TSTP Solution File: SWV696-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV696-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 21:14:28 EDT 2022
% Result : Timeout 300.02s 300.24s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV696-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n003.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 00:20:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.25/1.75 ============================== Prover9 ===============================
% 1.25/1.75 Prover9 (32) version 2009-11A, November 2009.
% 1.25/1.75 Process 10243 was started by sandbox2 on n003.cluster.edu,
% 1.25/1.75 Thu Jun 16 00:20:57 2022
% 1.25/1.75 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10090_n003.cluster.edu".
% 1.25/1.75 ============================== end of head ===========================
% 1.25/1.75
% 1.25/1.75 ============================== INPUT =================================
% 1.25/1.75
% 1.25/1.75 % Reading from file /tmp/Prover9_10090_n003.cluster.edu
% 1.25/1.75
% 1.25/1.75 set(prolog_style_variables).
% 1.25/1.75 set(auto2).
% 1.25/1.75 % set(auto2) -> set(auto).
% 1.25/1.75 % set(auto) -> set(auto_inference).
% 1.25/1.75 % set(auto) -> set(auto_setup).
% 1.25/1.75 % set(auto_setup) -> set(predicate_elim).
% 1.25/1.75 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.25/1.75 % set(auto) -> set(auto_limits).
% 1.25/1.75 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.25/1.75 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.25/1.75 % set(auto) -> set(auto_denials).
% 1.25/1.75 % set(auto) -> set(auto_process).
% 1.25/1.75 % set(auto2) -> assign(new_constants, 1).
% 1.25/1.75 % set(auto2) -> assign(fold_denial_max, 3).
% 1.25/1.75 % set(auto2) -> assign(max_weight, "200.000").
% 1.25/1.75 % set(auto2) -> assign(max_hours, 1).
% 1.25/1.75 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.25/1.75 % set(auto2) -> assign(max_seconds, 0).
% 1.25/1.75 % set(auto2) -> assign(max_minutes, 5).
% 1.25/1.75 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.25/1.75 % set(auto2) -> set(sort_initial_sos).
% 1.25/1.75 % set(auto2) -> assign(sos_limit, -1).
% 1.25/1.75 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.25/1.75 % set(auto2) -> assign(max_megs, 400).
% 1.25/1.75 % set(auto2) -> assign(stats, some).
% 1.25/1.75 % set(auto2) -> clear(echo_input).
% 1.25/1.75 % set(auto2) -> set(quiet).
% 1.25/1.75 % set(auto2) -> clear(print_initial_clauses).
% 1.25/1.75 % set(auto2) -> clear(print_given).
% 1.25/1.75 assign(lrs_ticks,-1).
% 1.25/1.75 assign(sos_limit,10000).
% 1.25/1.75 assign(order,kbo).
% 1.25/1.75 set(lex_order_vars).
% 1.25/1.75 clear(print_given).
% 1.25/1.75
% 1.25/1.75 % formulas(sos). % not echoed (1172 formulas)
% 1.25/1.75
% 1.25/1.75 ============================== end of input ==========================
% 1.25/1.75
% 1.25/1.75 % From the command line: assign(max_seconds, 300).
% 1.25/1.75
% 1.25/1.75 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.25/1.75
% 1.25/1.75 % Formulas that are not ordinary clauses:
% 1.25/1.75
% 1.25/1.75 ============================== end of process non-clausal formulas ===
% 1.25/1.75
% 1.25/1.75 ============================== PROCESS INITIAL CLAUSES ===============
% 1.25/1.75
% 1.25/1.75 ============================== PREDICATE ELIMINATION =================
% 1.25/1.75 1 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.25/1.75 2 -class_OrderedGroup_Oab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(1,a,2,a)].
% 1.25/1.75 3 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(3,a,2,a)].
% 1.25/1.75 4 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(4,a,2,a)].
% 1.25/1.75 5 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.25/1.75 6 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 1.25/1.75 7 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 1.25/1.75 8 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 1.25/1.75 9 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 1.25/1.75 10 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 1.25/1.75 11 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 1.25/1.75 12 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 1.25/1.75 13 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 1.25/1.75 14 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(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_HOL_Oplus__class_Oplus(B,D,A)),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 1.25/1.75 15 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oplus__class_Oplus(C,D,A)) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_class__semiring_Omul__d_0) # label(axiom). [assumption].
% 1.25/1.75 16 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oplus__class_Oplus(B,C,A)),D) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 1.25/1.75 17 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Omul__1_0) # label(axiom). [assumption].
% 1.25/1.75 18 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 1.25/1.75 19 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 1.25/1.75 20 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 1.25/1.75 21 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(B,A),C),A),D) = hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) # label(cls_class__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 1.25/1.75 22 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 1.25/1.75 23 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 1.25/1.75 24 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,B,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A)),B) # label(cls_class__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 1.25/1.75 25 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A)),C) # label(cls_class__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 1.25/1.75 26 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oplus__class_Oplus(C,c_HOL_Oone__class_Oone(A),A)),B) # label(cls_class__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 1.25/1.75 27 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),B) = hAPP(c_Power_Opower__class_Opower(B,A),c_Suc(C)) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 1.25/1.75 28 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C)) = hAPP(c_Power_Opower__class_Opower(B,A),c_Suc(C)) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 1.25/1.75 29 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),hAPP(c_Power_Opower__class_Opower(B,A),D)) = hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Oplus__class_Oplus(C,D,tc_nat)) # label(cls_class__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 1.25/1.75 30 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C)) # label(cls_class__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 1.25/1.75 31 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C)) # label(cls_class__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 1.25/1.75 32 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 1.25/1.75 33 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 1.25/1.75 34 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 1.25/1.75 35 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 1.25/1.75 36 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.25/1.75 37 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.25/1.75 38 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.25/1.75 39 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.25/1.75 40 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.25/1.75 41 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),D)),hAPP(c_Power_Opower__class_Opower(C,A),D)) # label(cls_class__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 1.25/1.75 42 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.25/1.75 43 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.25/1.75 44 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.25/1.75 45 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.25/1.75 46 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat). [resolve(5,a,6,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). [resolve(5,a,7,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat). [resolve(5,a,8,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = A. [resolve(5,a,11,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(5,a,12,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(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_HOL_Oplus__class_Oplus(A,C,tc_nat)),B). [resolve(5,a,14,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oplus__class_Oplus(B,C,tc_nat)) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat). [resolve(5,a,15,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat)),C) = c_HOL_Oplus__class_Oplus(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(5,a,16,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(5,a,17,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(5,a,18,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,D,tc_nat),tc_nat). [resolve(5,a,20,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),C) = hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(5,a,21,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) = c_HOL_Oplus__class_Oplus(B,A,tc_nat). [resolve(5,a,22,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)),A). [resolve(5,a,24,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),B,tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),B). [resolve(5,a,25,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),A). [resolve(5,a,26,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)),A) = hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_Suc(B)). [resolve(5,a,27,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)) = hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_Suc(B)). [resolve(5,a,28,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C)) = hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat)). [resolve(5,a,29,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)). [resolve(5,a,30,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(5,a,32,a)].
% 1.25/1.75 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(5,a,33,a)].
% 1.25/1.75 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(5,a,34,a)].
% 1.25/1.75 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(5,a,36,a)].
% 1.25/1.75 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(5,a,37,a)].
% 1.25/1.75 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(5,a,39,a)].
% 1.25/1.75 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(5,a,40,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C)),hAPP(c_Power_Opower__class_Opower(B,tc_nat),C)). [resolve(5,a,41,a)].
% 1.25/1.75 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(5,a,44,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(5,a,45,a)].
% 1.25/1.75 47 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint). [resolve(47,a,6,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(47,a,7,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(47,a,8,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = A. [resolve(47,a,11,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(47,a,12,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(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_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint)),B). [resolve(47,a,14,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint)) = c_HOL_Oplus__class_Oplus(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(47,a,15,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint)),C) = c_HOL_Oplus__class_Oplus(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(47,a,16,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(47,a,17,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(47,a,18,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint),tc_Int_Oint). [resolve(47,a,20,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),C) = hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(47,a,21,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,A,tc_Int_Oint). [resolve(47,a,22,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)),A). [resolve(47,a,24,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),B,tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)),B). [resolve(47,a,25,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)),A). [resolve(47,a,26,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)),A) = hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Suc(B)). [resolve(47,a,27,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)) = hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Suc(B)). [resolve(47,a,28,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C)) = hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_nat)). [resolve(47,a,29,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)). [resolve(47,a,30,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(47,a,32,a)].
% 1.25/1.75 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(47,a,33,a)].
% 1.25/1.75 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(47,a,34,a)].
% 1.25/1.75 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(47,a,36,a)].
% 1.25/1.75 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(47,a,37,a)].
% 1.25/1.75 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(47,a,39,a)].
% 1.25/1.75 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(47,a,40,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C)),hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),C)). [resolve(47,a,41,a)].
% 1.25/1.75 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(47,a,44,a)].
% 1.25/1.75 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(47,a,45,a)].
