TSTP Solution File: ALG370-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG370-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 : Thu Jul 14 17:54:36 EDT 2022
% Result : Timeout 300.01s 300.28s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ALG370-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 8 21:53:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.88/1.20 ============================== Prover9 ===============================
% 0.88/1.20 Prover9 (32) version 2009-11A, November 2009.
% 0.88/1.20 Process 8330 was started by sandbox on n019.cluster.edu,
% 0.88/1.20 Wed Jun 8 21:53:26 2022
% 0.88/1.20 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7880_n019.cluster.edu".
% 0.88/1.20 ============================== end of head ===========================
% 0.88/1.20
% 0.88/1.20 ============================== INPUT =================================
% 0.88/1.20
% 0.88/1.20 % Reading from file /tmp/Prover9_7880_n019.cluster.edu
% 0.88/1.20
% 0.88/1.20 set(prolog_style_variables).
% 0.88/1.20 set(auto2).
% 0.88/1.20 % set(auto2) -> set(auto).
% 0.88/1.20 % set(auto) -> set(auto_inference).
% 0.88/1.20 % set(auto) -> set(auto_setup).
% 0.88/1.20 % set(auto_setup) -> set(predicate_elim).
% 0.88/1.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.88/1.20 % set(auto) -> set(auto_limits).
% 0.88/1.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.88/1.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.88/1.20 % set(auto) -> set(auto_denials).
% 0.88/1.20 % set(auto) -> set(auto_process).
% 0.88/1.20 % set(auto2) -> assign(new_constants, 1).
% 0.88/1.20 % set(auto2) -> assign(fold_denial_max, 3).
% 0.88/1.20 % set(auto2) -> assign(max_weight, "200.000").
% 0.88/1.20 % set(auto2) -> assign(max_hours, 1).
% 0.88/1.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.88/1.20 % set(auto2) -> assign(max_seconds, 0).
% 0.88/1.20 % set(auto2) -> assign(max_minutes, 5).
% 0.88/1.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.88/1.20 % set(auto2) -> set(sort_initial_sos).
% 0.88/1.20 % set(auto2) -> assign(sos_limit, -1).
% 0.88/1.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.88/1.20 % set(auto2) -> assign(max_megs, 400).
% 0.88/1.20 % set(auto2) -> assign(stats, some).
% 0.88/1.20 % set(auto2) -> clear(echo_input).
% 0.88/1.20 % set(auto2) -> set(quiet).
% 0.88/1.20 % set(auto2) -> clear(print_initial_clauses).
% 0.88/1.20 % set(auto2) -> clear(print_given).
% 0.88/1.20 assign(lrs_ticks,-1).
% 0.88/1.20 assign(sos_limit,10000).
% 0.88/1.20 assign(order,kbo).
% 0.88/1.20 set(lex_order_vars).
% 0.88/1.20 clear(print_given).
% 0.88/1.20
% 0.88/1.20 % formulas(sos). % not echoed (614 formulas)
% 0.88/1.20
% 0.88/1.20 ============================== end of input ==========================
% 0.88/1.20
% 0.88/1.20 % From the command line: assign(max_seconds, 300).
% 0.88/1.20
% 0.88/1.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.88/1.20
% 0.88/1.20 % Formulas that are not ordinary clauses:
% 0.88/1.20
% 0.88/1.20 ============================== end of process non-clausal formulas ===
% 0.88/1.20
% 0.88/1.20 ============================== PROCESS INITIAL CLAUSES ===============
% 0.88/1.20
% 0.88/1.20 ============================== PREDICATE ELIMINATION =================
% 0.88/1.20 1 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].
% 0.88/1.20 2 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 0.88/1.20 3 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 0.88/1.20 4 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 0.88/1.20 5 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 0.88/1.20 6 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 0.88/1.20 7 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 0.88/1.20 8 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 0.88/1.20 9 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 0.88/1.20 10 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 0.88/1.20 11 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 0.88/1.20 12 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 0.88/1.20 13 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 0.88/1.20 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(1,a,2,a)].
% 0.88/1.20 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,3,a)].
% 0.88/1.20 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(1,a,4,a)].
% 0.88/1.20 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,5,a)].
% 0.88/1.20 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(1,a,6,a)].
% 0.88/1.20 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(1,a,7,a)].
% 0.88/1.20 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(1,a,8,a)].
% 0.88/1.20 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,9,a)].
% 0.88/1.20 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(1,a,10,a)].
% 0.88/1.20 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,11,a)].
% 0.88/1.20 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(1,a,12,a)].
% 0.88/1.20 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(1,a,13,a)].
% 0.88/1.21 14 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.88/1.21 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(14,a,2,a)].
% 0.88/1.21 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(14,a,3,a)].
% 0.88/1.21 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(14,a,4,a)].
% 0.88/1.21 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(14,a,5,a)].
% 0.88/1.21 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(14,a,6,a)].
% 0.88/1.21 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(14,a,7,a)].
% 0.88/1.21 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(14,a,8,a)].
% 0.88/1.21 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(14,a,9,a)].
% 0.88/1.21 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(14,a,10,a)].
% 0.88/1.21 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(14,a,11,a)].
% 0.88/1.21 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(14,a,12,a)].
% 0.88/1.21 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(14,a,13,a)].
% 0.88/1.21 15 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.88/1.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(15,a,2,a)].
% 0.88/1.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(15,a,3,a)].
% 0.88/1.21 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)). [resolve(15,a,4,a)].
% 0.88/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(15,a,5,a)].
% 0.88/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(15,a,6,a)].
% 0.88/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(15,a,7,a)].
% 0.88/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(15,a,8,a)].
% 0.88/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(D,B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(15,a,9,a)].
% 0.88/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(15,a,10,a)].
% 0.88/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(15,a,11,a)].
% 0.88/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(15,a,12,a)].
% 0.88/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(15,a,13,a)].
% 0.88/1.23 16 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.23 17 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 0.88/1.23 18 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 0.88/1.23 19 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 0.88/1.23 20 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 0.88/1.25 21 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(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_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(16,a,18,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(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_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(16,a,20,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(16,a,21,a)].
% 0.88/1.25 22 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(22,a,18,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(22,a,20,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(22,a,21,a)].
% 0.88/1.25 23 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(23,a,18,a)].
% 0.88/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(23,a,20,a)].
% 0.88/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(23,a,21,a)].
% 0.88/1.25 24 class_Orderings_Opreorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Opreorder) # label(axiom). [assumption].
% 0.88/1.25 25 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_order__less__imp__le_0) # label(axiom). [assumption].
% 0.88/1.25 26 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_less__le__not__le_2) # label(axiom). [assumption].
