80/4.03 471 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_lessequals(C,B,A) # label(cls_le__imp__neg__le_0) # label(axiom). [assumption].
% 3.80/4.03 472 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__0__le__iff__le_0) # label(axiom). [assumption].
% 3.80/4.03 473 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__le__iff__le_1) # label(axiom). [assumption].
% 3.80/4.03 474 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__0__iff__less_1) # label(axiom). [assumption].
% 3.80/4.03 475 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__less__0__iff__less_0) # label(axiom). [assumption].
% 3.80/4.03 476 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,C,A) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 3.80/4.03 477 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 3.80/4.03 478 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 3.80/4.03 479 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 3.80/4.03 480 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__less__iff_1) # label(axiom). [assumption].
% 3.80/4.03 481 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__less__iff_0) # label(axiom). [assumption].
% 3.80/4.03 482 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_HOL_Oord__class_Oless(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__minus__iff_1) # label(axiom). [assumption].
% 3.80/4.03 483 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_HOL_Oord__class_Oless(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__minus__iff_0) # label(axiom). [assumption].
% 3.80/4.03 484 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__le__iff_1) # label(axiom). [assumption].
% 3.80/4.03 485 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__le__iff_0) # label(axiom). [assumption].
% 3.80/4.03 486 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_lessequals(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_le__minus__iff_1) # label(axiom). [assumption].
% 3.80/4.03 487 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_lessequals(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_le__minus__iff_0) # label(axiom). [assumption].
% 3.80/4.03 488 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(E,D,A) | -c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E),A) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 3.80/4.04 489 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__0__less__iff__less_0) # label(axiom). [assumption].
% 3.80/4.04 490 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__less__iff__less_1) # label(axiom). [assumption].
% 3.80/4.04 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(461,a,462,a)].
% 3.80/4.04 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(461,a,463,a)].
% 3.80/4.04 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(461,a,464,a)].
% 3.80/4.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(461,a,465,a)].
% 3.80/4.04 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) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,D,tc_Int_Oint). [resolve(461,a,466,a)].
% 3.80/4.04 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) | c_HOL_Oord__class_Oless(C,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(461,a,467,a)].
% 3.80/4.04 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) | c_lessequals(B,A,tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint). [resolve(461,a,468,a)].
% 3.80/4.04 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) | c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(461,a,469,a)].
% 3.80/4.04 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(461,a,470,a)].
% 3.80/4.04 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(461,a,471,a)].
% 3.80/4.04 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(461,a,472,a)].
% 3.80/4.04 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(461,a,473,a)].
% 3.80/4.04 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(461,a,474,a)].
% 3.80/4.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(461,a,475,a)].
% 3.80/4.04 Derived: c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(461,a,476,a)].
% 3.80/4.04 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(461,a,477,a)].
% 3.80/4.04 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(461,a,478,a)].
% 3.85/4.14 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(461,a,479,a)].
% 3.85/4.14 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),A,tc_Int_Oint). [resolve(461,a,480,a)].
% 3.85/4.14 Derived: c_HOL_Oord__class_Oless(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(461,a,482,a)].
% 3.85/4.14 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),A,tc_Int_Oint). [resolve(461,a,484,a)].
% 3.85/4.14 Derived: c_lessequals(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),tc_Int_Oint) | -c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(461,a,486,a)].
% 3.85/4.14 Derived: c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D),tc_Int_Oint). [resolve(461,a,488,a)].
% 3.85/4.14 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(461,a,489,a)].
% 3.85/4.14 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(461,a,490,a)].
% 3.85/4.14 491 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.85/4.14 492 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 3.85/4.14 493 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 3.85/4.14 494 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 3.85/4.14 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(491,a,492,a)].
% 3.85/4.14 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(491,a,493,a)].
% 3.85/4.14 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(491,a,494,a)].
% 3.85/4.14 495 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.85/4.14 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(495,a,492,a)].
% 3.85/4.14 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(495,a,493,a)].
% 3.85/4.14 Derived: c_lessequals(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) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(495,a,494,a)].
% 4.10/4.37 496 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 4.10/4.37 497 -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].
% 4.10/4.37 498 -class_RealVector_Oreal__normed__algebra__1(A) | c_Series_Osuminf(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),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].
% 4.10/4.37 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(496,a,497,b)].
% 4.10/4.37 Derived: c_Series_Osuminf(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(496,a,498,a)].
% 4.10/4.37 499 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 4.10/4.37 500 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 4.10/4.37 501 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 4.10/4.37 502 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 4.10/4.37 503 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 4.10/4.37 504 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 4.10/4.37 505 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 4.10/4.37 506 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),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].
% 4.10/4.37 507 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 4.10/4.37 508 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 4.10/4.37 509 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 4.10/4.37 510 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 4.10/4.37 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(499,a,500,a)].
% 4.10/4.37 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(499,a,501,a)].
% 4.10/4.37 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(499,a,502,a)].
% 4.10/4.37 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(499,a,503,a)].
% 4.10/4.37 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(499,a,504,a)].
% 4.10/4.37 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(499,a,505,a)].
% 4.10/4.37 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(499,a,507,a)].
% 4.10/4.37 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(499,a,508,a)].
% 4.10/4.37 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(499,a,510,a)].
% 4.10/4.37 511 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 4.10/4.37 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(511,a,500,a)].
% 4.10/4.37 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(511,a,501,a)].
% 4.25/4.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(511,a,502,a)].
% 4.25/4.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(511,a,503,a)].
% 4.25/4.49 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(511,a,504,a)].
% 4.25/4.49 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(511,a,505,a)].
% 4.25/4.49 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(511,a,507,a)].
% 4.25/4.49 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(511,a,508,a)].
% 4.25/4.49 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(511,a,510,a)].
% 4.25/4.49 512 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 4.25/4.49 513 -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].
% 4.25/4.49 514 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__divide__right_0) # label(axiom). [assumption].
% 4.25/4.49 515 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) # label(cls_minus__divide__left_0) # label(axiom). [assumption].
% 4.25/4.49 516 -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].
% 4.25/4.49 517 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__divide_0) # label(axiom). [assumption].
% 4.25/4.49 518 -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].
% 4.25/4.49 519 -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].
% 4.25/4.49 520 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__right_0) # label(axiom). [assumption].
% 4.25/4.49 521 -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].
% 4.25/4.49 522 -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].
% 4.25/4.49 523 -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].
% 4.25/4.49 524 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) # label(cls_minus__divide__divide_0) # label(axiom). [assumption].
% 4.25/4.49 525 -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)) | -c_lessequals(D,C,tc_nat) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff_0) # label(axiom). [assumption].
% 4.25/4.49 526 -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].
% 4.25/4.49 527 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) # label(cls_divide__minus1_0) # label(axiom). [assumption].
% 4.25/4.49 528 -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].
% 4.25/4.49 529 -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].
% 4.25/4.49 530 -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].
% 4.25/4.49 531 -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].
% 4.25/4.49 532 -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].
% 4.25/4.49 533 -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].
% 4.25/4.49 534 -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].
% 4.25/4.49 535 -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].
% 4.25/4.49 536 -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].
% 4.25/4.49 537 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_minus1__divide_0) # label(axiom). [assumption].
% 4.25/4.49 538 -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].
% 4.25/4.49 539 -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].
% 4.25/4.49 540 -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].
% 4.25/4.49 541 -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].
% 4.25/4.49 542 -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].
% 4.25/4.49 543 -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].
% 4.25/4.49 544 -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].
% 4.25/4.49 545 -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].
% 4.25/4.49 546 -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].
% 4.25/4.49 547 -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].
% 4.25/4.49 548 -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].
% 4.25/4.49 549 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A) # label(cls_setsum__divide__distrib_0) # label(axiom). [assumption].
% 4.25/4.49 550 -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].
% 4.25/4.49 551 -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].
% 4.25/4.49 552 -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].
% 4.25/4.49 553 -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].
% 4.25/4.49 554 -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].
% 4.25/4.49 555 -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].
% 4.25/4.49 556 -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].
% 4.25/4.49 557 -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].
% 4.25/4.49 558 -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].
% 4.25/4.49 559 -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].
% 4.25/4.49 560 -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].
% 4.25/4.49 561 -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].
% 4.25/4.49 562 -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].
% 4.25/4.49 563 -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].
% 4.25/4.49 564 -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].
% 4.25/4.49 565 -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].
% 4.25/4.49 566 -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].
% 4.25/4.49 567 -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].
% 4.25/4.49 568 -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].
% 4.25/4.49 569 -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].
% 4.25/4.49 570 -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].
% 4.25/4.49 571 -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].
% 4.25/4.49 572 -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].
% 4.25/4.49 573 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OPls,A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__Numeral0_0) # label(axiom). [assumption].