% 1.25/1.75 48 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex). [resolve(48,a,6,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(48,a,7,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(48,a,8,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A. [resolve(48,a,11,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(48,a,12,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex)),B). [resolve(48,a,14,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex). [resolve(48,a,15,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex)),C) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex). [resolve(48,a,16,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(48,a,17,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(48,a,18,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(48,a,20,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C) = hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(48,a,21,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(B,A,tc_Complex_Ocomplex). [resolve(48,a,22,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)),A). [resolve(48,a,24,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),B,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)),B). [resolve(48,a,25,a)].
% 1.25/1.75 Derived: c_HOL_Oplus__class_Oplus(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)),A). [resolve(48,a,26,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)),A) = hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_Suc(B)). [resolve(48,a,27,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)) = hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_Suc(B)). [resolve(48,a,28,a)].
% 1.25/1.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)) = hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,C,tc_nat)). [resolve(48,a,29,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)). [resolve(48,a,30,a)].
% 1.25/1.75 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(48,a,32,a)].
% 1.58/1.82 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(48,a,33,a)].
% 1.58/1.82 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(48,a,34,a)].
% 1.58/1.82 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(48,a,36,a)].
% 1.58/1.82 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(48,a,37,a)].
% 1.58/1.82 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(48,a,39,a)].
% 1.58/1.82 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(48,a,40,a)].
% 1.58/1.82 Derived: hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)),hAPP(c_Power_Opower__class_Opower(B,tc_Complex_Ocomplex),C)). [resolve(48,a,41,a)].
% 1.58/1.82 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(48,a,44,a)].
% 1.58/1.82 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(48,a,45,a)].
% 1.58/1.82 49 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.58/1.82 50 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.58/1.82 51 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.58/1.82 52 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) | hBOOL(hAPP(c_lessequals(B,A),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.58/1.82 53 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.58/1.82 54 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.58/1.82 55 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.58/1.82 56 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.58/1.82 57 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OlessThan(B,A) != c_SetInterval_Oord__class_OlessThan(C,A) | B = C # label(cls_lessThan__eq__iff_0) # label(axiom). [assumption].
% 1.58/1.82 58 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.58/1.83 59 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | C = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.58/1.83 60 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.58/1.83 61 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.58/1.83 62 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.58/1.83 63 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.58/1.83 64 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.58/1.83 65 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 1.58/1.83 66 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 1.58/1.83 67 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.58/1.83 68 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.58/1.83 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(49,a,50,a)].
% 1.58/1.83 Derived: -hBOOL(hAPP(c_lessequals(A,tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)). [resolve(49,a,51,a)].
% 1.58/1.83 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(49,a,53,a)].
% 1.58/1.83 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B. [resolve(49,a,57,a)].
% 1.58/1.83 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)) | B = A. [resolve(49,a,58,a)].
% 1.58/1.83 Derived: A = B | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(49,a,62,a)].
% 1.58/1.83 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)). [resolve(49,a,64,a)].
% 1.58/1.83 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(49,a,67,a)].
% 1.58/1.83 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)). [resolve(49,a,68,a)].
% 1.58/1.83 69 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 1.58/1.83 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(69,a,50,a)].
% 1.58/1.83 Derived: -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),A)). [resolve(69,a,51,a)].
% 1.58/1.83 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(69,a,53,a)].
% 1.58/1.83 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_Int_Oint) != c_SetInterval_Oord__class_OlessThan(B,tc_Int_Oint) | A = B. [resolve(69,a,57,a)].
% 1.60/1.90 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | B = A. [resolve(69,a,58,a)].
% 1.60/1.90 Derived: A = B | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(69,a,62,a)].
% 1.60/1.90 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),A)). [resolve(69,a,64,a)].
% 1.60/1.90 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(69,a,67,a)].
% 1.60/1.90 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)). [resolve(69,a,68,a)].
% 1.60/1.90 70 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.60/1.90 71 -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].
% 1.60/1.90 72 -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].
% 1.60/1.90 73 -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].
% 1.60/1.90 74 -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(c_Power_Opower__class_Opower(B,A),C)) = hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B),A),C) # label(cls_power__one__over_0) # label(axiom). [assumption].
% 1.60/1.90 75 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B) # label(cls_class__fieldgb_Oinverse__divide_0) # label(axiom). [assumption].
% 1.60/1.90 76 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Oinverse(B,A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B) # label(cls_inverse__eq__divide_0) # label(axiom). [assumption].
% 1.60/1.90 77 -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].
% 1.60/1.90 78 -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].
% 1.60/1.90 79 -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].
% 1.60/1.90 80 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oone__class_Oone(A) | B = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_0) # label(axiom). [assumption].
% 1.60/1.90 81 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oplus__class_Oplus(B,C,A)),D) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D),A) # label(cls_add__divide__distrib_0) # label(axiom). [assumption].
% 1.60/1.90 82 -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].
% 1.60/1.90 83 -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].
% 1.60/1.90 84 -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].
% 1.60/1.90 85 -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].
% 1.60/1.90 86 -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].
% 1.60/1.90 87 -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].
% 1.60/1.90 88 -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].
% 1.60/1.90 89 -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].
% 1.60/1.90 90 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),B) # label(cls_inverse__divide_0) # label(axiom). [assumption].
% 1.60/1.90 91 -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].
% 1.60/1.90 92 -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].
% 1.60/1.90 93 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E),A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom). [assumption].
% 1.60/1.90 94 -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].
% 1.60/1.90 95 -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].
% 1.60/1.90 96 -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].
% 1.60/1.90 97 -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].
% 1.60/1.90 98 -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].
% 1.60/1.90 99 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oplus__class_Oplus(B,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D),A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oplus__class_Oplus(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A)),D) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom). [assumption].
% 1.60/1.90 100 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oplus__class_Oplus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom). [assumption].
% 1.60/1.90 101 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oinverse__class_Oinverse(B,A))),c_HOL_Oinverse__class_Oinverse(C,A)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__add_0) # label(axiom). [assumption].
% 1.60/1.90 102 -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].
% 1.60/1.90 103 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(B,A)),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__inverse_0) # label(axiom). [assumption].
% 1.60/1.90 104 -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].
% 1.60/1.90 105 -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].
% 1.60/1.90 106 -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].
% 1.60/1.90 107 -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].
% 1.60/1.90 108 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(B,A)),c_HOL_Oinverse__class_Oinverse(C,A)) # label(cls_inverse__mult__distrib_0) # label(axiom). [assumption].
% 1.60/1.90 109 -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].
% 1.60/1.90 110 -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].
% 1.60/1.90 111 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))),hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),E),C))) = hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_Power_Opower__class_Opower(B,A),D)),hAPP(c_Power_Opower__class_Opower(B,A),E)),A),C) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__divides__special_0) # label(axiom). [assumption].
% 1.60/1.90 112 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Oinverse(B,A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__divide_0) # label(axiom). [assumption].
% 1.60/1.90 113 -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].
% 1.60/1.90 114 -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].
% 1.60/1.90 115 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),hAPP(c_Power_Opower__class_Opower(B,A),D)) = hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),C)) | hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff__rev__if_1) # label(axiom). [assumption].
% 1.60/1.90 116 -class_Ring__and__Field_Ofield(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_Power_Opower__class_Opower(B,A),D)),hAPP(c_Power_Opower__class_Opower(B,A),C)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff__inverse_0) # label(axiom). [assumption].
% 1.60/1.90 117 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_Power_Opower__class_Opower(B,A),D)),hAPP(c_Power_Opower__class_Opower(C,A),D)) # label(cls_power__divide_0) # label(axiom). [assumption].
% 1.60/1.90 118 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),hAPP(c_Power_Opower__class_Opower(B,A),D)) = hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff__rev__if_0) # label(axiom). [assumption].
% 1.60/1.90 119 -class_Ring__and__Field_Ofield(A) | hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),hAPP(c_Power_Opower__class_Opower(B,A),D)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff_0) # label(axiom). [assumption].
% 1.60/1.90 120 -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].
% 1.60/1.90 121 -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].
% 1.60/1.90 122 -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].
% 1.60/1.90 123 -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].
% 1.60/1.90 124 -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].
% 1.60/1.90 125 -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].
% 1.60/1.90 126 -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].
% 1.60/1.90 127 -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].
% 1.60/1.90 128 -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].
% 1.60/1.90 129 -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].
% 1.60/1.90 130 -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].
% 1.60/1.90 131 -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].
% 1.60/1.90 132 -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].
% 1.60/1.90 133 -class_Ring__and__Field_Ofield(A) | hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),A),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_Power_Opower__class_Opower(B,A),D)),hAPP(c_Power_Opower__class_Opower(C,A),D)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__divide_0) # label(axiom). [assumption].
% 1.60/1.90 134 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_1) # label(axiom). [assumption].
% 1.60/1.90 135 -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].
% 1.60/1.90 136 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oinverse__class_Oinverse(C,A)) # label(cls_divide__inverse_0) # label(axiom). [assumption].