% 0.88/1.25 27 -class_Orderings_Opreorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_less__le__not__le_1) # label(axiom). [assumption].
% 0.88/1.25 28 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__le__less__trans_0) # label(axiom). [assumption].
% 0.88/1.25 29 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_order__less__le__trans_0) # label(axiom). [assumption].
% 0.88/1.25 30 -class_Orderings_Opreorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__refl_0) # label(axiom). [assumption].
% 0.88/1.25 31 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_lessequals(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__trans_0) # label(axiom). [assumption].
% 0.88/1.25 32 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_0) # label(axiom). [assumption].
% 0.88/1.25 33 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_H_0) # label(axiom). [assumption].
% 0.88/1.25 34 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__irrefl_0) # label(axiom). [assumption].
% 0.88/1.25 35 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_order__less__trans_0) # label(axiom). [assumption].
% 0.88/1.25 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(24,a,25,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(24,a,26,a)].
% 0.88/1.25 Derived: -c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(24,a,27,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(24,a,28,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(24,a,29,a)].
% 0.88/1.25 Derived: c_lessequals(A,A,tc_Int_Oint). [resolve(24,a,30,a)].
% 0.88/1.25 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(24,a,31,a)].
% 0.88/1.25 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(24,a,32,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(24,a,35,a)].
% 0.88/1.25 36 class_Orderings_Opreorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Opreorder) # label(axiom). [assumption].
% 0.88/1.25 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(36,a,25,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(36,a,26,a)].
% 0.88/1.25 Derived: -c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(36,a,27,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(36,a,28,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(36,a,29,a)].
% 0.88/1.25 Derived: c_lessequals(A,A,tc_RealDef_Oreal). [resolve(36,a,30,a)].
% 0.88/1.25 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(36,a,31,a)].
% 0.88/1.25 Derived: -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(36,a,32,a)].
% 0.88/1.25 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(36,a,35,a)].
% 0.88/1.25 37 class_Orderings_Opreorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Opreorder) # label(axiom). [assumption].
% 0.88/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(37,a,25,a)].
% 0.88/1.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(37,a,26,a)].
% 0.88/1.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)). [resolve(37,a,27,a)].
% 0.88/1.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(37,a,28,a)].
% 0.88/1.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(37,a,29,a)].
% 0.88/1.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,B,tc_Polynomial_Opoly(A)). [resolve(37,a,30,a)].
% 0.88/1.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(37,a,31,a)].
% 0.88/1.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)). [resolve(37,a,32,a)].
% 0.88/1.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(37,a,35,a)].
% 0.88/1.27 38 class_Orderings_Oorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Oorder) # label(axiom). [assumption].
% 0.88/1.27 39 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_order__le__less_1) # label(axiom). [assumption].
% 0.88/1.27 40 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | -c_lessequals(B,C,A) # label(cls_xt1_I11_J_0) # label(axiom). [assumption].
% 0.88/1.27 41 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) | C = B # label(cls_xt1_I12_J_0) # label(axiom). [assumption].
% 0.88/1.27 42 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) | B = C # label(cls_order__neq__le__trans_0) # label(axiom). [assumption].
% 0.88/1.27 43 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | B = C | -c_lessequals(B,C,A) # label(cls_order__le__neq__trans_0) # label(axiom). [assumption].
% 0.88/1.27 44 -class_Orderings_Oorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_order__le__less_0) # label(axiom). [assumption].
% 0.88/1.27 45 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | B = C | -c_lessequals(B,C,A) # label(cls_order__less__le_2) # label(axiom). [assumption].
% 0.88/1.27 46 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I8_J_0) # label(axiom). [assumption].
% 0.88/1.27 47 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_xt1_I7_J_0) # label(axiom). [assumption].
% 0.88/1.27 48 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__antisym_0) # label(axiom). [assumption].
% 0.88/1.27 49 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__eq__iff_2) # label(axiom). [assumption].
% 0.88/1.27 50 -class_Orderings_Oorder(A) | B = C | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) # label(cls_order__antisym__conv_0) # label(axiom). [assumption].
% 0.88/1.27 51 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__iff_0) # label(axiom). [assumption].
% 0.88/1.27 52 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I6_J_0) # label(axiom). [assumption].
% 0.88/1.27 53 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_xt1_I9_J_0) # label(axiom). [assumption].
% 0.88/1.27 54 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__le_1) # label(axiom). [assumption].
% 0.88/1.28 55 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_xt1_I10_J_0) # label(axiom). [assumption].
% 0.88/1.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | B = A | -c_lessequals(A,B,tc_Int_Oint). [resolve(38,a,40,a)].
% 0.88/1.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint) | A = B. [resolve(38,a,42,a)].
% 0.88/1.28 Derived: A = B | -c_lessequals(B,A,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(38,a,48,a)].
% 0.88/1.28 56 class_Orderings_Oorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Oorder) # label(axiom). [assumption].
% 0.88/1.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | B = A | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(56,a,40,a)].
% 0.88/1.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal) | A = B. [resolve(56,a,42,a)].
% 0.88/1.28 Derived: A = B | -c_lessequals(B,A,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(56,a,48,a)].
% 0.88/1.28 57 class_Orderings_Oorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Oorder) # label(axiom). [assumption].
% 0.88/1.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | C = B | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(57,a,40,a)].
% 0.88/1.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | B = C. [resolve(57,a,42,a)].
% 0.88/1.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = C | -c_lessequals(C,B,tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(57,a,48,a)].
% 0.88/1.28 58 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 0.88/1.28 59 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 0.88/1.28 60 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 0.88/1.28 61 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 0.88/1.28 62 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 0.88/1.28 63 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 0.88/1.28 64 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 0.88/1.28 65 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 0.88/1.28 66 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 0.88/1.28 67 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 0.88/1.28 68 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | -c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 0.88/1.28 69 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 0.88/1.28 70 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_1) # label(axiom). [assumption].
% 0.88/1.29 71 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.88/1.29 72 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 0.88/1.29 73 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.88/1.29 74 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.88/1.29 75 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 0.88/1.29 76 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 0.88/1.29 77 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 0.88/1.29 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(58,a,61,a)].
% 0.88/1.29 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) | c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(58,a,70,a)].
% 0.88/1.29 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(58,a,71,a)].
% 0.88/1.29 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(58,a,74,a)].
% 0.88/1.29 78 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 0.88/1.29 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal). [resolve(78,a,61,a)].
% 0.88/1.29 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(78,a,70,a)].
% 0.88/1.29 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal). [resolve(78,a,71,a)].
% 0.88/1.29 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(78,a,74,a)].
% 0.88/1.29 79 class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [assumption].
% 0.88/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(79,a,61,a)].