% 4.25/4.49 574 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A)) = B # label(cls_divide__numeral__1_0) # label(axiom). [assumption].
% 4.25/4.49 575 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A)) = B # label(cls_divide__Numeral1_0) # label(axiom). [assumption].
% 4.25/4.49 576 -class_Ring__and__Field_Ofield(A) | c_Finite__Set_Osetsum(hAPP(c_Power_Opower__class_Opower(A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A) = 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].
% 4.25/4.49 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(512,a,513,a)].
% 4.25/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Ouminus__class_Ouminus(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),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(512,a,514,a)].
% 4.25/4.49 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B). [resolve(512,a,515,a)].
% 4.25/4.49 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(512,a,516,a)].
% 4.25/4.49 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(512,a,517,a)].
% 4.25/4.49 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(512,a,518,a)].
% 4.25/4.49 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(512,a,519,a)].
% 4.25/4.49 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(512,a,520,a)].
% 4.25/4.49 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(512,a,521,a)].
% 4.25/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B). [resolve(512,a,524,a)].
% 4.25/4.49 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)) | -c_lessequals(C,B,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(512,a,525,a)].
% 4.25/4.49 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(512,a,526,a)].
% 4.25/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A). [resolve(512,a,527,a)].
% 4.25/4.49 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(512,a,528,a)].
% 4.25/4.49 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(512,a,529,a)].
% 4.25/4.49 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(512,a,530,a)].
% 4.25/4.49 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(512,a,531,a)].
% 4.25/4.50 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(512,a,533,a)].
% 4.25/4.50 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(512,a,534,a)].
% 4.25/4.50 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(512,a,535,a)].
% 4.25/4.50 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(512,a,536,a)].
% 4.25/4.50 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A)). [resolve(512,a,537,a)].
% 4.25/4.50 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(512,a,538,a)].
% 4.25/4.50 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(512,a,539,a)].
% 4.25/4.50 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(512,a,540,a)].
% 4.25/4.50 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)),B) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(512,a,541,a)].
% 4.25/4.50 Derived: -class_Ring__and__Field_Odivision__by__zero(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),B)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(512,a,542,a)].
% 4.25/4.50 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(512,a,543,a)].
% 4.25/4.50 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(512,a,544,a)].
% 4.25/4.50 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(512,a,545,a)].
% 4.25/4.50 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(512,a,546,a)].
% 4.25/4.50 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(512,a,547,a)].
% 4.25/4.50 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(512,a,548,a)].
% 4.25/4.50 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,B,C,tc_Complex_Ocomplex)),D) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),C),D,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex). [resolve(512,a,549,a)].
% 4.25/4.50 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(512,a,550,a)].
% 4.25/4.50 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(512,a,551,a)].
% 4.25/4.50 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(512,a,552,a)].
% 4.25/4.50 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(512,a,553,a)].
% 4.25/4.50 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(512,a,554,a)].
% 4.25/4.50 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(512,a,555,a)].
% 4.25/4.50 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(512,a,556,a)].
% 4.25/4.50 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(512,a,557,a)].
% 4.25/4.50 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(512,a,558,a)].
% 4.25/4.50 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(512,a,559,a)].
% 4.25/4.50 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(512,a,560,a)].
% 4.25/4.50 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(512,a,564,a)].
% 4.33/4.60 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(512,a,565,a)].
% 4.33/4.60 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(512,a,566,a)].
% 4.33/4.60 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(512,a,572,a)].
% 4.33/4.60 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(512,a,573,a)].
% 4.33/4.60 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Complex_Ocomplex)) = A. [resolve(512,a,574,a)].
% 4.33/4.60 Derived: c_Finite__Set_Osetsum(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),tc_nat,tc_Complex_Ocomplex) = 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(512,a,576,a)].
% 4.33/4.60 577 class_Divides_Oring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 4.33/4.60 578 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Divides_Odiv__class_Omod(B,C,A)),C,A) # label(cls_mod__minus__eq_0) # label(axiom). [assumption].
% 4.33/4.60 579 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__diff__eq_0) # label(axiom). [assumption].
% 4.33/4.60 580 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__diff__left__eq_0) # label(axiom). [assumption].
% 4.33/4.60 581 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__diff__right__eq_0) # label(axiom). [assumption].
% 4.44/4.71 582 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(A),D),C,A) # label(cls_mod__minus__cong_0) # label(axiom). [assumption].
% 4.44/4.71 583 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),F),D),C,A) # label(cls_mod__diff__cong_0) # label(axiom). [assumption].
% 4.44/4.71 Derived: c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)),B,tc_Int_Oint). [resolve(577,a,578,a)].
% 4.44/4.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(577,a,579,a)].
% 4.44/4.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B),C,tc_Int_Oint). [resolve(577,a,580,a)].
% 4.44/4.71 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(577,a,581,a)].
% 4.44/4.71 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),C),B,tc_Int_Oint). [resolve(577,a,582,a)].
% 4.44/4.71 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),E),C),B,tc_Int_Oint). [resolve(577,a,583,a)].
% 4.44/4.71 584 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 4.44/4.71 585 -class_OrderedGroup_Oab__group__add(A) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastAtMost(C,D,tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(B,C)),hAPP(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)))) | -c_lessequals(C,D,tc_nat) # label(cls_setsum__natinterval__difff_0) # label(axiom). [assumption].
% 4.44/4.71 586 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_diff__def_0) # label(axiom). [assumption].
% 4.44/4.71 587 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_ab__diff__minus_0) # label(axiom). [assumption].
% 4.44/4.71 588 -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].
% 4.44/4.71 589 -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].
% 4.44/4.71 590 -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].
% 4.44/4.71 591 -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].
% 4.44/4.71 592 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_ab__left__minus_0) # label(axiom). [assumption].
% 4.44/4.71 593 -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].
% 4.44/4.71 594 -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)) != C | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),D) # label(cls_add__cancel__end_0) # label(axiom). [assumption].
% 4.44/4.71 595 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B)) = C # label(cls_add__cancel__end_1) # label(axiom). [assumption].
% 4.44/4.71 596 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)) # label(cls_Lim_Ominus__diff__minus_0) # label(axiom). [assumption].
% 4.44/4.71 597 -class_OrderedGroup_Oab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),B) # label(cls_minus__diff__eq_0) # label(axiom). [assumption].
% 4.44/4.71 598 -class_OrderedGroup_Oab__group__add(A) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastAtMost(C,D,tc_nat),tc_nat,A) = c_HOL_Ozero__class_Ozero(A) | c_lessequals(C,D,tc_nat) # label(cls_setsum__natinterval__difff_1) # label(axiom). [assumption].
% 4.44/4.71 599 -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].
% 4.44/4.71 600 -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].
% 4.44/4.71 601 -class_OrderedGroup_Oab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__add__distrib_0) # label(axiom). [assumption].
% 4.44/4.71 602 -class_OrderedGroup_Oab__group__add(A) | c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,C),D,C,A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Finite__Set_Osetsum(B,D,C,A)) # label(cls_setsum__negf_0) # label(axiom). [assumption].
% 4.44/4.71 603 -class_OrderedGroup_Oab__group__add(A) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),C),D,C,A,A),E,C,A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Finite__Set_Osetsum(B,E,C,A)),c_Finite__Set_Osetsum(D,E,C,A)) # label(cls_setsum__subtractf_0) # label(axiom). [assumption].
% 4.44/4.72 604 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat),tc_nat,A)) = c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(E,D,tc_nat),tc_nat,A) | -c_lessequals(E,D,tc_nat) | -c_lessequals(C,E,tc_nat) # label(cls_setsum__diff__nat__ivl_0) # label(axiom). [assumption].
% 4.44/4.72 605 -class_OrderedGroup_Oab__group__add(A) | c_Finite__Set_Osetsum(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Finite__Set_Osetsum(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),tc_nat,A)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A)) # label(cls_sumr__offset_0) # label(axiom). [assumption].
% 4.44/4.72 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,tc_Int_Oint,tc_nat),tc_nat,tc_Int_Oint,tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(A,B)),hAPP(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)))) | -c_lessequals(B,C,tc_nat). [resolve(584,a,585,a)].
% 4.44/4.72 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(584,a,588,a)].
% 4.44/4.72 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(584,a,590,a)].
% 4.44/4.72 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(584,a,591,a)].
% 4.44/4.72 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(584,a,593,a)].
% 4.44/4.72 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) != B | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),C). [resolve(584,a,594,a)].
% 4.44/4.72 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),A)) = B. [resolve(584,a,595,a)].
% 4.44/4.72 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)). [resolve(584,a,596,a)].
% 4.44/4.72 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),A). [resolve(584,a,597,a)].
% 4.44/4.72 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,tc_Int_Oint,tc_nat),tc_nat,tc_Int_Oint,tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_lessequals(B,C,tc_nat). [resolve(584,a,598,a)].