% 1.60/1.90 137 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oinverse__class_Oinverse(C,A)) # label(cls_class__fieldgb_Odivide__inverse_0) # label(axiom). [assumption].
% 1.60/1.90 138 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(B,A),A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),c_Int_Onumber__class_Onumber__of(B,A)) # label(cls_inverse__eq__divide__number__of_0) # label(axiom). [assumption].
% 1.60/1.90 139 -class_Ring__and__Field_Ofield(A) | c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(B,A),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(c_Power_Opower__class_Opower(B,A),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].
% 1.60/1.90 140 -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].
% 1.60/1.90 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(70,a,71,a)].
% 1.60/1.90 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(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)) = hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A),tc_Complex_Ocomplex),B). [resolve(70,a,74,a)].
% 1.60/1.90 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A). [resolve(70,a,75,a)].
% 1.60/1.90 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A). [resolve(70,a,76,a)].
% 1.60/1.90 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(70,a,77,a)].
% 1.60/1.90 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(70,a,78,a)].
% 1.60/1.90 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(70,a,79,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(70,a,80,a)].
% 1.60/1.90 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex)),C) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex). [resolve(70,a,81,a)].
% 1.60/1.90 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(70,a,82,a)].
% 1.60/1.90 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(70,a,83,a)].
% 1.60/1.90 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(70,a,84,a)].
% 1.60/1.90 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(70,a,85,a)].
% 1.60/1.90 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(70,a,87,a)].
% 1.60/1.90 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(70,a,88,a)].
% 1.60/1.90 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(70,a,89,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A). [resolve(70,a,90,a)].
% 1.60/1.90 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(70,a,91,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,92,a)].
% 1.60/1.90 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,93,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),B)),B) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,94,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) = A | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,95,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,96,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),B)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,97,a)].
% 1.60/1.90 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(70,a,98,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex)),C) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,99,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B),C,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,100,a)].
% 1.60/1.90 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex))),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,101,a)].
% 1.60/1.90 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(70,a,102,a)].
% 1.60/1.90 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,103,a)].
% 1.60/1.90 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(70,a,104,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,105,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) = A | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,106,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex))),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)). [resolve(70,a,107,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)). [resolve(70,a,108,a)].
% 1.60/1.90 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(70,a,109,a)].
% 1.60/1.90 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(70,a,110,a)].
% 1.60/1.90 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),B))) = hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),D)),tc_Complex_Ocomplex),B) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,111,a)].
% 1.60/1.90 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(70,a,113,a)].
% 1.60/1.90 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(70,a,114,a)].
% 1.60/1.90 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)) = hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A),tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),B)) | hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,115,a)].
% 1.60/1.90 Derived: hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,116,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)),hAPP(c_Power_Opower__class_Opower(B,tc_Complex_Ocomplex),C)). [resolve(70,a,117,a)].
% 1.60/1.90 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)) = hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,118,a)].
% 1.60/1.90 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,119,a)].
% 1.60/1.90 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(70,a,120,a)].
% 1.60/1.90 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(70,a,121,a)].
% 1.60/1.90 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(70,a,122,a)].
% 1.60/1.90 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(70,a,123,a)].
% 1.60/1.90 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(70,a,124,a)].
% 1.60/1.90 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(70,a,125,a)].
% 1.60/1.90 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(70,a,126,a)].
% 1.73/1.99 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(70,a,127,a)].
% 1.73/1.99 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(70,a,128,a)].
% 1.73/1.99 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(70,a,131,a)].
% 1.73/1.99 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(70,a,132,a)].
% 1.73/1.99 Derived: hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)),hAPP(c_Power_Opower__class_Opower(B,tc_Complex_Ocomplex),C)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(70,a,133,a)].
% 1.73/1.99 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(70,a,134,a)].
% 1.73/1.99 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(70,a,135,a)].
% 1.73/1.99 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)). [resolve(70,a,136,a)].
% 1.73/1.99 Derived: c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),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(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),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(70,a,139,a)].
% 1.73/1.99 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(70,a,140,a)].
% 1.73/1.99 141 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.73/1.99 142 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.73/1.99 143 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.73/1.99 144 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.73/1.99 145 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(D,B,A),A),c_HOL_Oplus__class_Oplus(D,C,A))) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.73/1.99 146 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(B,D,A))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.73/1.99 147 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,D,A),A),c_HOL_Oplus__class_Oplus(C,D,A))) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.73/1.99 148 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,C,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.73/1.99 149 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.73/1.99 150 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,A),A),c_HOL_Oplus__class_Oplus(D,C,A))) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.73/1.99 151 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.73/1.99 152 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,A),A),c_HOL_Oplus__class_Oplus(C,D,A))) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.73/1.99 153 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.73/1.99 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(141,a,142,a)].
% 1.73/1.99 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(141,a,143,a)].
% 1.73/1.99 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)). [resolve(141,a,144,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat))). [resolve(141,a,145,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(141,a,146,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))). [resolve(141,a,147,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(141,a,148,a)].
% 1.73/1.99 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(141,a,149,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat))). [resolve(141,a,150,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(141,a,151,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))). [resolve(141,a,152,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(141,a,153,a)].
% 1.73/1.99 154 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.73/1.99 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(154,a,142,a)].
% 1.73/1.99 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(154,a,143,a)].
% 1.73/1.99 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)). [resolve(154,a,144,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint))). [resolve(154,a,145,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)). [resolve(154,a,146,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))). [resolve(154,a,147,a)].
% 1.73/1.99 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(154,a,148,a)].
% 1.73/1.99 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(154,a,149,a)].
% 1.73/2.04 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint))). [resolve(154,a,150,a)].
% 1.73/2.04 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)). [resolve(154,a,151,a)].
% 1.73/2.04 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))). [resolve(154,a,152,a)].
% 1.73/2.04 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(154,a,153,a)].
% 1.73/2.04 155 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.73/2.04 156 -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)),c_HOL_Oplus__class_Oplus(C,D,A)) = c_HOL_Oplus__class_Oplus(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),A) # label(cls_right__distrib__number__of_0) # label(axiom). [assumption].
% 1.73/2.04 157 -class_Ring__and__Field_Osemiring(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),E,A),A) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oplus__class_Oplus(B,D,A)),C),E,A) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 1.73/2.04 158 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_Int_Onumber__class_Onumber__of(D,A)) = c_HOL_Oplus__class_Oplus(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)),A) # label(cls_left__distrib__number__of_0) # label(axiom). [assumption].
% 1.73/2.04 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),D,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat)),B),D,tc_nat). [resolve(155,a,157,a)].
% 1.73/2.04 159 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.73/2.04 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint)),B),D,tc_Int_Oint). [resolve(159,a,157,a)].
% 1.73/2.04 160 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.73/2.04 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex)),B),D,tc_Complex_Ocomplex). [resolve(160,a,157,a)].
% 1.73/2.04 161 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 1.73/2.04 162 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_add__cancel__21_1) # label(axiom). [assumption].
% 1.73/2.04 163 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) != c_HOL_Oplus__class_Oplus(C,E,A) | c_HOL_Oplus__class_Oplus(B,D,A) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 1.73/2.04 164 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Oplus__class_Oplus(B,C,A)),c_HOL_Oplus__class_Oplus(D,E,A)) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E),A) # label(cls_Deriv_Oadd__diff__add_0) # label(axiom). [assumption].
% 1.73/2.04 165 -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) | -hBOOL(hAPP(c_lessequals(E,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),E)) # label(cls_setsum__diff__nat__ivl_0) # label(axiom). [assumption].
% 1.73/2.04 166 -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].
% 1.73/2.04 167 -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].
% 1.73/2.04 168 -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].
% 1.73/2.04 169 -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].
% 1.73/2.04 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) = D. [resolve(161,a,163,a)].
% 1.73/2.04 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint)),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint)) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),D),tc_Int_Oint). [resolve(161,a,164,a)].
% 1.73/2.04 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) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)). [resolve(161,a,165,a)].
% 1.73/2.04 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(161,a,166,a)].
% 1.73/2.04 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(161,a,167,a)].
% 1.73/2.04 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),C) | A = B. [resolve(161,a,168,a)].
% 1.73/2.04 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(161,a,169,a)].
% 1.73/2.04 170 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 1.73/2.04 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(B,D,tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) = D. [resolve(170,a,163,a)].
% 1.81/2.07 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex)),c_HOL_Oplus__class_Oplus(C,D,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D),tc_Complex_Ocomplex). [resolve(170,a,164,a)].
% 1.81/2.07 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) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)). [resolve(170,a,165,a)].
% 1.81/2.07 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(170,a,166,a)].
% 1.81/2.07 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(170,a,167,a)].
% 1.81/2.07 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(170,a,168,a)].
% 1.81/2.07 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(170,a,169,a)].
% 1.81/2.07 171 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.81/2.07 172 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 1.81/2.07 173 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 1.81/2.07 174 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 1.81/2.07 175 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 1.81/2.07 176 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 1.81/2.07 177 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 1.81/2.07 178 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 1.81/2.07 179 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 1.81/2.07 180 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.81/2.07 181 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 1.81/2.07 182 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.81/2.07 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(171,a,173,a)].