% 0.88/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(tc_Polynomial_Opoly(A)) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(79,a,70,a)].
% 0.88/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(79,a,71,a)].
% 0.88/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = C | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(79,a,74,a)].
% 0.88/1.29 80 class_Int_Onumber__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Onumber__ring) # label(axiom). [assumption].
% 0.88/1.29 81 -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].
% 0.88/1.29 82 -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].
% 0.88/1.30 83 -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].
% 0.88/1.30 84 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A) != c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,E,A),A) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 0.88/1.30 85 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 0.88/1.30 86 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 0.88/1.30 87 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 0.88/1.30 88 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 0.88/1.30 89 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 0.88/1.30 90 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 0.88/1.30 91 -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].
% 0.88/1.30 92 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(B,A),A) = c_Int_Onumber__class_Onumber__of(B,A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__number__of_1) # label(axiom). [assumption].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(80,a,81,b)].
% 0.88/1.30 Derived: -class_Int_Oring__char__0(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(80,a,82,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(80,a,83,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),tc_Int_Oint) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(80,a,84,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | B = D | A = C. [resolve(80,a,85,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(80,a,87,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(80,a,89,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(80,a,90,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(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(80,a,91,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(80,a,92,b)].
% 0.88/1.30 93 class_Int_Onumber__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Int_Onumber__ring) # label(axiom). [assumption].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,81,b)].
% 0.88/1.30 Derived: -class_Int_Oring__char__0(tc_RealDef_Oreal) | c_Int_Onumber__class_Onumber__of(A,tc_RealDef_Oreal) != c_Int_Onumber__class_Onumber__of(B,tc_RealDef_Oreal) | A = B. [resolve(93,a,82,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | A != c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(93,a,83,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | C = D | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(93,a,84,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | B = D | A = C. [resolve(93,a,85,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,87,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Ominus__class_Ominus(A,A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(93,a,89,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(93,a,90,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal) | B = C. [resolve(93,a,91,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,92,b)].
% 0.88/1.30 94 class_Int_Onumber__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Onumber__ring) # label(axiom). [assumption].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(94,a,81,b)].
% 0.88/1.30 Derived: -class_Int_Oring__char__0(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(94,a,82,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(94,a,83,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(94,a,84,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = D | A = C. [resolve(94,a,85,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(94,a,87,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(94,a,89,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(94,a,90,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oidom(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(94,a,91,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Oordered__idom(tc_Complex_Ocomplex) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(94,a,92,b)].
% 0.88/1.30 95 class_Int_Onumber__ring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring__1(A) # label(clsarity_Polynomial__Opoly__Int_Onumber__ring) # label(axiom). [assumption].
% 0.88/1.30 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | B = c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(95,a,81,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Int_Oring__char__0(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)) != c_Int_Onumber__class_Onumber__of(C,tc_Polynomial_Opoly(A)) | B = C. [resolve(95,a,82,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | B != c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(95,a,83,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | D = E | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(95,a,84,b)].
% 0.88/1.30 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = E | B = D. [resolve(95,a,85,b)].
% 0.88/1.32 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(95,a,87,b)].
% 0.88/1.32 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Ominus__class_Ominus(B,B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(95,a,89,b)].
% 0.88/1.32 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = C. [resolve(95,a,90,b)].
% 0.88/1.32 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)) | C = D. [resolve(95,a,91,b)].
% 0.88/1.32 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(A)) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(95,a,92,b)].
% 0.88/1.32 96 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.88/1.32 97 -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].
% 0.88/1.32 98 -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].
% 0.88/1.32 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = A. [resolve(96,a,97,a)].
% 0.88/1.32 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(96,a,98,a)].
% 0.88/1.32 99 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.88/1.32 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = A. [resolve(99,a,97,a)].
% 0.88/1.32 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(99,a,98,a)].
% 0.88/1.32 100 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.88/1.32 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A. [resolve(100,a,97,a)].
% 0.88/1.32 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(100,a,98,a)].
% 0.88/1.32 101 class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.88/1.32 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = B. [resolve(101,a,97,a)].
% 0.88/1.32 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(101,a,98,a)].
% 0.88/1.32 102 class_RealVector_Ometric__space(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Ometric__space) # label(axiom). [assumption].
% 0.88/1.32 103 -class_RealVector_Ometric__space(A) | B = C | -c_lessequals(c_RealVector_Odist__class_Odist(B,C,A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_dist__le__zero__iff_0) # label(axiom). [assumption].
% 0.88/1.32 104 -class_RealVector_Ometric__space(A) | c_RealVector_Odist__class_Odist(B,C,A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = C # label(cls_dist__eq__0__iff_0) # label(axiom). [assumption].
% 0.88/1.32 105 -class_RealVector_Ometric__space(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(B,B,A),tc_RealDef_Oreal) # label(cls_zero__less__dist__iff_0) # label(axiom). [assumption].
% 0.88/1.32 106 -class_RealVector_Ometric__space(A) | c_RealVector_Odist__class_Odist(B,B,A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_dist__self_0) # label(axiom). [assumption].
% 0.88/1.32 107 -class_RealVector_Ometric__space(A) | c_lessequals(c_RealVector_Odist__class_Odist(B,B,A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_dist__le__zero__iff_1) # label(axiom). [assumption].
% 0.88/1.32 108 -class_RealVector_Ometric__space(A) | -c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(B,C,A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_dist__not__less__zero_0) # label(axiom). [assumption].
% 0.88/1.32 109 -class_RealVector_Ometric__space(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(B,C,A),tc_RealDef_Oreal) | B = C # label(cls_zero__less__dist__iff_1) # label(axiom). [assumption].
% 0.88/1.32 110 -class_RealVector_Ometric__space(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(B,C,A),tc_RealDef_Oreal) # label(cls_zero__le__dist_0) # label(axiom). [assumption].
% 0.88/1.32 111 -class_RealVector_Ometric__space(A) | c_RealVector_Odist__class_Odist(B,C,A) = c_RealVector_Odist__class_Odist(C,B,A) # label(cls_dist__commute_0) # label(axiom). [assumption].
% 0.88/1.32 Derived: A = B | -c_lessequals(c_RealVector_Odist__class_Odist(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(102,a,103,a)].
% 0.88/1.32 Derived: c_RealVector_Odist__class_Odist(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(102,a,104,a)].
% 0.88/1.32 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(A,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(102,a,105,a)].
% 0.88/1.32 Derived: c_RealVector_Odist__class_Odist(A,A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(102,a,106,a)].
% 0.88/1.32 Derived: c_lessequals(c_RealVector_Odist__class_Odist(A,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(102,a,107,a)].
% 0.88/1.32 Derived: -c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(102,a,108,a)].