% 4.44/4.72 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(584,a,601,a)].
% 4.44/4.72 Derived: c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),C,B,tc_Int_Oint) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_Finite__Set_Osetsum(A,C,B,tc_Int_Oint)). [resolve(584,a,602,a)].
% 4.44/4.72 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),B),C,B,tc_Int_Oint,tc_Int_Oint),D,B,tc_Int_Oint) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Finite__Set_Osetsum(A,D,B,tc_Int_Oint)),c_Finite__Set_Osetsum(C,D,B,tc_Int_Oint)). [resolve(584,a,603,a)].
% 4.44/4.72 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Int_Oint)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_Int_Oint)) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(D,C,tc_nat),tc_nat,tc_Int_Oint) | -c_lessequals(D,C,tc_nat) | -c_lessequals(B,D,tc_nat). [resolve(584,a,604,a)].
% 4.44/4.72 Derived: c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),B,tc_nat,tc_nat,tc_nat),tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Finite__Set_Osetsum(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),tc_nat,tc_Int_Oint)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Int_Oint)). [resolve(584,a,605,a)].
% 4.44/4.72 606 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 4.44/4.72 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(A,B)),hAPP(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)))) | -c_lessequals(B,C,tc_nat). [resolve(606,a,585,a)].
% 4.44/4.72 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(606,a,588,a)].
% 4.44/4.72 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(606,a,590,a)].
% 4.44/4.72 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(606,a,591,a)].
% 4.44/4.72 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(606,a,593,a)].
% 4.44/4.72 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) != B | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),C). [resolve(606,a,594,a)].
% 4.44/4.72 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),A)) = B. [resolve(606,a,595,a)].
% 4.53/4.82 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)). [resolve(606,a,596,a)].
% 4.53/4.82 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),A). [resolve(606,a,597,a)].
% 4.53/4.82 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_lessequals(B,C,tc_nat). [resolve(606,a,598,a)].
% 4.53/4.82 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(606,a,601,a)].
% 4.53/4.82 Derived: c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,B),C,B,tc_Complex_Ocomplex) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,C,B,tc_Complex_Ocomplex)). [resolve(606,a,602,a)].
% 4.53/4.82 Derived: c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),B),C,B,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,B,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,D,B,tc_Complex_Ocomplex)),c_Finite__Set_Osetsum(C,D,B,tc_Complex_Ocomplex)). [resolve(606,a,603,a)].
% 4.53/4.82 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Complex_Ocomplex)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(D,C,tc_nat),tc_nat,tc_Complex_Ocomplex) | -c_lessequals(D,C,tc_nat) | -c_lessequals(B,D,tc_nat). [resolve(606,a,604,a)].
% 4.53/4.82 Derived: c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),B,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(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),tc_nat,tc_Complex_Ocomplex)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex)). [resolve(606,a,605,a)].
% 4.60/4.82 607 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 4.60/4.82 608 -class_RealVector_Oreal__normed__field(A) | c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),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].
% 4.60/4.82 609 -class_RealVector_Oreal__normed__field(A) | c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),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].
% 4.60/4.83 610 -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].
% 4.60/4.83 611 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OZseq(B,A) # label(cls_divide_OZseq_0) # label(axiom). [assumption].
% 4.60/4.83 612 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),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].
% 4.60/4.83 613 -class_RealVector_Oreal__normed__field(A) | c_Lim_OLIM(c_COMBC(c_HOL_Oinverse__class_Odivide(A),B,A,A,A),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),B),A,A) # label(cls_divide_Ocont_0) # label(axiom). [assumption].
% 4.60/4.83 614 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)) # label(cls_divide_Ominus_0) # label(axiom). [assumption].
% 4.60/4.83 615 -class_RealVector_Oreal__normed__field(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),C,A,tc_fun(A,A),B),D,B,A,A),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].
% 4.60/4.83 616 -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].
% 4.60/4.83 617 -class_RealVector_Oreal__normed__field(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),C,A,tc_fun(A,A),B),D,B,A,A),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].
% 4.60/4.83 618 -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].
% 4.60/4.83 619 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),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].
% 4.60/4.83 620 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A) # label(cls_divide_Osetsum_0) # label(axiom). [assumption].
% 4.60/4.83 Derived: c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(607,a,608,a)].
% 4.60/4.83 Derived: c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(607,a,611,a)].
% 4.60/4.83 Derived: c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(607,a,612,a)].
% 4.70/4.93 Derived: c_Lim_OLIM(c_COMBC(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(607,a,613,a)].
% 4.70/4.93 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)). [resolve(607,a,614,a)].
% 4.70/4.93 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),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(607,a,615,a)].
% 4.70/4.93 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),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(607,a,617,a)].
% 4.70/4.93 Derived: c_SEQ_OLIMSEQ(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),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(607,a,619,a)].
% 4.70/4.93 621 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.70/4.93 622 -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].
% 4.70/4.93 623 -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].
% 4.70/4.93 624 -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].
% 4.70/4.93 625 -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].
% 4.70/4.93 626 -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].
% 4.70/4.93 627 -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].
% 4.70/4.93 628 -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].
% 4.70/4.93 629 -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].
% 4.70/4.93 630 -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].
% 4.70/4.93 631 -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].
% 4.70/4.93 632 -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].
% 4.70/4.93 633 -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].
% 4.70/4.93 634 -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].
% 4.70/4.93 635 -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].
% 4.70/4.93 636 -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].
% 4.70/4.93 637 -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].
% 4.70/4.93 638 -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].
% 4.70/4.93 639 -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].
% 4.70/4.93 640 -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].
% 4.70/4.93 641 -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].
% 4.70/4.93 642 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_class__semiring_Ogb__semiring__axioms_H_0) # label(axiom). [assumption].
% 4.70/4.93 643 -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].
% 4.70/4.93 644 -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].
% 4.70/4.93 645 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_class__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 4.70/4.93 646 -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].
% 4.70/4.93 647 -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].
% 4.70/4.93 648 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_class__semiring_Osemiring__rules_I29_J_0) # label(axiom). [assumption].
% 4.70/4.93 649 -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].
% 4.70/4.93 650 -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].
% 4.70/4.93 651 -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].
% 4.70/4.93 652 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),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),C))) # label(cls_class__semiring_Osemiring__rules_I37_J_0) # label(axiom). [assumption].
% 4.70/4.93 653 -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].
% 4.70/4.93 654 -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].
% 4.70/4.93 655 -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].
% 4.70/4.93 656 -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].
% 4.70/4.94 657 -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].
% 4.70/4.94 658 -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].
% 4.70/4.94 659 -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].
% 4.70/4.94 660 -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].
% 4.70/4.94 661 -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].
% 4.70/4.94 662 -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].
% 4.70/4.94 663 -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].
% 4.70/4.94 664 -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].
% 4.70/4.94 665 -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].
% 4.70/4.94 666 -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].
% 4.70/4.94 667 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = 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),C)) # label(cls_class__semiring_Osemiring__rules_I36_J_0) # label(axiom). [assumption].
% 4.70/4.94 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(621,a,622,a)].
% 4.70/4.94 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(621,a,623,a)].
% 4.70/4.94 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(621,a,625,a)].
% 4.70/4.94 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(621,a,630,a)].
% 4.70/4.94 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(621,a,631,a)].
% 4.70/4.94 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(621,a,632,a)].
% 4.70/4.94 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(621,a,636,a)].
% 4.70/4.94 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(621,a,637,a)].
% 4.70/4.94 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(621,a,638,a)].
% 4.70/4.94 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(621,a,639,a)].
% 4.70/4.94 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(621,a,640,a)].
% 4.70/4.94 Derived: c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(621,a,642,a)].
% 4.70/4.94 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(621,a,643,a)].
% 4.70/4.94 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(621,a,644,a)].
% 4.70/4.94 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(621,a,645,a)].
% 4.70/4.94 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(621,a,646,a)].
% 4.70/4.94 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(621,a,647,a)].
% 4.70/4.94 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(621,a,648,a)].
% 4.70/4.94 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(621,a,649,a)].
% 4.70/4.94 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(621,a,650,a)].
% 4.70/4.94 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),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),B))). [resolve(621,a,652,a)].
% 4.70/4.94 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(621,a,653,a)].
% 4.70/4.94 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(621,a,654,a)].
% 4.70/4.94 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(621,a,656,a)].
% 4.70/4.94 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(621,a,657,a)].
% 4.70/4.94 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(621,a,658,a)].
% 4.70/4.94 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(621,a,661,a)].
% 4.70/4.94 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(621,a,662,a)].
% 4.70/4.94 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(621,a,663,a)].
% 4.70/4.94 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(621,a,665,a)].
% 4.70/4.94 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = 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),B)). [resolve(621,a,667,a)].