% 1.81/2.07 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(171,a,174,a)].
% 1.81/2.07 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(171,a,175,a)].
% 1.81/2.07 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(171,a,176,a)].
% 1.81/2.07 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(171,a,177,a)].
% 1.81/2.07 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(171,a,178,a)].
% 1.81/2.07 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(171,a,179,a)].
% 1.81/2.07 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(171,a,180,a)].
% 1.81/2.07 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(171,a,181,a)].
% 1.84/2.09 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(171,a,182,a)].
% 1.84/2.09 183 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.84/2.09 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(183,a,173,a)].
% 1.84/2.09 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(183,a,174,a)].
% 1.84/2.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(183,a,175,a)].
% 1.84/2.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(183,a,176,a)].
% 1.84/2.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(183,a,177,a)].
% 1.84/2.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(183,a,178,a)].
% 1.84/2.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(183,a,179,a)].
% 1.84/2.09 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(183,a,180,a)].
% 1.84/2.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(183,a,181,a)].
% 1.84/2.09 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(183,a,182,a)].
% 1.84/2.09 184 class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) # label(axiom). [assumption].
% 1.84/2.09 185 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A) = B # label(cls_inverse__inverse__eq_0) # label(axiom). [assumption].
% 1.84/2.09 186 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__zero__imp__zero_0) # label(axiom). [assumption].
% 1.84/2.09 187 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_0) # label(axiom). [assumption].
% 1.84/2.09 188 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A) = B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__inverse__eq_0) # label(axiom). [assumption].
% 1.84/2.09 189 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_1) # label(axiom). [assumption].
% 1.84/2.09 190 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oinverse__class_Oinverse(C,A) | B = C | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__imp__eq_0) # label(axiom). [assumption].
% 1.84/2.09 191 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Oone__class_Oone(A) | c_HOL_Oinverse__class_Oinverse(B,A) = C # label(cls_inverse__unique_0) # label(axiom). [assumption].
% 1.84/2.09 192 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oinverse__class_Oinverse(C,A) | B = C # label(cls_inverse__eq__iff__eq_0) # label(axiom). [assumption].
% 1.84/2.09 193 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(B,A)),c_HOL_Oplus__class_Oplus(B,C,A))),c_HOL_Oinverse__class_Oinverse(C,A)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_division__ring__inverse__add_0) # label(axiom). [assumption].
% 1.84/2.09 194 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oinverse__class_Oinverse(B,A)) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_right__inverse_0) # label(axiom). [assumption].
% 1.84/2.09 195 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(B,A)),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_left__inverse_0) # label(axiom). [assumption].
% 1.84/2.09 196 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(hAPP(c_Power_Opower__class_Opower(B,A),C),A) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),A),C) # label(cls_power__inverse_0) # label(axiom). [assumption].
% 1.84/2.09 197 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(C,A)),c_HOL_Oinverse__class_Oinverse(B,A)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__mult__distrib_0) # label(axiom). [assumption].
% 1.84/2.09 198 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(hAPP(c_Power_Opower__class_Opower(B,A),C),A) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),A),C) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__inverse_0) # label(axiom). [assumption].
% 1.84/2.09 199 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__1_0) # label(axiom). [assumption].
% 1.84/2.09 200 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Oinverse__class_Oinverse(B,A)),c_HOL_Oinverse__class_Oinverse(C,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(B,A)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),B))),c_HOL_Oinverse__class_Oinverse(C,A)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_division__ring__inverse__diff_0) # label(axiom). [assumption].
% 1.84/2.09 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(184,a,185,a)].
% 1.84/2.09 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(184,a,186,a)].
% 1.84/2.09 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(184,a,188,a)].
% 1.84/2.09 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(184,a,189,a)].
% 1.84/2.09 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex) | A = B | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(184,a,190,a)].
% 1.84/2.09 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) = B. [resolve(184,a,191,a)].
% 1.84/2.09 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex) | A = B. [resolve(184,a,192,a)].
% 1.84/2.09 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex))),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(184,a,193,a)].
% 1.84/2.09 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(184,a,194,a)].
% 1.84/2.09 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B). [resolve(184,a,196,a)].
% 1.84/2.09 Derived: c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(184,a,197,a)].
% 1.84/2.09 Derived: c_HOL_Oinverse__class_Oinverse(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(184,a,198,a)].
% 1.84/2.09 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(184,a,199,a)].
% 1.84/2.12 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),A))),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(184,a,200,a)].
% 1.84/2.12 201 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.84/2.12 202 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 1.84/2.12 203 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 1.84/2.12 204 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 1.84/2.12 205 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 1.84/2.12 206 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A))) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.84/2.12 207 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.84/2.12 208 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),c_Suc(D)),A),hAPP(c_Power_Opower__class_Opower(C,A),c_Suc(D)))) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 1.84/2.12 209 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_Suc(C)) != hAPP(c_Power_Opower__class_Opower(D,A),c_Suc(C)) | B = D | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 1.84/2.12 210 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),D),A),hAPP(c_Power_Opower__class_Opower(C,A),D))) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 1.84/2.12 211 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(D,A),B),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 1.84/2.12 212 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(D,A),B),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 1.84/2.12 213 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 1.84/2.12 214 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A))) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 1.84/2.12 215 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 1.84/2.12 216 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),c_Suc(C)),A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.84/2.12 217 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 1.84/2.12 218 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 1.84/2.12 219 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 1.84/2.12 220 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),A))) # label(cls_of__nat__fact__gt__zero_0) # label(axiom). [assumption].
% 1.84/2.12 221 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),A))) # label(cls_of__nat__fact__ge__zero_0) # label(axiom). [assumption].
% 1.84/2.12 222 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C)),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 1.84/2.12 223 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(c_Power_Opower__class_Opower(B,A),C) != hAPP(c_Power_Opower__class_Opower(D,A),C) | B = D | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 1.84/2.12 224 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.84/2.12 225 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.84/2.12 226 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 1.84/2.12 227 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.84/2.12 228 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 1.84/2.12 229 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.84/2.12 230 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.84/2.12 231 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.84/2.12 232 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.84/2.12 233 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 1.84/2.12 234 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_power__mono_0) # label(axiom). [assumption].
% 1.84/2.12 235 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(c_Power_Opower__class_Opower(B,A),c_Suc(C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.84/2.12 236 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.84/2.12 237 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.84/2.12 238 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.84/2.12 239 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(c_Power_Opower__class_Opower(B,A),C) != hAPP(c_Power_Opower__class_Opower(B,A),D) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.84/2.12 240 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(D,A),B),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.84/2.12 241 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.84/2.12 242 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(D,A),B),A),hAPP(c_Power_Opower__class_Opower(D,A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.84/2.12 243 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),hAPP(c_Power_Opower__class_Opower(B,A),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.84/2.12 244 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.84/2.12 245 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.84/2.12 246 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.84/2.12 247 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D),tc_nat),tc_nat,A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(C,A)),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),E)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(E,B,C,A),tc_nat),C)) # label(cls_real__setsum__nat__ivl__bounded2_0) # label(axiom). [assumption].
% 1.84/2.12 248 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D),tc_nat),tc_nat,A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(C,A)),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),E)) | -hBOOL(hAPP(c_lessequals(hAPP(B,c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(E,B,C,A)),A),E)) # label(cls_real__setsum__nat__ivl__bounded2_1) # label(axiom). [assumption].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(201,a,202,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(201,a,203,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(201,a,204,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(201,a,205,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))). [resolve(201,a,206,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(201,a,207,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_Suc(C)),tc_nat),hAPP(c_Power_Opower__class_Opower(B,tc_nat),c_Suc(C)))). [resolve(201,a,208,a)].
% 1.84/2.12 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_Suc(B)) != hAPP(c_Power_Opower__class_Opower(C,tc_nat),c_Suc(B)) | A = C | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(201,a,209,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),C),tc_nat),hAPP(c_Power_Opower__class_Opower(B,tc_nat),C))). [resolve(201,a,210,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(C,tc_nat),A),tc_nat),hAPP(c_Power_Opower__class_Opower(C,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)). [resolve(201,a,211,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(201,a,213,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat))). [resolve(201,a,214,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(201,a,215,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_Suc(B)),tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(201,a,216,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(C,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(201,a,217,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(201,a,218,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(201,a,219,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_nat))). [resolve(201,a,220,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_nat))). [resolve(201,a,221,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(201,a,222,a)].
% 1.84/2.12 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),B) != hAPP(c_Power_Opower__class_Opower(C,tc_nat),B) | A = C | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(201,a,223,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(201,a,224,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(201,a,225,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(201,a,226,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(201,a,227,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(201,a,228,a)].
% 1.84/2.12 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(201,a,229,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(201,a,230,a)].
% 1.84/2.12 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(201,a,231,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(201,a,232,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(201,a,233,a)].
% 1.84/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(C,tc_nat),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(201,a,234,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_Suc(B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(201,a,235,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(201,a,236,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(201,a,237,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(201,a,238,a)].