% 0.88/1.32 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | A = B. [resolve(102,a,109,a)].
% 0.88/1.32 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(102,a,110,a)].
% 0.88/1.32 Derived: c_RealVector_Odist__class_Odist(A,B,tc_RealDef_Oreal) = c_RealVector_Odist__class_Odist(B,A,tc_RealDef_Oreal). [resolve(102,a,111,a)].
% 0.88/1.32 112 class_RealVector_Ometric__space(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Ometric__space) # label(axiom). [assumption].
% 0.88/1.32 Derived: A = B | -c_lessequals(c_RealVector_Odist__class_Odist(A,B,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(112,a,103,a)].
% 0.88/1.32 Derived: c_RealVector_Odist__class_Odist(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(112,a,104,a)].
% 0.88/1.32 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(A,A,tc_Complex_Ocomplex),tc_RealDef_Oreal). [resolve(112,a,105,a)].
% 0.88/1.34 Derived: c_RealVector_Odist__class_Odist(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(112,a,106,a)].
% 0.88/1.34 Derived: c_lessequals(c_RealVector_Odist__class_Odist(A,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(112,a,107,a)].
% 0.88/1.34 Derived: -c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(A,B,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(112,a,108,a)].
% 0.88/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(A,B,tc_Complex_Ocomplex),tc_RealDef_Oreal) | A = B. [resolve(112,a,109,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(A,B,tc_Complex_Ocomplex),tc_RealDef_Oreal). [resolve(112,a,110,a)].
% 0.88/1.34 Derived: c_RealVector_Odist__class_Odist(A,B,tc_Complex_Ocomplex) = c_RealVector_Odist__class_Odist(B,A,tc_Complex_Ocomplex). [resolve(112,a,111,a)].
% 0.88/1.34 113 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 0.88/1.34 114 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__pos_0) # label(axiom). [assumption].
% 0.88/1.34 115 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__triangle__ineq_0) # label(axiom). [assumption].
% 0.88/1.34 116 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_1) # label(axiom). [assumption].
% 0.88/1.34 117 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),A) # label(cls_abs__triangle__ineq3_0) # label(axiom). [assumption].
% 0.88/1.34 118 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D1_0) # label(axiom). [assumption].
% 0.88/1.34 119 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_0) # label(axiom). [assumption].
% 0.88/1.34 120 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__nonneg_0) # label(axiom). [assumption].
% 0.88/1.34 121 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,B,A),A) # label(cls_abs__minus__commute_0) # label(axiom). [assumption].
% 0.88/1.34 122 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),A) # label(cls_abs__triangle__ineq2_0) # label(axiom). [assumption].
% 0.88/1.34 123 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_1) # label(axiom). [assumption].
% 0.88/1.34 124 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,E,A),A),A),A) # label(cls_abs__diff__triangle__ineq_0) # label(axiom). [assumption].
% 0.88/1.34 125 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__idempotent_0) # label(axiom). [assumption].
% 0.88/1.34 126 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(B,A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__abs__iff_1) # label(axiom). [assumption].
% 0.88/1.34 127 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__self_0) # label(axiom). [assumption].
% 0.88/1.34 128 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__not__less__zero_0) # label(axiom). [assumption].
% 0.88/1.34 129 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__triangle__ineq4_0) # label(axiom). [assumption].
% 0.88/1.34 130 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_abs__add__abs_0) # label(axiom). [assumption].
% 0.88/1.34 131 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_0) # label(axiom). [assumption].
% 0.88/1.34 132 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A),A) # label(cls_zero__less__abs__iff_0) # label(axiom). [assumption].
% 0.88/1.34 133 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__zero_0) # label(axiom). [assumption].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(113,a,114,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(113,a,115,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,116,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(113,a,117,a)].
% 0.88/1.34 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(113,a,118,a)].
% 0.88/1.34 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(113,a,119,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(113,a,120,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(113,a,121,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(113,a,122,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(113,a,123,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(113,a,124,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oabs__class_Oabs(A,tc_Int_Oint). [resolve(113,a,125,a)].
% 0.88/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,126,a)].
% 0.88/1.34 Derived: c_lessequals(A,c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint). [resolve(113,a,127,a)].
% 0.88/1.34 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(113,a,128,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(113,a,129,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint). [resolve(113,a,130,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,131,a)].
% 0.88/1.34 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(113,a,132,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint). [resolve(113,a,133,a)].
% 0.88/1.34 134 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(134,a,114,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,115,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(134,a,116,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,117,a)].
% 0.88/1.34 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(134,a,118,a)].
% 0.88/1.34 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,119,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(134,a,120,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,121,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,122,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,123,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,124,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal). [resolve(134,a,125,a)].
% 0.88/1.34 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(134,a,126,a)].
% 0.88/1.34 Derived: c_lessequals(A,c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,127,a)].
% 0.88/1.34 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,128,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,129,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,130,a)].
% 0.88/1.34 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(134,a,131,a)].
% 0.88/1.34 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,132,a)].
% 0.88/1.34 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(134,a,133,a)].
% 0.88/1.34 135 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) = B | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(135,a,114,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,115,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(135,a,116,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,117,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(135,a,118,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,119,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) = B | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(135,a,120,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,121,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,122,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,123,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,124,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)). [resolve(135,a,125,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(135,a,126,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,127,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,128,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,129,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,130,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(135,a,131,a)].
% 0.88/1.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,132,a)].
% 0.88/1.35 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,133,a)].
% 0.88/1.35 136 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 0.88/1.35 137 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 0.88/1.35 138 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,C,A),c_HOL_Otimes__class_Otimes(B,B,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 0.88/1.35 139 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 0.88/1.35 140 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 0.88/1.35 141 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 0.88/1.35 142 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 0.88/1.35 143 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 0.88/1.35 144 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 0.88/1.35 145 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),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].
% 0.88/1.35 146 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),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].
% 0.88/1.35 147 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),A) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 0.88/1.35 148 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 0.88/1.35 149 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 0.88/1.36 150 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 0.88/1.36 151 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 0.88/1.36 152 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 0.88/1.36 153 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 0.88/1.36 154 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 0.88/1.36 155 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 0.88/1.36 156 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 0.88/1.36 157 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 0.88/1.36 158 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 0.88/1.36 159 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 0.88/1.36 160 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 0.88/1.36 161 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 0.88/1.36 162 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,B,A),A) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 0.88/1.36 163 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 0.88/1.36 164 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 0.88/1.36 165 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 0.88/1.36 166 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 0.88/1.36 167 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 0.88/1.36 168 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 0.88/1.36 169 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 0.88/1.36 170 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 0.88/1.36 171 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom). [assumption].