% 4.70/4.94 668 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.70/4.94 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(668,a,622,a)].
% 4.70/4.94 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(668,a,623,a)].
% 4.70/4.94 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(668,a,625,a)].
% 4.70/4.94 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(668,a,630,a)].
% 4.70/4.95 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(668,a,631,a)].
% 4.70/4.95 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(668,a,632,a)].
% 4.70/4.95 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(668,a,636,a)].
% 4.70/4.95 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(668,a,637,a)].
% 4.70/4.95 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(668,a,638,a)].
% 4.70/4.95 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(668,a,639,a)].
% 4.70/4.95 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(668,a,640,a)].
% 4.70/4.95 Derived: c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(668,a,642,a)].
% 4.70/4.95 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(668,a,643,a)].
% 4.70/4.95 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(668,a,644,a)].
% 4.70/4.95 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(668,a,645,a)].
% 4.70/4.95 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(668,a,646,a)].
% 4.70/4.95 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(668,a,647,a)].
% 4.70/4.95 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(668,a,648,a)].
% 4.70/4.95 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(668,a,649,a)].
% 4.70/4.95 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(668,a,650,a)].
% 4.70/4.95 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),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),B))). [resolve(668,a,652,a)].
% 4.70/4.95 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(668,a,653,a)].
% 4.70/4.95 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(668,a,654,a)].
% 4.70/4.95 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(668,a,656,a)].
% 4.70/4.95 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(668,a,657,a)].
% 4.70/4.95 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(668,a,658,a)].
% 4.70/4.95 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(668,a,661,a)].
% 4.70/4.95 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(668,a,662,a)].
% 4.70/4.95 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(668,a,663,a)].
% 4.70/4.95 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(668,a,665,a)].
% 4.70/4.95 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = 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),B)). [resolve(668,a,667,a)].
% 4.70/4.95 669 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 4.70/4.95 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(669,a,622,a)].
% 4.70/4.95 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(669,a,623,a)].
% 4.70/4.95 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(669,a,625,a)].
% 4.70/4.95 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(669,a,630,a)].
% 4.70/4.96 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(669,a,631,a)].
% 4.70/4.96 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(669,a,632,a)].
% 4.70/4.96 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(669,a,636,a)].
% 4.70/4.96 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(669,a,639,a)].
% 4.70/4.96 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(669,a,640,a)].
% 4.70/4.96 Derived: c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(669,a,642,a)].
% 4.70/4.96 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(669,a,643,a)].
% 4.70/4.96 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(669,a,644,a)].
% 4.70/4.96 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(669,a,645,a)].
% 4.70/4.96 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(669,a,646,a)].
% 4.70/4.96 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(669,a,647,a)].
% 4.70/4.96 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(669,a,648,a)].
% 4.70/4.96 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),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),B))). [resolve(669,a,652,a)].
% 4.70/4.96 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(669,a,653,a)].
% 4.70/4.96 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(669,a,654,a)].
% 4.93/5.17 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(669,a,656,a)].
% 4.93/5.17 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(669,a,657,a)].
% 4.93/5.17 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(669,a,658,a)].
% 4.93/5.18 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(669,a,661,a)].
% 4.93/5.18 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(669,a,662,a)].
% 4.93/5.18 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(669,a,663,a)].
% 4.93/5.18 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(669,a,665,a)].
% 4.93/5.18 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = 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),B)). [resolve(669,a,667,a)].
% 4.93/5.18 670 class_Ring__and__Field_Oabs__if(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 4.93/5.18 671 -class_Ring__and__Field_Oabs__if(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_0) # label(axiom). [assumption].
% 4.93/5.18 672 -class_Ring__and__Field_Oabs__if(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_1) # label(axiom). [assumption].
% 4.93/5.18 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(670,a,672,a)].
% 4.93/5.18 673 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 4.93/5.18 674 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F),A) | -c_lessequals(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),A) # label(cls_le__add__iff2_1) # label(axiom). [assumption].
% 4.93/5.18 675 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,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),A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F),A) # label(cls_le__add__iff2_0) # label(axiom). [assumption].
% 4.93/5.18 676 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F),A) | -c_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),F,A) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 4.93/5.18 677 -class_Ring__and__Field_Opordered__ring(A) | 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),F,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F),A) # label(cls_le__add__iff1_0) # label(axiom). [assumption].
% 4.93/5.18 678 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)),E),F,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F),A) # label(cls_less__add__iff1_0) # label(axiom). [assumption].
% 4.93/5.18 679 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D),F,A) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 4.93/5.18 680 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)),E)),F),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F),A) # label(cls_less__add__iff2_0) # label(axiom). [assumption].
% 4.93/5.18 681 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F),A) | -c_HOL_Oord__class_Oless(D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F),A) # label(cls_less__add__iff2_1) # label(axiom). [assumption].
% 4.93/5.18 682 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,C,A) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 4.93/5.18 683 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 4.93/5.18 684 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 4.93/5.18 685 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 4.93/5.18 686 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 4.93/5.18 Derived: 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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E),tc_Int_Oint) | -c_lessequals(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),tc_Int_Oint). [resolve(673,a,674,a)].
% 4.93/5.18 Derived: c_lessequals(A,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),tc_Int_Oint) | -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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)),E),tc_Int_Oint). [resolve(673,a,675,a)].
% 4.93/5.18 Derived: 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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E),tc_Int_Oint) | -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),E,tc_Int_Oint). [resolve(673,a,676,a)].
% 4.93/5.18 Derived: 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),E,tc_Int_Oint) | -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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),E),tc_Int_Oint). [resolve(673,a,677,a)].
% 4.93/5.18 Derived: 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),E,tc_Int_Oint) | -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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),E),tc_Int_Oint). [resolve(673,a,678,a)].
% 4.93/5.18 Derived: 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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E),tc_Int_Oint) | -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),E,tc_Int_Oint). [resolve(673,a,679,a)].
% 4.93/5.18 Derived: c_HOL_Oord__class_Oless(A,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),tc_Int_Oint) | -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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)),E),tc_Int_Oint). [resolve(673,a,680,a)].
% 4.93/5.18 Derived: 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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E),tc_Int_Oint) | -c_HOL_Oord__class_Oless(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),tc_Int_Oint). [resolve(673,a,681,a)].
% 5.02/5.28 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint). [resolve(673,a,682,a)].
% 5.02/5.28 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,A,tc_Int_Oint). [resolve(673,a,683,a)].
% 5.02/5.28 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(673,a,684,a)].
% 5.02/5.28 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(673,a,685,a)].
% 5.02/5.28 687 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 5.02/5.28 688 -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].
% 5.02/5.28 689 -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].
% 5.02/5.28 690 -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].
% 5.02/5.28 691 -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].
% 5.02/5.28 692 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 5.02/5.28 693 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 5.02/5.28 694 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 5.02/5.28 695 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 5.02/5.28 696 -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].
% 5.02/5.28 697 -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].
% 5.02/5.28 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(687,a,688,a)].
% 5.02/5.28 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(687,a,689,a)].
% 5.02/5.28 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(687,a,690,a)].
% 5.02/5.28 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(687,a,691,a)].
% 5.02/5.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(687,a,692,a)].
% 5.02/5.28 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B). [resolve(687,a,693,a)].
% 5.02/5.28 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(687,a,694,a)].
% 5.02/5.28 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(tc_Int_Oint),A)),B). [resolve(687,a,695,a)].
% 5.02/5.28 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(687,a,696,a)].
% 5.15/5.39 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(687,a,697,a)].
% 5.15/5.39 698 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 5.15/5.39 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(698,a,688,a)].
% 5.15/5.39 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(698,a,689,a)].
% 5.15/5.39 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(698,a,690,a)].
% 5.15/5.39 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(698,a,691,a)].
% 5.15/5.39 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(698,a,692,a)].
% 5.15/5.39 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B). [resolve(698,a,693,a)].
% 5.15/5.39 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(698,a,694,a)].
% 5.15/5.39 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B). [resolve(698,a,695,a)].
% 5.15/5.39 699 class_Ring__and__Field_Olordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Olordered__ring) # label(axiom). [assumption].
% 5.15/5.39 700 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(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)),A) # label(cls_abs__le__mult_0) # label(axiom). [assumption].
% 5.28/5.55 Derived: c_lessequals(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)),tc_Int_Oint). [resolve(699,a,700,a)].
% 5.28/5.55 701 c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(621,a,642,a)].