% 1.88/2.12 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),B) != hAPP(c_Power_Opower__class_Opower(A,tc_nat),C) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | B = C. [resolve(201,a,239,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(C,tc_nat),A),tc_nat),hAPP(c_Power_Opower__class_Opower(C,tc_nat),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)). [resolve(201,a,240,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(201,a,241,a)].
% 1.88/2.12 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(201,a,244,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(201,a,245,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_lessequals(c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),tc_nat),tc_nat,tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(D,A,B,tc_nat),tc_nat),B)). [resolve(201,a,247,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_lessequals(c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),tc_nat),tc_nat,tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),D)) | -hBOOL(hAPP(c_lessequals(hAPP(A,c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(D,A,B,tc_nat)),tc_nat),D)). [resolve(201,a,248,a)].
% 1.88/2.12 249 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.88/2.12 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))). [resolve(249,a,202,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(249,a,203,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,204,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,205,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint))). [resolve(249,a,206,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(249,a,207,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Suc(C)),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),c_Suc(C)))). [resolve(249,a,208,a)].
% 1.88/2.12 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Suc(B)) != hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),c_Suc(B)) | A = C | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,209,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),C))). [resolve(249,a,210,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),A),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),C)). [resolve(249,a,211,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,213,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint))). [resolve(249,a,214,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(249,a,215,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Suc(B)),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,216,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(249,a,217,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,218,a)].
% 1.88/2.12 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,219,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_Int_Oint))). [resolve(249,a,220,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_Int_Oint))). [resolve(249,a,221,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,222,a)].
% 1.88/2.13 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B) != hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B) | A = C | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,223,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(249,a,224,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint))). [resolve(249,a,225,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,226,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(249,a,227,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(249,a,228,a)].
% 1.88/2.13 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(249,a,229,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(249,a,230,a)].
% 1.88/2.13 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(249,a,231,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,232,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,233,a)].
% 1.88/2.13 Derived: hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(249,a,234,a)].
% 1.90/2.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Suc(B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(249,a,235,a)].
% 1.90/2.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))). [resolve(249,a,236,a)].
% 1.90/2.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(249,a,237,a)].
% 1.90/2.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(249,a,238,a)].
% 1.90/2.15 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B) != hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | B = C. [resolve(249,a,239,a)].
% 1.90/2.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),A),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(C,tc_Int_Oint),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),C)). [resolve(249,a,240,a)].
% 1.90/2.15 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(249,a,241,a)].
% 1.90/2.15 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(249,a,244,a)].
% 1.90/2.15 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint))). [resolve(249,a,245,a)].
% 1.90/2.15 Derived: hBOOL(hAPP(c_lessequals(c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),tc_nat),tc_nat,tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(D,A,B,tc_Int_Oint),tc_nat),B)). [resolve(249,a,247,a)].
% 1.90/2.15 Derived: hBOOL(hAPP(c_lessequals(c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),tc_nat),tc_nat,tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(hAPP(A,c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1(D,A,B,tc_Int_Oint)),tc_Int_Oint),D)). [resolve(249,a,248,a)].
% 1.90/2.15 250 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 1.90/2.15 251 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_1) # label(axiom). [assumption].
% 1.90/2.15 252 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_0) # label(axiom). [assumption].
% 1.90/2.15 253 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 1.90/2.15 254 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__right__le__one__le_0) # label(axiom). [assumption].
% 1.90/2.15 255 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__left__le__one__le_0) # label(axiom). [assumption].
% 1.90/2.15 256 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_3) # label(axiom). [assumption].
% 1.90/2.15 257 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq__number__of_1) # label(axiom). [assumption].
% 1.90/2.15 258 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__less__power__eq__number__of_2) # label(axiom). [assumption].
% 1.90/2.15 259 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) # label(cls_zero__less__power__eq__number__of_3) # label(axiom). [assumption].
% 1.90/2.15 260 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_0) # label(axiom). [assumption].
% 1.90/2.15 261 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__power__iff_1) # label(axiom). [assumption].
% 1.90/2.15 262 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq_1) # label(axiom). [assumption].
% 1.90/2.15 263 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_3) # label(axiom). [assumption].
% 1.90/2.15 264 -class_Ring__and__Field_Oordered__idom(A) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_0) # label(axiom). [assumption].
% 1.90/2.16 265 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat)))) # label(cls_zero__less__power__eq_3) # label(axiom). [assumption].
% 1.90/2.16 266 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),B))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__less__power__eq_2) # label(axiom). [assumption].
% 1.90/2.16 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(250,a,252,a)].
% 1.90/2.16 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(250,a,254,a)].
% 1.90/2.16 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(250,a,255,a)].
% 1.90/2.16 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(250,a,256,a)].
% 1.90/2.16 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(250,a,257,a)].
% 1.90/2.16 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(250,a,258,a)].
% 1.90/2.16 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)))). [resolve(250,a,259,a)].
% 1.90/2.16 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(250,a,260,a)].
% 1.90/2.16 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(250,a,262,a)].
% 1.90/2.16 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(250,a,263,a)].
% 1.90/2.16 Derived: -hBOOL(hAPP(c_lessequals(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(250,a,264,a)].
% 1.90/2.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat)))). [resolve(250,a,265,a)].
% 1.90/2.18 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(250,a,266,a)].
% 1.90/2.18 267 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.90/2.18 268 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 1.90/2.18 269 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 1.90/2.18 270 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(B,B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom). [assumption].
% 1.90/2.18 271 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom). [assumption].
% 1.90/2.18 272 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,B,A))) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 1.90/2.18 273 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,B,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 1.90/2.18 274 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,B,A))) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 1.90/2.18 275 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(B,B,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 1.90/2.18 276 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 1.90/2.18 277 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 1.90/2.18 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(267,a,270,a)].
% 1.90/2.18 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint))). [resolve(267,a,272,a)].
% 1.97/2.26 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint))). [resolve(267,a,274,a)].
% 1.97/2.26 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(267,a,276,a)].
% 1.97/2.26 278 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 1.97/2.26 279 -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].
% 1.97/2.26 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(278,a,279,a)].
% 1.97/2.26 280 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption].
% 1.97/2.26 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(280,a,279,a)].
% 1.97/2.26 281 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.97/2.26 282 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oplus__class_Oplus(B,C,A)),D) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D),A) # label(cls_divide_Oadd_0) # label(axiom). [assumption].
% 1.97/2.26 283 -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].
% 1.97/2.26 284 -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].
% 1.97/2.26 285 -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].
% 1.97/2.26 286 -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].
% 1.97/2.26 287 -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].
% 1.97/2.26 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(281,a,284,a)].
% 1.97/2.26 288 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.97/2.26 289 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 2.04/2.29 290 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 2.04/2.29 291 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 2.04/2.29 292 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(B,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 2.04/2.29 293 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 2.04/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(288,a,289,a)].
% 2.04/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(288,a,290,a)].
% 2.04/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(288,a,291,a)].
% 2.04/2.29 294 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.04/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(294,a,289,a)].
% 2.04/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(294,a,290,a)].
% 2.04/2.29 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(294,a,291,a)].
% 2.04/2.29 295 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.04/2.29 296 -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].
% 2.04/2.29 297 -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].
% 2.04/2.29 298 -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(c_Power_Opower__class_Opower(B,A),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].
% 2.04/2.29 299 -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(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),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].
% 2.04/2.29 300 -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(c_Power_Opower__class_Opower(C,A),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].
% 2.04/2.29 301 -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(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),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].
% 2.04/2.29 302 -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(c_Power_Opower__class_Opower(B,A),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 2.04/2.29 303 -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(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 2.04/2.29 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(295,a,296,a)].
% 2.04/2.29 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(295,a,297,a)].
% 2.04/2.29 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(295,a,298,a)].
% 2.04/2.29 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),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(295,a,299,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(B,tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(295,a,300,a)].
% 2.04/2.29 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(295,a,301,a)].
% 2.04/2.29 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(c_Power_Opower__class_Opower(A,tc_nat),B) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(295,a,302,a)].
% 2.04/2.29 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(295,a,303,a)].
% 2.04/2.29 304 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.04/2.29 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(304,a,296,a)].
% 2.04/2.29 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,297,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,298,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),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(304,a,299,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,300,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(304,a,301,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(A,tc_Int_Oint),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,302,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,303,a)].
% 2.04/2.29 305 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.04/2.29 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(305,a,296,a)].
% 2.04/2.29 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(305,a,297,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(305,a,298,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),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(305,a,299,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(B,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(305,a,300,a)].
% 2.04/2.29 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(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(305,a,301,a)].
% 2.04/2.32 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(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(305,a,302,a)].
% 2.04/2.32 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(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(305,a,303,a)].
% 2.04/2.32 306 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 2.04/2.32 307 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != c_HOL_Oplus__class_Oplus(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 2.04/2.32 308 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 2.04/2.32 309 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) != c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 2.04/2.32 310 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) != c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 2.04/2.32 311 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 2.04/2.32 312 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 2.04/2.32 313 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 2.04/2.32 314 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) != c_HOL_Oplus__class_Oplus(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E),A) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 2.04/2.32 315 -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].