% 0.88/1.36 172 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 0.88/1.36 173 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(D,B,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 0.88/1.36 174 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 0.88/1.36 175 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 0.88/1.36 176 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 0.88/1.36 177 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 0.88/1.36 178 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 0.88/1.36 179 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 0.88/1.36 180 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 0.88/1.36 181 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 0.88/1.36 182 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 0.88/1.36 183 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 0.88/1.36 184 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 0.88/1.36 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,137,a)].
% 0.88/1.36 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,138,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(136,a,139,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(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),tc_Int_Oint). [resolve(136,a,140,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,142,a)].
% 0.88/1.36 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,143,a)].
% 0.88/1.36 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(136,a,145,a)].
% 0.88/1.36 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(136,a,146,a)].
% 0.88/1.36 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(136,a,147,a)].
% 0.88/1.36 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,148,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(136,a,149,a)].
% 0.88/1.36 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(136,a,150,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,151,a)].
% 0.88/1.36 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,152,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(136,a,153,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(136,a,154,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,155,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,156,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,157,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,158,a)].
% 0.88/1.36 Derived: -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,159,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,160,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,161,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,162,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(136,a,163,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,164,a)].
% 0.88/1.36 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,166,a)].
% 0.88/1.36 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,167,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(136,a,169,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,170,a)].
% 0.88/1.36 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(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(136,a,171,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,172,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,173,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(136,a,174,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,176,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(136,a,177,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(136,a,180,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(136,a,182,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,183,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(136,a,184,a)].
% 0.88/1.36 185 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 0.88/1.36 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,137,a)].
% 0.88/1.36 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,138,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,139,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,140,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,142,a)].
% 0.88/1.36 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,143,a)].
% 0.88/1.36 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(185,a,145,a)].
% 0.88/1.36 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(185,a,146,a)].
% 0.88/1.36 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,147,a)].
% 0.88/1.36 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,148,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(185,a,149,a)].
% 0.88/1.36 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(185,a,150,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,151,a)].
% 0.88/1.36 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,152,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(185,a,153,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(185,a,154,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,155,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,156,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,157,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,158,a)].
% 0.88/1.36 Derived: -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,159,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,160,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,161,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,162,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(185,a,163,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,164,a)].
% 0.88/1.36 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,166,a)].
% 0.88/1.36 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,167,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(185,a,169,a)].
% 0.88/1.36 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,170,a)].
% 0.88/1.36 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(185,a,171,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,172,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,173,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(185,a,174,a)].
% 0.88/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,176,a)].
% 0.88/1.37 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(185,a,177,a)].
% 0.88/1.37 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(185,a,180,a)].
% 0.88/1.37 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,182,a)].
% 0.88/1.37 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,183,a)].
% 0.88/1.37 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(185,a,184,a)].
% 0.88/1.37 186 class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,137,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,138,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,139,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,140,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,142,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,143,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(186,a,145,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(186,a,146,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,147,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,148,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(186,a,149,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(186,a,150,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,151,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,152,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(186,a,153,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(186,a,154,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,155,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,156,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,157,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,158,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,159,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,160,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,161,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,162,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(186,a,163,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,164,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,166,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,167,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(186,a,169,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,170,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(186,a,171,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,172,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,173,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(186,a,174,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,176,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(186,a,177,a)].
% 0.88/1.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(186,a,180,a)].
% 0.88/1.39 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,182,a)].
% 0.88/1.39 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,183,a)].
% 0.88/1.39 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(186,a,184,a)].
% 0.88/1.39 187 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.88/1.39 188 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 0.88/1.39 189 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | 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].
% 0.88/1.39 190 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 0.88/1.39 191 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 0.88/1.39 192 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 0.88/1.39 193 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 0.88/1.39 194 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 0.88/1.39 195 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 0.88/1.39 196 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 0.88/1.39 197 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 0.88/1.39 198 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(187,a,188,a)].
% 0.88/1.39 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(187,a,190,a)].
% 0.88/1.39 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(187,a,191,a)].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(187,a,192,a)].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(187,a,193,a)].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(187,a,194,a)].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(187,a,195,a)].
% 0.88/1.39 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(187,a,196,a)].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(187,a,197,a)].
% 0.88/1.39 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(187,a,198,a)].
% 0.88/1.39 199 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(199,a,188,a)].
% 0.88/1.39 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(199,a,190,a)].
% 0.88/1.39 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(199,a,191,a)].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(199,a,192,a)].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(199,a,193,a)].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(199,a,194,a)].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(199,a,195,a)].
% 0.88/1.39 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(199,a,196,a)].
% 0.88/1.39 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(199,a,197,a)].
% 0.88/1.39 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(199,a,198,a)].
% 0.88/1.39 200 class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.88/1.39 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(200,a,188,a)].
% 0.88/1.39 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(200,a,189,a)].
% 0.88/1.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(200,a,190,a)].
% 0.88/1.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(200,a,191,a)].
% 0.88/1.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(200,a,192,a)].
% 0.88/1.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(200,a,193,a)].
% 0.88/1.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(200,a,194,a)].
% 0.88/1.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(200,a,195,a)].
% 0.88/1.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(200,a,196,a)].
% 0.88/1.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(200,a,197,a)].
% 0.88/1.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(200,a,198,a)].
% 0.88/1.41 201 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 0.88/1.41 202 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A) # label(cls_right__distrib__number__of_0) # label(axiom). [assumption].
% 0.88/1.41 203 -class_Ring__and__Field_Osemiring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,A),C,A),E,A) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 0.88/1.41 204 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,A),A),A) # label(cls_left__distrib__number__of_0) # label(axiom). [assumption].
% 0.88/1.41 Derived: -class_Int_Onumber(tc_Int_Oint) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),C,tc_Int_Oint),tc_Int_Oint). [resolve(201,a,202,a)].
% 0.88/1.41 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint),D,tc_Int_Oint). [resolve(201,a,203,a)].
% 0.88/1.41 Derived: -class_Int_Onumber(tc_Int_Oint) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(201,a,204,a)].
% 0.88/1.41 205 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 0.88/1.41 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_RealDef_Oreal),C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(205,a,202,a)].
% 0.88/1.41 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal),D,tc_RealDef_Oreal). [resolve(205,a,203,a)].
% 0.88/1.41 Derived: -class_Int_Onumber(tc_RealDef_Oreal) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(205,a,204,a)].
% 0.88/1.41 206 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 0.88/1.41 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(206,a,202,a)].
% 0.88/1.43 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex). [resolve(206,a,203,a)].
% 0.88/1.43 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(206,a,204,a)].
% 0.88/1.43 207 class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 0.88/1.43 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Int_Onumber(tc_Polynomial_Opoly(A)) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(207,a,202,a)].