% 5.28/5.55 702 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,E),D)) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D) | -c_Groebner__Basis_Ogb__semiring(A,B,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 5.28/5.55 703 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),D) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D) | -c_Groebner__Basis_Ogb__semiring(A,B,F,V6,E,V7) # label(cls_gb__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 5.28/5.55 704 hAPP(hAPP(A,B),hAPP(hAPP(C,D),B)) = hAPP(hAPP(C,hAPP(hAPP(A,D),E)),B) | -c_Groebner__Basis_Ogb__semiring(A,C,F,V6,E,V7) # label(cls_gb__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 5.28/5.55 705 hAPP(hAPP(A,B),B) = hAPP(hAPP(C,hAPP(hAPP(A,D),D)),B) | -c_Groebner__Basis_Ogb__semiring(A,C,E,F,D,V6) # label(cls_gb__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 5.28/5.55 706 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,V6) # label(cls_gb__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 5.28/5.55 707 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(A,D,E,C,F,V6) # label(cls_gb__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 5.28/5.55 708 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 5.28/5.55 709 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E)) | -c_Groebner__Basis_Ogb__semiring(B,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 5.28/5.55 710 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,V6) # label(cls_gb__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 5.28/5.55 711 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,C,F,V6) # label(cls_gb__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 5.28/5.55 712 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,V6) # label(cls_gb__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 5.28/5.55 713 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,C,V6) # label(cls_gb__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 5.28/5.55 714 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 5.28/5.55 715 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),hAPP(hAPP(A,D),E))) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 5.28/5.55 716 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,D),hAPP(hAPP(A,hAPP(hAPP(A,B),C)),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 5.28/5.55 717 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 5.28/5.55 718 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 5.28/5.55 719 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 5.28/5.56 720 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 5.28/5.56 721 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E)) | -c_Groebner__Basis_Ogb__semiring(A,F,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 5.28/5.56 722 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 5.28/5.56 723 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 5.28/5.56 724 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 5.28/5.56 725 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(A,D,E,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 5.28/5.56 726 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 5.28/5.56 727 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,V6) # label(cls_gb__semiring_Oadd__0_0) # label(axiom). [assumption].
% 5.28/5.56 728 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Oadd__a_0) # label(axiom). [assumption].
% 5.28/5.56 729 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(A,D,E,F,V6,V7) # label(cls_gb__semiring_Oadd__c_0) # label(axiom). [assumption].
% 5.28/5.56 730 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,V6) # label(cls_gb__semiring_Omul__0_0) # label(axiom). [assumption].
% 5.28/5.56 731 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,V6) # label(cls_gb__semiring_Omul__1_0) # label(axiom). [assumption].
% 5.28/5.56 732 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Omul__a_0) # label(axiom). [assumption].
% 5.28/5.56 733 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,V6,V7) # label(cls_gb__semiring_Omul__c_0) # label(axiom). [assumption].
% 5.28/5.56 734 hAPP(hAPP(A,B),hAPP(hAPP(C,D),E)) = hAPP(hAPP(C,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,B),E)) | -c_Groebner__Basis_Ogb__semiring(C,A,F,V6,V7,V8) # label(cls_gb__semiring_Omul__d_0) # label(axiom). [assumption].
% 5.28/5.56 735 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E)) | -c_Groebner__Basis_Ogb__semiring(F,B,A,V6,V7,V8) # label(cls_gb__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 5.28/5.56 736 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E)) = hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,B,V6,V7,V8) # label(cls_gb__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 5.28/5.56 737 hAPP(hAPP(A,B),c_HOL_Oone__class_Oone(tc_nat)) = B | -c_Groebner__Basis_Ogb__semiring(C,D,A,E,F,V6) # label(cls_gb__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 5.28/5.56 738 hAPP(hAPP(A,B),c_HOL_Ozero__class_Ozero(tc_nat)) = C | -c_Groebner__Basis_Ogb__semiring(D,E,A,F,C,V6) # label(cls_gb__semiring_Opwr__0_0) # label(axiom). [assumption].
% 5.28/5.56 739 hAPP(hAPP(A,B),hAPP(c_Suc,C)) = hAPP(hAPP(D,B),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 5.28/5.56 740 hAPP(hAPP(A,B),hAPP(c_Suc,C)) = hAPP(hAPP(D,B),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 5.28/5.56 741 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),C) = hAPP(hAPP(B,C),hAPP(c_Suc,D)) | -c_Groebner__Basis_Ogb__semiring(E,A,B,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 5.28/5.56 742 hAPP(hAPP(A,B),hAPP(hAPP(C,B),D)) = hAPP(hAPP(C,B),hAPP(c_Suc,D)) | -c_Groebner__Basis_Ogb__semiring(E,A,C,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 5.28/5.56 743 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) | -c_Groebner__Basis_Ogb__semiring(E,F,A,V6,V7,V8) # label(cls_gb__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 5.28/5.56 744 hAPP(hAPP(A,B),B) = hAPP(hAPP(C,B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) | -c_Groebner__Basis_Ogb__semiring(D,A,C,E,F,V6) # label(cls_gb__semiring_Osemiring__rules_I29_J_0) # label(axiom). [assumption].
% 5.28/5.56 745 hAPP(hAPP(A,B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = hAPP(hAPP(D,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I36_J_0) # label(axiom). [assumption].
% 5.28/5.56 746 hAPP(hAPP(A,B),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))) = hAPP(hAPP(D,B),hAPP(hAPP(D,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,B),C))) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I37_J_0) # label(axiom). [assumption].
% 5.28/5.56 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(701,a,702,b)].
% 5.28/5.56 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(701,a,703,b)].
% 5.28/5.56 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(701,a,704,b)].
% 5.28/5.56 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(701,a,705,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(701,a,706,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(701,a,707,b)].
% 5.28/5.56 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(701,a,709,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(701,a,712,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(701,a,713,b)].
% 5.28/5.56 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(701,a,721,b)].
% 5.28/5.56 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(701,a,722,b)].
% 5.28/5.56 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(701,a,723,b)].
% 5.28/5.56 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(701,a,724,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(701,a,725,b)].
% 5.28/5.56 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(701,a,726,b)].
% 5.28/5.56 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(701,a,734,b)].
% 5.28/5.56 747 c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(668,a,642,a)].
% 5.28/5.56 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(747,a,702,b)].
% 5.28/5.56 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(747,a,703,b)].
% 5.28/5.56 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(747,a,704,b)].
% 5.28/5.56 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(747,a,705,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(747,a,706,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(747,a,707,b)].
% 5.28/5.56 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(747,a,709,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(747,a,712,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(747,a,713,b)].
% 5.28/5.56 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(747,a,721,b)].
% 5.28/5.56 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(747,a,722,b)].
% 5.28/5.56 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(747,a,723,b)].
% 5.28/5.56 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(747,a,724,b)].
% 5.28/5.56 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(747,a,725,b)].
% 5.28/5.56 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(747,a,726,b)].
% 5.28/5.56 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(747,a,734,b)].
% 5.28/5.56 748 c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(669,a,642,a)].
% 5.28/5.56 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(748,a,702,b)].
% 5.28/5.56 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(748,a,703,b)].
% 5.28/5.56 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(748,a,704,b)].
% 5.28/5.56 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(748,a,705,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(748,a,706,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(748,a,707,b)].
% 5.28/5.56 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(748,a,709,b)].
% 5.28/5.56 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(748,a,710,b)].
% 5.28/5.56 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(748,a,711,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(748,a,712,b)].
% 5.28/5.56 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(748,a,713,b)].
% 5.28/5.56 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(748,a,721,b)].
% 5.33/5.61 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(748,a,722,b)].
% 5.33/5.61 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(748,a,723,b)].
% 5.33/5.61 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(748,a,724,b)].
% 5.33/5.61 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(748,a,725,b)].
% 5.33/5.61 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(748,a,726,b)].
% 5.33/5.61 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(748,a,734,b)].
% 5.33/5.61 749 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 5.33/5.61 750 -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].
% 5.33/5.61 751 -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].
% 5.33/5.61 752 -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].
% 5.33/5.61 753 -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].
% 5.33/5.61 754 -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].
% 5.33/5.61 755 -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].
% 5.33/5.61 756 -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].
% 5.33/5.61 757 -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) # label(cls_square__eq__iff_1) # label(axiom). [assumption].
% 5.33/5.61 758 -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_square__eq__iff_0) # label(axiom). [assumption].
% 5.33/5.61 759 -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].
% 5.33/5.61 760 -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].
% 5.33/5.61 761 -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].
% 5.33/5.61 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(749,a,750,a)].
% 5.33/5.61 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(749,a,752,a)].
% 5.33/5.61 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(749,a,754,a)].
% 5.33/5.61 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(749,a,755,a)].
% 5.33/5.61 Derived: 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 = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B) | A = B. [resolve(749,a,758,a)].
% 5.33/5.61 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(749,a,761,a)].
% 5.33/5.61 762 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 5.33/5.61 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(762,a,750,a)].
% 5.33/5.61 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(762,a,752,a)].
% 5.33/5.61 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(762,a,754,a)].
% 5.33/5.61 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(762,a,755,a)].
% 5.67/5.93 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),B) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B) | A = B. [resolve(762,a,758,a)].