% 2.04/2.32 316 -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].
% 2.13/2.37 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(306,a,307,a)].
% 2.13/2.37 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(306,a,308,a)].
% 2.13/2.37 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) | B = D | A = C. [resolve(306,a,309,a)].
% 2.13/2.37 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C. [resolve(306,a,313,a)].
% 2.13/2.37 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D),tc_Int_Oint) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(306,a,314,a)].
% 2.13/2.37 317 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 2.13/2.37 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(317,a,307,a)].
% 2.13/2.37 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(317,a,308,a)].
% 2.13/2.37 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | B = D | A = C. [resolve(317,a,309,a)].
% 2.13/2.37 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C. [resolve(317,a,313,a)].
% 2.13/2.37 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D),tc_Complex_Ocomplex) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(317,a,314,a)].
% 2.13/2.37 318 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.13/2.37 319 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 2.13/2.37 320 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 2.13/2.37 321 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.13/2.37 322 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.13/2.37 323 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.13/2.37 324 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 2.13/2.37 325 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 2.13/2.37 326 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 2.13/2.37 327 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 2.13/2.37 328 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 2.13/2.37 329 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 2.13/2.37 330 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 2.13/2.37 331 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 2.13/2.37 332 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 2.13/2.37 333 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 2.13/2.37 334 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 2.13/2.37 335 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 2.13/2.37 336 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 2.13/2.37 337 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 2.13/2.37 338 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 2.13/2.37 339 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(323,a,324,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(323,a,325,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(323,a,326,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))). [resolve(323,a,327,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(323,a,328,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(323,a,329,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))). [resolve(323,a,330,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(323,a,331,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(323,a,332,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(323,a,333,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))). [resolve(323,a,335,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A))). [resolve(323,a,336,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(323,a,337,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(323,a,338,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(323,a,339,a)].
% 2.13/2.37 340 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(340,a,324,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(340,a,325,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(340,a,326,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C))). [resolve(340,a,327,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))). [resolve(340,a,328,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(340,a,329,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C))). [resolve(340,a,330,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))). [resolve(340,a,331,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(340,a,332,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(340,a,333,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(340,a,335,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A))). [resolve(340,a,336,a)].
% 2.13/2.37 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(340,a,337,a)].
% 2.18/2.43 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(340,a,338,a)].
% 2.18/2.43 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)). [resolve(340,a,339,a)].
% 2.18/2.43 341 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.18/2.43 342 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(B,D,A))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 2.18/2.43 343 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,C,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 2.18/2.43 344 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(D,E,A))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 2.18/2.43 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(341,a,344,a)].
% 2.18/2.43 345 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.18/2.43 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(345,a,344,a)].
% 2.18/2.43 346 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.18/2.43 347 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(B,C,tc_nat),A) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 2.18/2.43 348 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 2.18/2.43 349 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__mult_0) # label(axiom). [assumption].
% 2.18/2.43 350 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Power_Opower__class_Opower(B,tc_nat),C),A) = hAPP(c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),C) # label(cls_of__nat__power_0) # label(axiom). [assumption].
% 2.18/2.43 351 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 2.18/2.43 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(346,a,347,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(346,a,348,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(346,a,349,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat) = hAPP(c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),B). [resolve(346,a,350,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(346,a,351,a)].
% 2.18/2.45 352 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint). [resolve(352,a,347,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint). [resolve(352,a,348,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)). [resolve(352,a,349,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_Int_Oint) = hAPP(c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint),B). [resolve(352,a,350,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(352,a,351,a)].
% 2.18/2.45 353 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(353,a,347,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(353,a,348,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)). [resolve(353,a,349,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_Complex_Ocomplex) = hAPP(c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B). [resolve(353,a,350,a)].
% 2.18/2.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(353,a,351,a)].
% 2.18/2.45 354 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 2.18/2.45 355 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(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].
% 2.18/2.45 356 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(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),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 2.18/2.45 357 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C),A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 2.18/2.45 358 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(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].
% 2.18/2.45 359 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 2.18/2.45 360 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 2.18/2.45 361 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 2.18/2.45 362 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 2.18/2.45 363 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 2.18/2.45 364 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C),A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 2.18/2.45 365 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(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].
% 2.18/2.45 366 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oplus__class_Oplus(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].
% 2.18/2.45 367 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 2.18/2.45 368 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 2.18/2.45 369 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 2.18/2.45 370 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 2.18/2.45 371 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 2.18/2.45 372 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 2.18/2.45 373 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom). [assumption].
% 2.18/2.45 374 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 2.18/2.45 375 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 2.18/2.45 376 -class_Ring__and__Field_Oordered__ring__strict(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 2.18/2.45 377 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 2.18/2.45 378 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 2.18/2.45 379 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 2.18/2.45 380 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 2.18/2.45 381 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 2.18/2.45 382 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 2.18/2.45 383 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 2.18/2.45 384 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 2.18/2.45 385 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B))) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 2.18/2.45 386 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C),A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_1) # label(axiom). [assumption].
% 2.18/2.45 387 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_0) # label(axiom). [assumption].
% 2.18/2.45 388 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 2.18/2.45 389 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 2.18/2.45 390 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 2.18/2.45 391 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 2.18/2.45 392 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 2.18/2.45 393 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 2.18/2.45 394 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 2.18/2.45 395 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),B)) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 2.18/2.45 396 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 2.18/2.45 397 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 2.18/2.45 398 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 2.18/2.45 399 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 2.18/2.45 400 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 2.18/2.45 401 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 2.18/2.45 402 -class_Ring__and__Field_Oordered__ring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 2.18/2.45 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(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(354,a,355,a)].
% 2.18/2.45 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(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),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,356,a)].
% 2.18/2.45 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(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),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,357,a)].
% 2.18/2.45 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(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(354,a,358,a)].
% 2.18/2.45 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(354,a,359,a)].
% 2.18/2.45 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,361,a)].
% 2.18/2.45 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,362,a)].
% 2.18/2.45 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A),tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,363,a)].
% 2.18/2.45 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(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),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,364,a)].
% 2.18/2.45 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(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(354,a,365,a)].
% 2.18/2.45 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(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(354,a,366,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(354,a,367,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(354,a,368,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(354,a,369,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(354,a,370,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(354,a,371,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(354,a,372,a)].
% 2.18/2.46 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(354,a,373,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,374,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(354,a,375,a)].
% 2.18/2.46 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,376,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(354,a,377,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(354,a,378,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(354,a,380,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A))). [resolve(354,a,381,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,383,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(354,a,384,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A))). [resolve(354,a,385,a)].
% 2.18/2.46 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(354,a,386,a)].
% 2.18/2.46 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(354,a,387,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,389,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,390,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,392,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,393,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,396,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)). [resolve(354,a,400,a)].
% 2.18/2.46 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(354,a,402,a)].
% 2.28/2.53 403 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.28/2.53 404 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 2.28/2.53 405 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 2.28/2.53 406 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.28/2.53 407 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.28/2.53 408 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oplus__class_Oplus(B,C,A)),D) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 2.28/2.53 409 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.28/2.53 410 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.28/2.53 411 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 2.28/2.53 412 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oplus__class_Oplus(B,C,A)),D) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult_Oadd__left_0) # label(axiom). [assumption].
% 2.28/2.53 413 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oplus__class_Oplus(B,C,A)),D) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__left_Oadd_0) # label(axiom). [assumption].
% 2.28/2.53 414 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oplus__class_Oplus(C,D,A)) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult_Oadd__right_0) # label(axiom). [assumption].
% 2.28/2.53 415 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oplus__class_Oplus(C,D,A)) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__right_Oadd_0) # label(axiom). [assumption].
% 2.28/2.53 416 -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].
% 2.28/2.53 417 -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].
% 2.28/2.53 418 -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].
% 2.28/2.54 419 -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)) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(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),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)),A) # label(cls_mult_Oprod__diff__prod_0) # label(axiom). [assumption].
% 2.28/2.54 420 -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].
% 2.28/2.54 421 -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].
% 2.28/2.54 422 -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].
% 2.28/2.54 423 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 2.28/2.54 424 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 2.28/2.54 425 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 2.28/2.54 426 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 2.28/2.54 427 -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].
% 2.28/2.54 428 -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].
% 2.28/2.54 429 -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].
% 2.28/2.54 430 -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].
% 2.28/2.54 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(411,a,416,a)].
% 2.28/2.56 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(411,a,417,a)].
% 2.28/2.56 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)) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(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),tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)),tc_Complex_Ocomplex). [resolve(411,a,419,a)].
% 2.28/2.56 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(411,a,420,a)].
% 2.28/2.56 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(411,a,421,a)].
% 2.28/2.56 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(411,a,427,a)].
% 2.28/2.56 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(411,a,429,a)].
% 2.28/2.56 431 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.28/2.56 432 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_mult__1__right_0) # label(axiom). [assumption].
% 2.28/2.56 433 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1__left_0) # label(axiom). [assumption].