% 0.88/1.43 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)). [resolve(207,a,203,a)].
% 0.88/1.43 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Int_Onumber(tc_Polynomial_Opoly(A)) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(207,a,204,a)].
% 0.88/1.43 208 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.43 209 -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].
% 0.88/1.43 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(208,a,209,a)].
% 0.88/1.43 210 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.43 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(210,a,209,a)].
% 0.88/1.43 211 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.44 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(211,a,209,a)].
% 0.88/1.44 212 class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.44 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(212,a,209,a)].
% 0.88/1.44 213 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 0.88/1.44 214 -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].
% 0.88/1.44 215 -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].
% 0.88/1.44 216 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 0.88/1.44 217 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 0.88/1.44 218 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 0.88/1.44 219 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 0.88/1.44 220 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 0.88/1.44 221 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 0.88/1.44 222 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 0.88/1.44 223 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 0.88/1.44 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(213,a,215,a)].
% 0.88/1.44 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(213,a,216,a)].
% 0.88/1.46 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(213,a,218,a)].
% 0.88/1.46 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(213,a,220,a)].
% 0.88/1.46 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(213,a,222,a)].
% 0.88/1.46 224 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 0.88/1.46 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(224,a,215,a)].
% 0.88/1.46 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(224,a,216,a)].
% 0.88/1.46 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(224,a,218,a)].
% 0.88/1.46 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(224,a,220,a)].
% 0.88/1.46 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(224,a,222,a)].
% 0.88/1.46 225 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 0.88/1.46 226 -class_RealVector_Oreal__normed__vector(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_RealVector_Onorm__class_Onorm(B,A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__le__zero__iff_0) # label(axiom). [assumption].
% 0.88/1.46 227 -class_RealVector_Oreal__normed__vector(A) | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__le__zero__iff_1) # label(axiom). [assumption].
% 0.88/1.46 228 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(B,A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_norm__eq__zero_0) # label(axiom). [assumption].
% 0.88/1.46 229 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__real_Ozero_0) # label(axiom). [assumption].
% 0.88/1.46 230 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(B,A),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__norm__iff_1) # label(axiom). [assumption].
% 0.88/1.46 231 -class_RealVector_Oreal__normed__vector(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(A),A),tc_RealDef_Oreal) # label(cls_zero__less__norm__iff_0) # label(axiom). [assumption].
% 0.88/1.46 232 -class_RealVector_Oreal__normed__vector(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(B,A),tc_RealDef_Oreal) # label(cls_norm__ge__zero_0) # label(axiom). [assumption].
% 0.88/1.46 233 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_norm__zero_0) # label(axiom). [assumption].
% 0.88/1.47 234 -class_RealVector_Oreal__normed__vector(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_RealVector_Onorm__class_Onorm(B,A),c_HOL_Otimes__class_Otimes(C,c_RealVector_Onorm__class_Onorm(D,A),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__ratiotest__lemma_0) # label(axiom). [assumption].
% 0.88/1.47 235 -class_RealVector_Oreal__normed__vector(A) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(B,A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__not__less__zero_0) # label(axiom). [assumption].
% 0.88/1.47 236 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(B,C,A),A) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(C,B,A),A) # label(cls_norm__minus__commute_0) # label(axiom). [assumption].
% 0.88/1.47 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(225,a,226,a)].
% 0.88/1.47 Derived: c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(225,a,227,a)].
% 0.88/1.47 Derived: c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(225,a,228,a)].
% 0.88/1.47 Derived: -class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(225,a,229,a)].
% 0.88/1.47 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(225,a,230,a)].
% 0.88/1.47 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(225,a,231,a)].
% 0.88/1.47 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(225,a,232,a)].
% 0.88/1.47 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(225,a,233,a)].
% 0.88/1.47 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,c_RealVector_Onorm__class_Onorm(C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(225,a,234,a)].
% 0.88/1.47 Derived: -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(225,a,235,a)].
% 0.88/1.47 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(225,a,236,a)].
% 0.88/1.47 237 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 0.88/1.47 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_lessequals(c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(237,a,226,a)].
% 0.88/1.47 Derived: c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(237,a,227,a)].
% 0.88/1.47 Derived: c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(237,a,228,a)].
% 0.88/1.47 Derived: -class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(237,a,229,a)].
% 0.88/1.50 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(237,a,230,a)].
% 0.88/1.50 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal). [resolve(237,a,231,a)].
% 0.88/1.50 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),tc_RealDef_Oreal). [resolve(237,a,232,a)].
% 0.88/1.50 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(237,a,233,a)].
% 0.88/1.50 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_lessequals(c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,c_RealVector_Onorm__class_Onorm(C,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(237,a,234,a)].
% 0.88/1.50 Derived: -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(237,a,235,a)].
% 0.88/1.50 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(B,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(237,a,236,a)].
% 0.88/1.50 238 class_Ring__and__Field_Olordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Olordered__ring) # label(axiom). [assumption].
% 0.88/1.50 239 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__le__mult_0) # label(axiom). [assumption].
% 0.88/1.50 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(238,a,239,a)].
% 0.88/1.50 240 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) # label(axiom). [assumption].
% 0.88/1.50 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(240,a,239,a)].
% 0.88/1.50 241 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.88/1.50 242 -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].
% 0.88/1.50 243 -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].
% 0.88/1.50 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(241,a,242,a)].
% 0.88/1.50 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(241,a,243,a)].
% 0.88/1.50 244 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.88/1.50 Derived: c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(244,a,242,a)].
% 0.88/1.50 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(244,a,243,a)].
% 0.88/1.50 245 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.88/1.54 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(245,a,242,a)].
% 0.88/1.54 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(245,a,243,a)].
% 0.88/1.54 246 class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.88/1.54 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(246,a,242,a)].
% 0.88/1.54 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(246,a,243,a)].
% 0.88/1.54 247 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.54 248 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 0.88/1.54 249 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 0.88/1.54 250 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 0.88/1.54 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(247,a,250,a)].
% 0.88/1.54 251 class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.54 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(251,a,250,a)].
% 0.88/1.54 252 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 0.88/1.54 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(252,a,250,a)].
% 0.88/1.54 253 class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 0.88/1.54 254 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_0) # label(axiom). [assumption].
% 0.88/1.54 255 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_1) # label(axiom). [assumption].
% 0.88/1.54 256 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_2) # label(axiom). [assumption].
% 0.88/1.54 257 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_3) # label(axiom). [assumption].
% 0.88/1.54 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(253,a,254,a)].
% 0.88/1.54 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(253,a,255,a)].
% 0.88/1.54 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(253,a,256,a)].