% 5.67/5.93 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(762,a,761,a)].
% 5.67/5.93 763 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.67/5.93 764 -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].
% 5.67/5.93 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(763,a,764,a)].
% 5.67/5.93 765 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.67/5.93 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(765,a,764,a)].
% 5.67/5.93 766 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 5.67/5.93 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(766,a,764,a)].
% 5.67/5.93 767 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.67/5.93 768 -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].
% 5.67/5.93 769 -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].
% 5.67/5.93 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(767,a,769,a)].
% 5.67/5.93 770 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.67/5.93 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(770,a,769,a)].
% 5.67/5.93 771 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.67/5.93 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(771,a,769,a)].
% 5.67/5.93 772 class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 5.67/5.93 773 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))),B) = c_HOL_Oone__class_Oone(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_minus__one__even__power_0) # label(axiom). [assumption].
% 5.67/5.93 774 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_neg__power__if_0) # label(axiom). [assumption].
% 5.67/5.93 775 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_neg__power__if_1) # label(axiom). [assumption].
% 5.67/5.93 776 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_minus__one__odd__power_0) # label(axiom). [assumption].
% 5.67/5.93 777 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = c_HOL_Oone__class_Oone(A) # label(cls_power__minus1__even_0) # label(axiom). [assumption].
% 5.67/5.93 778 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A)) # label(cls_power__minus1__odd_0) # label(axiom). [assumption].
% 5.67/5.93 779 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_power2__minus_0) # label(axiom). [assumption].
% 5.67/5.93 780 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) # label(cls_comm__ring__1__class_Opower__minus__even_0) # label(axiom). [assumption].
% 5.67/5.93 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))),A) = c_HOL_Oone__class_Oone(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(772,a,773,a)].
% 5.67/5.93 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(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(772,a,774,a)].
% 5.67/5.93 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(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(772,a,775,a)].
% 5.67/5.93 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)) | c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(772,a,776,a)].
% 5.67/5.93 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(772,a,777,a)].
% 5.67/5.93 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A))) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)). [resolve(772,a,778,a)].
% 5.72/6.04 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(772,a,779,a)].
% 5.72/6.04 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)). [resolve(772,a,780,a)].
% 5.72/6.04 781 class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 5.72/6.04 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(781,a,773,a)].
% 5.72/6.04 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(781,a,774,a)].
% 5.72/6.04 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(781,a,775,a)].
% 5.72/6.04 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) | c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(781,a,776,a)].
% 5.72/6.04 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(781,a,777,a)].
% 5.72/6.04 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A))) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)). [resolve(781,a,778,a)].
% 5.72/6.04 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(781,a,779,a)].
% 5.72/6.04 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)). [resolve(781,a,780,a)].
% 5.72/6.04 782 class_OrderedGroup_Olordered__ab__group__add__meet(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__meet) # label(axiom). [assumption].
% 6.08/6.35 783 -class_OrderedGroup_Olordered__ab__group__add__meet(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_add__inf__distrib__left_0) # label(axiom). [assumption].
% 6.08/6.35 784 -class_OrderedGroup_Olordered__ab__group__add__meet(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__inf__distrib__right_0) # label(axiom). [assumption].
% 6.08/6.35 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),tc_Int_Oint). [resolve(782,a,783,a)].
% 6.08/6.35 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint)),C) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(782,a,784,a)].
% 6.08/6.35 785 class_OrderedGroup_Olordered__ab__group__add__join(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__join) # label(axiom). [assumption].
% 6.08/6.35 786 -class_OrderedGroup_Olordered__ab__group__add__join(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__sup__distrib__right_0) # label(axiom). [assumption].
% 6.08/6.35 787 -class_OrderedGroup_Olordered__ab__group__add__join(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_add__sup__distrib__left_0) # label(axiom). [assumption].
% 6.08/6.35 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint)),C) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(785,a,786,a)].
% 6.08/6.35 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),tc_Int_Oint). [resolve(785,a,787,a)].
% 6.08/6.35 788 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 6.08/6.35 789 -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].
% 6.08/6.35 790 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 6.08/6.35 791 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 6.08/6.35 792 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 6.08/6.35 793 -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].
% 6.29/6.57 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(792,a,793,a)].
% 6.29/6.57 794 class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 6.29/6.57 795 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__eq__neg__nonpos_0) # label(axiom). [assumption].
% 6.29/6.57 796 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__eq__neg__nonpos_1) # label(axiom). [assumption].
% 6.29/6.57 797 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A) # label(cls_neg__less__eq__nonneg_0) # label(axiom). [assumption].
% 6.29/6.57 798 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__eq__nonneg_1) # label(axiom). [assumption].
% 6.29/6.57 799 -class_OrderedGroup_Oordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 6.29/6.57 800 -class_OrderedGroup_Oordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 6.29/6.57 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(794,a,795,a)].
% 6.29/6.57 Derived: c_lessequals(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(794,a,796,a)].
% 6.29/6.57 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),A,tc_Int_Oint). [resolve(794,a,797,a)].
% 6.29/6.57 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(794,a,798,a)].
% 6.29/6.57 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) != A | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(794,a,800,a)].
% 6.29/6.57 801 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 6.29/6.57 802 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 6.29/6.57 803 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 6.39/6.68 804 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 6.39/6.68 805 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 6.39/6.68 806 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 6.39/6.68 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(801,a,802,a)].
% 6.39/6.68 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(801,a,803,a)].
% 6.39/6.68 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(801,a,804,a)].
% 6.39/6.68 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(801,a,805,a)].
% 6.39/6.68 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(801,a,806,a)].
% 6.39/6.68 807 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 6.39/6.68 Derived: c_HOL_Oord__class_Oless(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) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(807,a,802,a)].
% 6.39/6.68 Derived: c_HOL_Oord__class_Oless(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) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(807,a,803,a)].
% 6.39/6.68 Derived: c_HOL_Oord__class_Oless(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) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(807,a,804,a)].
% 6.39/6.68 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(807,a,805,a)].
% 6.39/6.68 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(807,a,806,a)].
% 6.39/6.68 808 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 6.39/6.68 809 -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].
% 6.39/6.68 810 -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].
% 6.39/6.68 811 -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].
% 6.39/6.68 812 -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].
% 6.39/6.68 813 -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].
% 6.39/6.68 814 -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].
% 6.39/6.68 815 -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].
% 6.39/6.68 816 -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].
% 6.39/6.68 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(808,a,809,a)].
% 6.39/6.68 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(808,a,810,a)].
% 6.39/6.68 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(808,a,811,a)].
% 6.39/6.68 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(808,a,812,a)].
% 6.39/6.68 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(808,a,813,a)].
% 6.39/6.68 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(808,a,814,a)].
% 6.39/6.68 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(808,a,815,a)].
% 6.39/6.68 817 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 6.39/6.69 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(817,a,809,a)].
% 6.39/6.69 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(817,a,810,a)].
% 6.39/6.69 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(817,a,811,a)].
% 6.39/6.69 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(817,a,812,a)].
% 6.39/6.69 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(817,a,813,a)].
% 6.39/6.69 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(817,a,814,a)].
% 6.39/6.69 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(817,a,815,a)].
% 6.39/6.69 818 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 6.39/6.69 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(818,a,809,a)].
% 6.39/6.69 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(818,a,810,a)].
% 6.39/6.69 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(818,a,811,a)].
% 6.39/6.69 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(818,a,812,a)].
% 6.39/6.69 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(818,a,813,a)].
% 6.39/6.69 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(818,a,814,a)].
% 6.67/6.90 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(818,a,815,a)].
% 6.67/6.90 819 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 6.67/6.90 820 -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].
% 6.67/6.90 821 -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].
% 6.67/6.90 822 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 6.67/6.90 823 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 6.67/6.90 824 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 6.67/6.90 825 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 6.67/6.90 826 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 6.67/6.90 827 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 6.67/6.90 828 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 6.67/6.90 829 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 6.67/6.90 830 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 6.67/6.90 831 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 6.67/6.90 832 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 6.67/6.90 833 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 6.67/6.90 834 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 6.67/6.90 835 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 6.67/6.90 836 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 6.67/6.90 837 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 6.67/6.90 838 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 6.67/6.90 839 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 6.67/6.90 840 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(824,a,825,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(824,a,826,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(824,a,827,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat). [resolve(824,a,828,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat). [resolve(824,a,829,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(824,a,830,a)].
% 6.67/6.90 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat). [resolve(824,a,831,a)].
% 6.67/6.90 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat). [resolve(824,a,832,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(824,a,833,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(824,a,834,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(824,a,835,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A),tc_nat). [resolve(824,a,836,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat). [resolve(824,a,837,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(824,a,838,a)].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(824,a,839,a)].