% 2.28/2.56 434 -class_OrderedGroup_Omonoid__mult(A) | hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(B,A),C),A),D) # label(cls_power__mult_0) # label(axiom). [assumption].
% 2.28/2.56 435 -class_OrderedGroup_Omonoid__mult(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),A),B) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 2.28/2.56 436 -class_OrderedGroup_Omonoid__mult(A) | hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(C)),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D))),B) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_lemma__realpow__diff_0) # label(axiom). [assumption].
% 2.28/2.56 437 -class_OrderedGroup_Omonoid__mult(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),B) # label(cls_power__Suc2_0) # label(axiom). [assumption].
% 2.28/2.56 438 -class_OrderedGroup_Omonoid__mult(A) | hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Oplus__class_Oplus(C,D,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),hAPP(c_Power_Opower__class_Opower(B,A),D)) # label(cls_power__add_0) # label(axiom). [assumption].
% 2.28/2.56 439 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C)) # label(cls_power__commutes_0) # label(axiom). [assumption].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(A,tc_nat),B),tc_nat),C). [resolve(431,a,434,a)].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A) = c_HOL_Oone__class_Oone(tc_nat). [resolve(431,a,435,a)].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(B)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(431,a,436,a)].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)),A). [resolve(431,a,437,a)].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Power_Opower__class_Opower(A,tc_nat),B)),hAPP(c_Power_Opower__class_Opower(A,tc_nat),C)). [resolve(431,a,438,a)].
% 2.28/2.56 440 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B),tc_Int_Oint),C). [resolve(440,a,434,a)].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(440,a,435,a)].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(B)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(440,a,436,a)].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)),A). [resolve(440,a,437,a)].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B)),hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),C)). [resolve(440,a,438,a)].
% 2.28/2.56 441 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C). [resolve(441,a,434,a)].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(441,a,435,a)].
% 2.28/2.56 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(B)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(441,a,436,a)].
% 2.36/2.61 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)),A). [resolve(441,a,437,a)].
% 2.36/2.61 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,C,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B)),hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),C)). [resolve(441,a,438,a)].
% 2.36/2.61 442 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.36/2.61 443 -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].
% 2.36/2.61 444 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),D)),hAPP(c_Power_Opower__class_Opower(C,A),D)) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 2.36/2.61 445 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.36/2.61 446 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.36/2.61 447 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 2.36/2.61 448 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A),A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C),F,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),c_HOL_Oplus__class_Oplus(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].
% 2.36/2.61 449 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)),E),F,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),B,A),A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E),F,A))) # label(cls_less__add__iff2_0) # label(axiom). [assumption].
% 2.36/2.61 450 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A),A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C),F,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C),D,A),A),F)) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 2.36/2.61 451 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D),E,A),A),F)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),E,A),A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),F,A))) # label(cls_less__add__iff1_0) # label(axiom). [assumption].
% 2.36/2.61 452 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A),A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C),F,A))) | -hBOOL(hAPP(c_lessequals(D,A),c_HOL_Oplus__class_Oplus(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].
% 2.36/2.61 453 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)),E),F,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),B,A),A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E),F,A))) # label(cls_le__add__iff2_0) # label(axiom). [assumption].
% 2.36/2.61 454 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A),A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C),F,A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C),D,A),A),F)) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 2.36/2.61 455 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D),E,A),A),F)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),E,A),A),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),F,A))) # label(cls_le__add__iff1_0) # label(axiom). [assumption].
% 2.36/2.61 456 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 2.36/2.61 457 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 2.36/2.61 458 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 2.36/2.61 459 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),B)) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 2.36/2.61 460 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),C)) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 2.36/2.61 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B),E,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(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(447,a,448,a)].
% 2.36/2.61 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(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))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),A,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D),E,tc_Int_Oint))). [resolve(447,a,449,a)].
% 2.36/2.61 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B),E,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B),C,tc_Int_Oint),tc_Int_Oint),E)). [resolve(447,a,450,a)].
% 2.36/2.64 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),C),D,tc_Int_Oint),tc_Int_Oint),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),D,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),E,tc_Int_Oint))). [resolve(447,a,451,a)].
% 2.36/2.64 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B),E,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(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(447,a,452,a)].
% 2.36/2.64 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(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))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),A,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D),E,tc_Int_Oint))). [resolve(447,a,453,a)].
% 2.36/2.64 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B),E,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B),C,tc_Int_Oint),tc_Int_Oint),E)). [resolve(447,a,454,a)].
% 2.36/2.64 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),C),D,tc_Int_Oint),tc_Int_Oint),E)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),D,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),E,tc_Int_Oint))). [resolve(447,a,455,a)].
% 2.36/2.64 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),A)). [resolve(447,a,459,a)].
% 2.36/2.64 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),B)). [resolve(447,a,460,a)].
% 2.36/2.64 461 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 2.36/2.64 462 -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) = c_HOL_Oplus__class_Oplus(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),A) # label(cls_DERIV__mult__lemma_0) # label(axiom). [assumption].
% 2.36/2.64 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) = c_HOL_Oplus__class_Oplus(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),tc_Complex_Ocomplex). [resolve(461,a,462,a)].
% 2.43/2.71 463 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.43/2.71 464 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 2.43/2.71 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(A,C,tc_nat) | B = C. [resolve(463,a,464,a)].
% 2.43/2.71 465 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.43/2.71 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C. [resolve(465,a,464,a)].
% 2.43/2.71 466 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.43/2.71 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C. [resolve(466,a,464,a)].
% 2.43/2.71 467 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.43/2.71 468 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 2.43/2.71 469 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(D,C,A) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 2.43/2.71 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C. [resolve(467,a,469,a)].
% 2.43/2.71 470 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.43/2.71 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint) | A = C. [resolve(470,a,469,a)].
% 2.43/2.71 471 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 2.43/2.71 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(C,B,tc_Complex_Ocomplex) | A = C. [resolve(471,a,469,a)].
% 2.43/2.71 472 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 2.43/2.71 473 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 2.43/2.71 474 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_lessequals(C,A),B)) | -hBOOL(hAPP(c_lessequals(E,A),D)) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 2.43/2.71 475 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 2.43/2.71 476 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 2.43/2.74 477 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 2.43/2.74 478 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 2.43/2.74 479 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 2.43/2.74 480 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 2.43/2.74 481 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oplus__class_Oplus(C,D,A))) | -hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oplus__class_Oplus(C,E,A))) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 2.43/2.74 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(472,a,473,a)].
% 2.43/2.74 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)). [resolve(472,a,474,a)].
% 2.43/2.74 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(472,a,475,a)].
% 2.43/2.74 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),D)). [resolve(472,a,476,a)].
% 2.43/2.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(472,a,477,a)].
% 2.43/2.74 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(472,a,478,a)].
% 2.43/2.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(472,a,479,a)].
% 2.43/2.74 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(472,a,480,a)].
% 2.43/2.74 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint))). [resolve(472,a,481,a)].
% 2.43/2.74 482 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.43/2.74 483 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),C,A) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 2.43/2.74 484 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Oplus__class_Oplus(B,C,A)),C) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 2.43/2.76 485 -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].
% 2.43/2.76 486 -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].
% 2.43/2.76 487 -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].
% 2.43/2.76 488 -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].
% 2.43/2.76 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),B,tc_Int_Oint) = A. [resolve(482,a,483,a)].
% 2.43/2.76 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint)),B) = A. [resolve(482,a,484,a)].
% 2.43/2.76 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(482,a,486,a)].
% 2.43/2.76 489 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.43/2.76 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B),B,tc_Complex_Ocomplex) = A. [resolve(489,a,483,a)].
% 2.43/2.76 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex)),B) = A. [resolve(489,a,484,a)].
% 2.43/2.76 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(489,a,486,a)].
% 2.43/2.76 490 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.43/2.76 491 -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].
% 2.43/2.76 492 -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(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),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].
% 2.43/2.76 493 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Suc(B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 2.43/2.76 494 -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].
% 2.43/2.76 495 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),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].
% 2.43/2.76 496 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 2.43/2.76 497 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),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].
% 2.43/2.76 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(490,a,491,a)].
% 2.43/2.76 Derived: -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(490,a,492,a)].
% 2.43/2.76 Derived: -class_Power_Opower(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(490,a,493,a)].
% 2.43/2.76 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(490,a,494,a)].
% 2.43/2.76 Derived: -class_Power_Opower(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),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(490,a,495,a)].
% 2.43/2.76 Derived: -class_Power_Opower(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(490,a,497,a)].
% 2.43/2.76 498 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.43/2.76 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(498,a,491,a)].
% 2.43/2.76 Derived: -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(498,a,492,a)].
% 2.43/2.76 Derived: -class_Power_Opower(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(498,a,493,a)].
% 2.43/2.76 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(498,a,494,a)].
% 2.43/2.76 Derived: -class_Power_Opower(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),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(498,a,495,a)].
% 2.43/2.76 Derived: -class_Power_Opower(tc_Int_Oint) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(498,a,497,a)].