% 0.88/1.54 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(253,a,257,a)].
% 0.88/1.54 258 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 0.88/1.54 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(258,a,254,a)].
% 0.88/1.54 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(258,a,255,a)].
% 0.88/1.54 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(258,a,256,a)].
% 0.88/1.54 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(258,a,257,a)].
% 0.88/1.54 259 class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 0.88/1.54 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(259,a,254,a)].
% 0.88/1.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(259,a,255,a)].
% 0.88/1.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(259,a,256,a)].
% 0.88/1.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(259,a,257,a)].
% 0.88/1.56 260 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.88/1.56 261 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 0.88/1.56 262 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 0.88/1.56 263 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 0.88/1.56 264 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 0.88/1.56 265 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 0.88/1.56 266 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 0.88/1.56 267 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 0.88/1.56 268 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 0.88/1.56 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(260,a,261,a)].
% 0.88/1.56 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(260,a,262,a)].
% 0.88/1.56 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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),tc_Int_Oint). [resolve(260,a,263,a)].
% 0.88/1.56 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(260,a,264,a)].
% 0.88/1.56 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(260,a,265,a)].
% 0.88/1.56 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(260,a,266,a)].
% 0.88/1.56 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(260,a,267,a)].
% 0.88/1.56 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(260,a,268,a)].
% 0.88/1.56 269 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.88/1.56 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(269,a,261,a)].
% 0.88/1.56 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(269,a,262,a)].
% 0.88/1.56 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(269,a,263,a)].
% 0.88/1.56 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(269,a,264,a)].
% 0.88/1.56 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(269,a,265,a)].
% 0.88/1.56 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(269,a,266,a)].
% 0.88/1.56 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(269,a,267,a)].
% 0.88/1.56 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(269,a,268,a)].
% 0.88/1.56 270 class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.88/1.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(270,a,261,a)].
% 0.88/1.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(270,a,262,a)].
% 0.88/1.56 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(270,a,263,a)].
% 0.88/1.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(270,a,264,a)].
% 0.88/1.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(270,a,265,a)].
% 0.88/1.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(270,a,266,a)].
% 0.88/1.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(270,a,267,a)].
% 0.88/1.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(270,a,268,a)].
% 0.88/1.60 271 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 0.88/1.60 272 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 0.88/1.60 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(271,a,272,a)].
% 0.88/1.60 273 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 0.88/1.60 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(273,a,272,a)].
% 0.88/1.60 274 class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 0.88/1.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(274,a,272,a)].
% 0.88/1.60 275 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 0.88/1.60 276 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 0.88/1.60 277 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 0.88/1.60 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(275,a,277,a)].
% 0.88/1.60 278 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 0.88/1.60 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(278,a,277,a)].
% 0.88/1.62 279 class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 0.88/1.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(279,a,277,a)].
% 0.88/1.62 280 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 0.88/1.62 281 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,C,A) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 0.88/1.62 282 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 0.88/1.62 283 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A) | -c_lessequals(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A),A) # label(cls_le__add__iff2_1) # label(axiom). [assumption].
% 0.88/1.62 284 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,A),E,A),F,A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,A),B,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,A),F,A),A) # label(cls_le__add__iff2_0) # label(axiom). [assumption].
% 0.88/1.62 285 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),F,A) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 0.88/1.62 286 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A),E,A),F,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),E,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,A),F,A),A) # label(cls_le__add__iff1_0) # label(axiom). [assumption].
% 0.88/1.62 287 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 0.88/1.62 288 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 0.88/1.62 289 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 0.88/1.62 290 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A),A) # label(cls_less__add__iff2_1) # label(axiom). [assumption].
% 0.88/1.62 291 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,A),E,A),F,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,A),B,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,A),F,A),A) # label(cls_less__add__iff2_0) # label(axiom). [assumption].
% 0.88/1.62 292 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),F,A) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 0.88/1.62 293 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A),E,A),F,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),E,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,A),F,A),A) # label(cls_less__add__iff1_0) # label(axiom). [assumption].
% 0.88/1.62 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint). [resolve(280,a,281,a)].
% 0.88/1.62 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,A,tc_Int_Oint). [resolve(280,a,282,a)].
% 0.88/1.62 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(280,a,283,a)].
% 0.88/1.62 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),D,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(280,a,284,a)].
% 0.88/1.62 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint),E,tc_Int_Oint). [resolve(280,a,285,a)].
% 0.88/1.62 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint),D,tc_Int_Oint),E,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),D,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(280,a,286,a)].
% 0.88/1.62 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(280,a,290,a)].
% 0.88/1.62 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),D,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(280,a,291,a)].
% 0.88/1.62 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint),E,tc_Int_Oint). [resolve(280,a,292,a)].
% 0.88/1.62 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint),D,tc_Int_Oint),E,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),D,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(280,a,293,a)].
% 0.88/1.62 294 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 0.88/1.62 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal). [resolve(294,a,281,a)].
% 0.88/1.62 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,A,tc_RealDef_Oreal). [resolve(294,a,282,a)].
% 0.88/1.62 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(294,a,283,a)].
% 0.88/1.62 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(294,a,284,a)].
% 0.88/1.62 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal),B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),E,tc_RealDef_Oreal). [resolve(294,a,285,a)].
% 0.88/1.62 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),E,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(294,a,286,a)].
% 0.88/1.62 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(294,a,290,a)].
% 0.88/1.62 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(294,a,291,a)].
% 0.88/1.62 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal),B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),E,tc_RealDef_Oreal). [resolve(294,a,292,a)].
% 0.88/1.62 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),E,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(294,a,293,a)].
% 0.88/1.62 295 class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 0.88/1.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)). [resolve(295,a,281,a)].
% 0.88/1.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,B,tc_Polynomial_Opoly(A)). [resolve(295,a,282,a)].
% 0.88/1.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(295,a,283,a)].
% 0.88/1.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(295,a,284,a)].
% 0.88/1.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)). [resolve(295,a,285,a)].
% 0.88/1.62 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(295,a,286,a)].
% 0.88/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(295,a,290,a)].
% 0.88/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(295,a,291,a)].
% 0.88/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)). [resolve(295,a,292,a)].
% 0.88/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(295,a,293,a)].
% 0.88/1.63 296 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 0.88/1.63 297 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 0.88/1.63 298 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 0.88/1.63 299 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 0.88/1.63 300 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 0.88/1.63 301 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 0.88/1.63 302 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 0.88/1.63 303 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 0.88/1.63 304 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 0.88/1.63 305 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 0.88/1.63 306 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 0.88/1.63 307 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 0.88/1.63 308 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 0.88/1.63 309 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 0.88/1.63 310 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 0.88/1.63 311 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 0.88/1.63 312 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 0.88/1.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(296,a,297,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(296,a,298,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(296,a,299,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(296,a,300,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(296,a,301,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(296,a,302,a)].