% 6.67/6.90 841 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 6.67/6.90 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(841,a,825,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(841,a,826,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(841,a,827,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(841,a,828,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint). [resolve(841,a,829,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(841,a,830,a)].
% 6.67/6.91 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(841,a,831,a)].
% 6.67/6.91 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint). [resolve(841,a,832,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(841,a,833,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(841,a,834,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(841,a,835,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint). [resolve(841,a,836,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint). [resolve(841,a,837,a)].
% 6.67/6.91 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(841,a,838,a)].
% 6.69/7.01 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(841,a,839,a)].
% 6.69/7.01 842 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 6.69/7.01 843 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),A) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 6.69/7.01 844 -class_Ring__and__Field_Oordered__ring__strict(A) | 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))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 6.69/7.01 845 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 6.69/7.01 846 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 6.69/7.01 847 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 6.69/7.01 848 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 6.69/7.01 849 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 6.69/7.01 850 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 6.69/7.01 851 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -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)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 6.69/7.01 852 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -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)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 6.69/7.01 853 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 6.69/7.01 854 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 6.69/7.01 855 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 6.69/7.01 856 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 6.69/7.01 857 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 6.69/7.01 858 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 6.69/7.01 859 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 6.69/7.01 860 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 6.69/7.01 861 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 6.69/7.01 862 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 6.69/7.01 863 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 6.69/7.01 864 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 6.69/7.01 865 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 6.69/7.01 866 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(D,B,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 6.69/7.01 867 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 6.69/7.01 868 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 6.69/7.01 869 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 6.69/7.01 870 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 6.69/7.01 871 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 6.69/7.01 872 -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].
% 6.69/7.01 873 -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].
% 6.69/7.01 874 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),A) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 6.69/7.01 875 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 6.69/7.01 876 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 6.69/7.01 877 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 6.69/7.01 878 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 6.69/7.01 879 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 6.69/7.01 880 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 6.69/7.01 881 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 6.69/7.01 882 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 6.69/7.01 883 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 6.69/7.01 884 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 6.69/7.01 885 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 6.69/7.01 886 -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].
% 6.69/7.01 887 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Omonoid__mult(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__even__power_0) # label(axiom). [assumption].
% 6.69/7.01 888 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 6.69/7.01 889 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 6.69/7.01 890 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 6.69/7.01 891 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 6.69/7.01 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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))),tc_Int_Oint). [resolve(842,a,843,a)].
% 6.69/7.01 Derived: 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))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,844,a)].
% 6.69/7.01 Derived: -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)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,845,a)].
% 6.69/7.01 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(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)),tc_Int_Oint). [resolve(842,a,846,a)].
% 6.69/7.01 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(842,a,847,a)].
% 6.69/7.01 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,849,a)].
% 6.69/7.01 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,850,a)].
% 6.69/7.01 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -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)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,851,a)].
% 6.69/7.01 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -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)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,852,a)].
% 6.69/7.01 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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)),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(842,a,853,a)].
% 6.69/7.01 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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)),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(842,a,854,a)].
% 6.69/7.01 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint). [resolve(842,a,855,a)].
% 6.69/7.02 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint). [resolve(842,a,856,a)].
% 6.69/7.02 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,857,a)].
% 6.69/7.02 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,858,a)].
% 6.69/7.02 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(842,a,859,a)].
% 6.69/7.02 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,A,tc_Int_Oint). [resolve(842,a,864,a)].
% 6.69/7.02 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,867,a)].
% 6.69/7.02 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,869,a)].
% 6.69/7.02 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,870,a)].
% 6.69/7.02 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(842,a,872,a)].
% 6.69/7.02 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(842,a,873,a)].
% 6.69/7.02 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A),tc_Int_Oint). [resolve(842,a,874,a)].
% 6.69/7.02 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint). [resolve(842,a,878,a)].
% 6.69/7.02 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint). [resolve(842,a,879,a)].
% 6.69/7.02 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint). [resolve(842,a,881,a)].
% 6.88/7.13 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint). [resolve(842,a,882,a)].
% 6.88/7.13 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,883,a)].
% 6.88/7.13 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(842,a,884,a)].
% 6.88/7.13 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(842,a,885,a)].
% 6.88/7.13 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(842,a,886,a)].
% 6.88/7.13 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint). [resolve(842,a,888,a)].
% 6.88/7.13 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint). [resolve(842,a,889,a)].
% 6.88/7.13 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint). [resolve(842,a,890,a)].
% 6.88/7.13 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint). [resolve(842,a,891,a)].
% 6.88/7.13 892 class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 6.88/7.13 893 -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)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_3) # label(axiom). [assumption].
% 6.88/7.13 894 -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)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_2) # label(axiom). [assumption].
% 6.88/7.13 895 -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)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_1) # label(axiom). [assumption].
% 7.18/7.44 896 -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)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_0) # label(axiom). [assumption].
% 7.18/7.44 897 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 7.18/7.44 898 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 7.18/7.44 899 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 7.18/7.44 900 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 7.18/7.44 901 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 7.18/7.44 902 -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].
% 7.18/7.44 903 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 7.18/7.44 904 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 7.18/7.44 905 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 7.18/7.44 906 -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].
% 7.18/7.44 907 -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].
% 7.18/7.44 908 -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) | -c_lessequals(D,C,tc_nat) # label(cls_lemma__realpow__diff_0) # label(axiom). [assumption].
% 7.18/7.44 909 -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].
% 7.18/7.44 910 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_power__one__right_0) # label(axiom). [assumption].
% 7.18/7.44 911 -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].
% 7.18/7.44 912 -class_Ring__and__Field_Ocomm__ring(A) | -class_OrderedGroup_Omonoid__mult(A) | c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),A,tc_fun(A,A),tc_nat),hAPP(c_Power_Opower__class_Opower(A),B),tc_nat,A,A),A,tc_fun(A,A),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat),tc_nat,A) = c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(A),B),A,tc_fun(A,A),tc_nat),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),A,tc_fun(A,A),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),tc_nat,A,A),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat),tc_nat,A) # label(cls_lemma__termdiff1_0) # label(axiom). [assumption].
% 7.18/7.44 913 -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)),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(A),B),A,tc_fun(A,A),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,A,tc_nat),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat),tc_nat,A)) # label(cls_lemma__realpow__diff__sumr2_0) # label(axiom). [assumption].
% 7.18/7.44 914 -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_OrderedGroup_Omonoid__mult(A) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(A),B),A,tc_fun(A,A),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,D)),tc_nat,A,tc_nat),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(A),B),A,tc_fun(A,A),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat),tc_nat,A)) # label(cls_lemma__realpow__diff__sumr_0) # label(axiom). [assumption].
% 7.18/7.44 915 -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].
% 7.18/7.44 916 -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].
% 7.18/7.44 917 -class_OrderedGroup_Omonoid__mult(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(B,A)) # label(cls_power2__eq__square__number__of_0) # label(axiom). [assumption].
% 7.18/7.44 918 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) # label(cls_power__odd__eq_0) # label(axiom). [assumption].
% 7.18/7.44 919 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_power__even__eq_0) # label(axiom). [assumption].
% 7.18/7.44 920 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) # label(cls_power2__eq__square_0) # label(axiom). [assumption].
% 7.18/7.44 921 -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].
% 7.18/7.44 922 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),B) # label(cls_power3__eq__cube_0) # label(axiom). [assumption].
% 7.18/7.44 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) | -c_lessequals(C,B,tc_nat). [resolve(905,a,908,a)].
% 7.18/7.44 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(905,a,909,a)].
% 7.18/7.45 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(905,a,911,a)].
% 7.18/7.45 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_nat),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_nat,tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_nat,tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,tc_nat) = c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_nat,tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_nat,tc_nat),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),tc_nat,tc_nat). [resolve(905,a,912,b)].
% 7.18/7.45 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)),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,B),tc_nat),tc_nat,tc_nat)). [resolve(905,a,913,b)].
% 7.18/7.45 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_nat) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,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),hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A),tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_nat),B),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),hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat)). [resolve(905,a,914,b)].
% 7.18/7.45 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(905,a,915,a)].
% 7.18/7.45 Derived: -class_Int_Onumber(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat)),c_Int_Onumber__class_Onumber__of(A,tc_nat)). [resolve(905,a,917,a)].
% 7.18/7.45 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(905,a,918,a)].
% 7.18/7.45 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(905,a,919,a)].
% 7.18/7.45 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),A). [resolve(905,a,920,a)].
% 7.18/7.45 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(905,a,921,a)].
% 7.18/7.45 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),A)),A). [resolve(905,a,922,a)].
% 7.18/7.45 923 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 7.18/7.45 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) | -c_lessequals(C,B,tc_nat). [resolve(923,a,908,a)].
% 7.18/7.45 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(923,a,909,a)].
% 7.18/7.45 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(923,a,911,a)].