% 2.43/2.76 499 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.43/2.76 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(499,a,492,a)].
% 2.43/2.76 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(499,a,493,a)].
% 2.43/2.76 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),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(499,a,495,a)].
% 2.55/2.81 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(499,a,497,a)].
% 2.55/2.81 500 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 2.55/2.81 501 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(B,c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A),A) | hBOOL(hAPP(c_lessequals(C,tc_nat),c_Series_Osko__Series__Xseries__zero__1__1(B,C,A))) # label(cls_series__zero_0) # label(axiom). [assumption].
% 2.55/2.81 502 -class_RealVector_Oreal__normed__vector(A) | hAPP(B,c_Series_Osko__Series__Xseries__zero__1__1(B,C,A)) != c_HOL_Ozero__class_Ozero(A) | c_Series_Osums(B,c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A),A) # label(cls_series__zero_1) # label(axiom). [assumption].
% 2.55/2.81 Derived: c_Series_Osums(A,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) | hBOOL(hAPP(c_lessequals(B,tc_nat),c_Series_Osko__Series__Xseries__zero__1__1(A,B,tc_Complex_Ocomplex))). [resolve(500,a,501,a)].
% 2.55/2.81 Derived: hAPP(A,c_Series_Osko__Series__Xseries__zero__1__1(A,B,tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Series_Osums(A,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). [resolve(500,a,502,a)].
% 2.55/2.81 503 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.55/2.81 504 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 2.55/2.81 505 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 2.55/2.81 506 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 2.55/2.81 507 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 2.55/2.81 508 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 2.55/2.81 509 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.58/2.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(503,a,504,a)].
% 2.58/2.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(503,a,506,a)].
% 2.58/2.86 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(503,a,509,a)].
% 2.58/2.86 510 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.58/2.86 511 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.58/2.86 512 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 2.58/2.86 513 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 2.58/2.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(511,a,512,a)].
% 2.58/2.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(511,a,513,a)].
% 2.58/2.86 514 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.58/2.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(514,a,512,a)].
% 2.58/2.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(514,a,513,a)].
% 2.58/2.86 515 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.68/2.93 516 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 2.68/2.93 517 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 2.68/2.93 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(515,a,516,a)].
% 2.68/2.93 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(515,a,517,a)].
% 2.68/2.93 518 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.68/2.93 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(518,a,516,a)].
% 2.68/2.93 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)). [resolve(518,a,517,a)].
% 2.68/2.93 519 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.68/2.93 520 -class_Ring__and__Field_Omult__mono1(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 2.68/2.93 521 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.68/2.93 522 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 2.68/2.93 523 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 2.68/2.93 524 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].
% 2.68/2.93 525 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.68/2.93 526 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) != c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C),F,A) | D = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C),F,A) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 2.68/2.93 527 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) != c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C),F,A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C),D,A) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 2.68/2.93 528 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C),D,A),A) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 2.68/2.93 529 -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].
% 2.68/2.93 530 -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].
% 2.68/2.93 531 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B)),C),E,A),A) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),E,A) # label(cls_eq__add__iff2_1) # label(axiom). [assumption].
% 2.68/2.93 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B),E,tc_Int_Oint) | C = c_HOL_Oplus__class_Oplus(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(525,a,526,a)].
% 2.68/2.93 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B),E,tc_Int_Oint) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B),C,tc_Int_Oint) = E. [resolve(525,a,527,a)].
% 2.68/2.93 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B),C,tc_Int_Oint),tc_Int_Oint). [resolve(525,a,528,a)].
% 2.68/2.93 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(525,a,529,a)].
% 2.68/2.93 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(525,a,530,a)].
% 2.68/2.93 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),A)),B),D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),D,tc_Int_Oint). [resolve(525,a,531,a)].
% 2.68/2.97 532 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.68/2.97 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B),E,tc_Complex_Ocomplex) | C = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),A)),B),E,tc_Complex_Ocomplex). [resolve(532,a,526,a)].
% 2.68/2.97 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B),E,tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B),C,tc_Complex_Ocomplex) = E. [resolve(532,a,527,a)].
% 2.68/2.97 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B),C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(532,a,528,a)].
% 2.68/2.97 Derived: c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),A)),B),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),D,tc_Complex_Ocomplex). [resolve(532,a,531,a)].
% 2.68/2.97 533 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 2.68/2.97 534 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__fact__not__zero_0) # label(axiom). [assumption].
% 2.68/2.97 535 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 2.68/2.97 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(533,a,534,a)].
% 2.68/2.97 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(533,a,535,a)].
% 2.68/2.97 536 class_Nat_Osemiring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 2.68/2.97 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(536,a,534,a)].
% 2.68/2.97 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint) | A = B. [resolve(536,a,535,a)].
% 2.68/2.97 537 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 2.68/2.97 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(537,a,534,a)].
% 2.68/2.97 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex) | A = B. [resolve(537,a,535,a)].
% 2.68/2.97 538 class_Ring__and__Field_Oring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 2.68/2.97 539 -class_Ring__and__Field_Oring__1(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),C,tc_nat),tc_nat,A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(C,A)),D)) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),D,tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A) # label(cls_sumr__diff__mult__const2_0) # label(axiom). [assumption].
% 2.68/3.00 540 -class_Ring__and__Field_Oring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)) # label(cls_of__nat__diff_0) # label(axiom). [assumption].
% 2.68/3.00 Derived: 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),B,tc_nat),tc_nat,tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)),C)) = c_Finite__Set_Osetsum(c_COMBC(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,tc_nat,tc_Int_Oint,tc_Int_Oint),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Int_Oint). [resolve(538,a,539,a)].
% 2.68/3.00 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(538,a,540,a)].
% 2.68/3.00 541 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 2.68/3.00 Derived: 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),B,tc_nat),tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)),C)) = c_Finite__Set_Osetsum(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),C,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex). [resolve(541,a,539,a)].
% 2.68/3.00 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(541,a,540,a)].
% 2.68/3.00 542 class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.68/3.00 543 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 2.68/3.00 544 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 2.68/3.00 545 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 2.68/3.00 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(542,a,545,a)].
% 3.25/3.52 546 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].
% 3.25/3.52 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(546,a,545,a)].
% 3.25/3.52 547 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.25/3.52 548 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 3.25/3.52 549 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.25/3.52 550 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.25/3.52 551 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].
% 3.25/3.52 552 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | hAPP(c_Power_Opower__class_Opower(B,A),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 3.25/3.52 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Int_Oint),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(551,a,552,a)].
% 3.25/3.52 553 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].
% 3.25/3.52 Derived: hAPP(c_Power_Opower__class_Opower(A,tc_Complex_Ocomplex),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(553,a,552,a)].
% 3.25/3.52 554 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 3.25/3.52 555 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 3.25/3.52 Derived: A = A. [resolve(554,b,555,a)].
% 3.25/3.52
% 3.25/3.52 ============================== end predicate elimination =============
% 3.25/3.52
% 3.25/3.52 Auto_denials: (non-Horn, no changes).
% 3.25/3.52
% 3.25/3.52 Term ordering decisions:
% 3.25/3.52 Function symbol KB weights: tc_nat=1. tc_Int_Oint=1. tc_Complex_Ocomplex=1. tc_bool=1. v_n=1. v_i=1. hAPP=1. c_HOL_Oord__class_Oless=1. c_lessequals=1. c_Power_Opower__class_Opower=1. c_Int_Onumber__class_Onumber__of=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_HOL_Oinverse__class_Oinverse=1. tc_fun=1. c_Fact_Ofact__class_Ofact=1. c_SetInterval_Oord__class_OlessThan=1. c_Finite__Set_Ocard=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Ominus__class_Ominus=1. c_Suc=1. c_HOL_Oone__class_Oone=1. c_HOL_Oinverse__class_Odivide=1. c_Orderings_Obot__class_Obot=1. c_FFT__Mirabelle_Oroot=1. v_a=1. c_HOL_Oplus__class_Oplus=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1=1. c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1=1. c_Series_Osko__Series__Xseries__zero__1__1=1. c_Finite__Set_Osetsum=1. c_Transcendental_Osko__Transcendental__Xreal__setsum__nat__ivl__bounded2__1__1=1. c_COMBB=1. c_COMBC=1. c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1=1.
% 3.25/3.52
% 3.25/3.52 ============================== end of process initial clauses ========
% 3.25/3.52
% 3.25/3.52 ============================== CLAUSES FOR SEARCH ====================
% 3.25/3.52
% 3.25/3.52 ============================== end of clauses for search =============
% 3.25/3.52
% 3.25/3.52 ============================== SEARCH ================================
% 3.25/3.52
% 3.25/3.52 % Starting search at 1.68 seconds.
% 3.25/3.52
% 3.25/3.52 Low Water (keep): wt=66.000, iters=3565
% 3.25/3.52
% 3.25/3.52 Low Water (keep): wt=62.000, iters=3521
% 3.25/3.52
% 3.25/3.52 Low Water (keep): wt=55.000, iters=3410
% 3.25/3.52
% 3.25/3.52 Low Water (keep): Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------