% 7.18/7.45 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Int_Oint,tc_nat),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),tc_nat,tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),tc_nat,tc_Int_Oint,tc_Int_Oint),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,tc_Int_Oint) = c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Int_Oint,tc_nat),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Int_Oint,tc_nat),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),tc_nat,tc_Int_Oint). [resolve(923,a,912,b)].
% 7.18/7.45 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)),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),tc_nat,tc_Int_Oint,tc_nat),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),tc_nat,tc_Int_Oint)). [resolve(923,a,913,b)].
% 7.18/7.45 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C)),tc_nat,tc_Int_Oint,tc_nat),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),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Int_Oint,tc_nat),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),tc_nat,tc_Int_Oint)). [resolve(923,a,914,b)].
% 7.18/7.45 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(923,a,915,a)].
% 7.18/7.45 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)). [resolve(923,a,917,a)].
% 7.18/7.45 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(923,a,918,a)].
% 7.18/7.45 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(923,a,919,a)].
% 7.18/7.45 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A). [resolve(923,a,920,a)].
% 7.18/7.45 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(923,a,921,a)].
% 7.18/7.45 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),A). [resolve(923,a,922,a)].
% 7.18/7.45 924 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 7.18/7.45 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) | -c_lessequals(C,B,tc_nat). [resolve(924,a,908,a)].
% 7.18/7.45 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(924,a,909,a)].
% 7.18/7.45 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(924,a,911,a)].
% 7.18/7.45 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,tc_Complex_Ocomplex) = c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),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),tc_nat,tc_Complex_Ocomplex). [resolve(924,a,912,b)].
% 7.18/7.45 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)),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),tc_nat,tc_Complex_Ocomplex,tc_nat),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),tc_nat,tc_Complex_Ocomplex)). [resolve(924,a,913,b)].
% 7.18/7.45 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) | c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C)),tc_nat,tc_Complex_Ocomplex,tc_nat),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),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,tc_Complex_Ocomplex,tc_nat),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),tc_nat,tc_Complex_Ocomplex)). [resolve(924,a,914,b)].
% 7.18/7.45 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(924,a,915,a)].
% 7.18/7.46 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)). [resolve(924,a,917,a)].
% 7.18/7.46 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(924,a,918,a)].
% 7.41/7.67 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(924,a,919,a)].
% 7.41/7.67 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A). [resolve(924,a,920,a)].
% 7.41/7.67 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(924,a,921,a)].
% 7.41/7.67 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A)),A). [resolve(924,a,922,a)].
% 7.41/7.67 925 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 7.41/7.67 926 -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].
% 7.41/7.67 927 -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].
% 7.41/7.67 928 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 7.41/7.67 929 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 7.41/7.67 930 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 7.41/7.67 931 -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].
% 7.41/7.67 932 -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].
% 7.41/7.67 933 -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].
% 7.41/7.67 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(930,a,931,a)].
% 7.71/7.99 934 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 7.71/7.99 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(934,a,931,a)].
% 7.71/7.99 935 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 7.71/7.99 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(935,a,931,a)].
% 7.71/7.99 936 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 7.71/7.99 937 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 7.71/7.99 938 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].
% 7.71/7.99 939 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 7.71/7.99 940 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 7.71/7.99 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(939,a,940,a)].
% 7.71/7.99 941 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 7.71/7.99 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(941,a,940,a)].
% 7.71/7.99 942 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 7.71/7.99 943 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 7.71/7.99 944 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 7.71/7.99 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(942,a,944,a)].
% 7.71/7.99 945 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 7.71/7.99 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(945,a,944,a)].
% 7.95/8.20 946 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 7.95/8.20 947 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 7.95/8.20 948 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 7.95/8.20 949 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 7.95/8.20 950 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 7.95/8.20 951 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 7.95/8.20 952 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 7.95/8.20 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(946,a,947,a)].
% 7.95/8.20 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(946,a,948,a)].
% 7.95/8.20 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(946,a,949,a)].
% 7.95/8.20 953 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 7.95/8.20 954 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 7.95/8.20 955 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 7.95/8.20 956 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 8.23/8.50 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(954,a,955,a)].
% 8.23/8.50 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(954,a,956,a)].
% 8.23/8.50 957 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 8.23/8.50 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(957,a,955,a)].
% 8.23/8.50 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(957,a,956,a)].
% 8.23/8.50 958 class_Ring__and__Field_Oring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 8.23/8.50 959 -class_Ring__and__Field_Oring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_power__minus_0) # label(axiom). [assumption].
% 8.23/8.50 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(958,a,959,a)].
% 8.23/8.50 960 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 8.23/8.50 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(960,a,959,a)].
% 8.23/8.50 961 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 8.23/8.50 962 -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].
% 8.23/8.50 963 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 8.23/8.50 964 -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].
% 8.23/8.50 965 -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].
% 8.23/8.50 966 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,E),D,E,A) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 8.23/8.50 967 -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].
% 8.23/8.50 968 -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].
% 8.23/8.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Finite__Set_Osetsum(A,B,C,tc_nat)),D) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),A,tc_nat,tc_fun(tc_nat,tc_nat),C),D,C,tc_nat,tc_nat),B,C,tc_nat). [resolve(961,a,963,a)].
% 8.23/8.50 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(961,a,964,a)].
% 8.23/8.50 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(961,a,965,a)].
% 8.23/8.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Finite__Set_Osetsum(B,C,D,tc_nat)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B,tc_nat,tc_nat,D),C,D,tc_nat). [resolve(961,a,966,a)].
% 8.23/8.50 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(961,a,967,a)].
% 8.23/8.50 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(961,a,968,a)].
% 8.23/8.50 969 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 8.23/8.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Finite__Set_Osetsum(A,B,C,tc_Int_Oint)),D) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),C),D,C,tc_Int_Oint,tc_Int_Oint),B,C,tc_Int_Oint). [resolve(969,a,963,a)].
% 8.23/8.50 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(969,a,964,a)].
% 8.23/8.50 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(969,a,965,a)].
% 8.23/8.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Finite__Set_Osetsum(B,C,D,tc_Int_Oint)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B,tc_Int_Oint,tc_Int_Oint,D),C,D,tc_Int_Oint). [resolve(969,a,966,a)].
% 8.45/8.71 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(969,a,967,a)].
% 8.45/8.71 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(969,a,968,a)].
% 8.45/8.71 970 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 8.45/8.71 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(970,a,964,a)].
% 8.45/8.71 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(970,a,965,a)].
% 8.45/8.71 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(970,a,967,a)].
% 8.45/8.71 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(970,a,968,a)].
% 8.45/8.71 971 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 8.45/8.71 972 -class_Ring__and__Field_Osemiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oone__class_Oone(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_one__power2_0) # label(axiom). [assumption].
% 8.45/8.71 973 -class_Ring__and__Field_Osemiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__power2_0) # label(axiom). [assumption].
% 8.45/8.71 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(971,a,973,a)].
% 8.45/8.71 974 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 8.45/8.71 975 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 8.45/8.71 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(975,a,973,a)].
% 8.45/8.71 976 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].
% 8.45/8.71 977 -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].
% 8.45/8.71 978 -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].
% 8.45/8.71 979 -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].
% 9.23/9.50 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(976,a,979,a)].
% 9.23/9.50 980 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].
% 9.23/9.50 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(980,a,979,a)].
% 9.23/9.50 981 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 9.23/9.50 982 -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].
% 9.23/9.50 983 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 9.23/9.50 984 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 9.23/9.50 985 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].
% 9.23/9.50 986 -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].
% 9.23/9.50 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(985,a,986,a)].
% 9.23/9.50 987 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].
% 9.23/9.50 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(987,a,986,a)].
% 9.23/9.50 988 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 9.23/9.50 989 -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].
% 9.23/9.50 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(988,a,989,a)].
% 9.23/9.50 990 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption].
% 9.23/9.50 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(990,a,989,a)].
% 9.23/9.50 991 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 9.23/9.50 992 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 9.23/9.50 Derived: A = A. [resolve(991,b,992,a)].
% 9.23/9.50
% 9.23/9.50 ============================== end predicate elimination =============
% 9.23/9.50
% 9.23/9.50 Auto_denials: (non-Horn, no changes).
% 9.23/9.50
% 9.23/9.50 Term ordering decisions:
% 9.23/9.50 Function symbol KB weights: tc_nat=1. tc_Int_Oint=1. tc_Complex_Ocomplex=1. c_Suc=1. c_Int_OPls=1. tc_bool=1. c_Int_OMin=1. v_i=1. v_m=1. v_a=1. c_Complex_Oii=1. hAPP=1. c_Int_Onumber__class_Onumber__of=1. tc_fun=1. c_Series_Osuminf=1. c_HOL_Ozero__class_Ozero=1.Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------