% 0.88/1.64 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(296,a,303,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(296,a,305,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(296,a,306,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(296,a,308,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(296,a,309,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(296,a,310,a)].
% 0.88/1.64 313 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(313,a,297,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(313,a,298,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(313,a,299,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(313,a,300,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(313,a,301,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(313,a,302,a)].
% 0.88/1.64 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(313,a,303,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(313,a,305,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(313,a,306,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(313,a,308,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(313,a,309,a)].
% 0.88/1.64 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(313,a,310,a)].
% 0.88/1.64 314 class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 0.88/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(314,a,297,a)].
% 0.88/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(314,a,298,a)].
% 0.88/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(314,a,299,a)].
% 0.88/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(314,a,300,a)].
% 0.88/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(314,a,301,a)].
% 0.88/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(314,a,302,a)].
% 0.88/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(314,a,303,a)].
% 0.88/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(314,a,305,a)].
% 0.88/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(314,a,306,a)].
% 0.88/1.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(314,a,308,a)].
% 0.88/1.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(314,a,309,a)].
% 0.88/1.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(314,a,310,a)].
% 0.88/1.67 315 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 0.88/1.67 316 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 0.88/1.67 317 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 0.88/1.67 318 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 0.88/1.67 319 class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 0.88/1.67 320 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].
% 0.88/1.67 321 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 0.88/1.67 322 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 0.88/1.67 323 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != 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].
% 0.88/1.67 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(320,a,321,a)].
% 0.88/1.67 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(320,a,322,a)].
% 0.88/1.67 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint) != 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(320,a,323,a)].
% 0.88/1.67 324 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.44/1.70 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(324,a,321,a)].
% 1.44/1.70 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(324,a,322,a)].
% 1.44/1.70 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(324,a,323,a)].
% 1.44/1.70 325 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].
% 1.44/1.70 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(325,a,321,a)].
% 1.44/1.70 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(325,a,322,a)].
% 1.44/1.70 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex) != 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(325,a,323,a)].
% 1.44/1.70 326 class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.44/1.70 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(326,a,321,a)].
% 1.44/1.70 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(326,a,322,a)].
% 1.44/1.70 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(326,a,323,a)].
% 1.44/1.70 327 class_Ring__and__Field_Omult__zero(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.44/1.70 328 -class_Ring__and__Field_Omult__zero(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__right_0) # label(axiom). [assumption].
% 1.44/1.70 329 -class_Ring__and__Field_Omult__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__left_0) # label(axiom). [assumption].
% 1.44/1.70 330 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.44/1.70 331 class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.44/1.70 332 class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.44/1.70 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(332,a,328,a)].
% 1.44/1.70 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(332,a,329,a)].
% 1.44/1.70 333 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.44/1.70 334 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 1.44/1.70 335 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 1.44/1.70 336 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 1.44/1.70 337 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 1.44/1.70 338 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_Oadd__left_0) # label(axiom). [assumption].
% 1.44/1.70 339 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_Oadd_0) # label(axiom). [assumption].
% 1.44/1.70 340 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_Oadd__right_0) # label(axiom). [assumption].
% 1.44/1.70 341 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_Oadd_0) # label(axiom). [assumption].
% 1.44/1.70 342 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,E,A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,D,A),E,A),A),c_HOL_Otimes__class_Otimes(D,c_HOL_Ominus__class_Ominus(C,E,A),A),A) # label(cls_mult_Oprod__diff__prod_0) # label(axiom). [assumption].
% 1.44/1.70 343 -class_RealVector_Oreal__normed__algebra(A) | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(B,C,A),A),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(B,A),c_RealVector_Onorm__class_Onorm(C,A),tc_RealDef_Oreal),tc_RealDef_Oreal) # label(cls_norm__mult__ineq_0) # label(axiom). [assumption].
% 1.44/1.70 344 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(B,C,A),A),c_HOL_Otimes__class_Otimes(D,E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(C,A),E,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(B,A),D,tc_RealDef_Oreal) # label(cls_norm__mult__less_0) # label(axiom). [assumption].
% 1.44/1.70 345 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ominus__class_Ominus(C,D,A),A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_Odiff_0) # label(axiom). [assumption].
% 1.44/1.70 346 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ominus__class_Ominus(C,D,A),A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_Odiff__right_0) # label(axiom). [assumption].
% 1.44/1.70 347 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_Odiff__left_0) # label(axiom). [assumption].
% 1.44/1.70 348 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_Odiff_0) # label(axiom). [assumption].
% 1.44/1.71 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(333,a,338,a)].
% 1.44/1.71 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(333,a,340,a)].
% 1.44/1.71 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(333,a,342,a)].
% 1.44/1.71 Derived: c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(333,a,343,a)].
% 1.44/1.71 Derived: c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(B,tc_RealDef_Oreal),D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(333,a,344,a)].
% 1.44/1.71 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(333,a,345,a)].
% 1.44/1.71 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(333,a,347,a)].
% 1.44/1.71 349 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.44/1.71 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(349,a,338,a)].
% 1.44/1.71 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(349,a,340,a)].
% 1.44/1.71 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(349,a,342,a)].
% 1.44/1.71 Derived: c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(B,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(349,a,343,a)].
% 1.44/1.75 Derived: c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(B,tc_Complex_Ocomplex),D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),C,tc_RealDef_Oreal). [resolve(349,a,344,a)].
% 1.44/1.75 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(349,a,345,a)].
% 1.44/1.75 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(349,a,347,a)].
% 1.44/1.75 350 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.44/1.75 351 -class_Ring__and__Field_Ocomm__semiring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 1.44/1.75 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(350,a,351,a)].
% 1.44/1.75 352 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.44/1.75 353 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.44/1.75 354 class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.44/1.75 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(354,a,351,a)].
% 1.44/1.75 355 class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.44/1.75 356 -class_Ring__and__Field_Ono__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divisors_0) # label(axiom). [assumption].
% 1.44/1.75 357 -class_Ring__and__Field_Ono__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divirors__neq0_0) # label(axiom). [assumption].
% 1.44/1.75 358 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.44/1.75 359 class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.44/1.75 360 class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.44/1.75 361 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.53/1.78 362 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_mult__1__right_0) # label(axiom). [assumption].
% 1.53/1.78 363 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_mult__1__left_0) # label(axiom). [assumption].
% 1.53/1.78 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(361,a,362,a)].
% 1.53/1.78 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) = A. [resolve(361,a,363,a)].
% 1.53/1.78 364 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.53/1.78 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(364,a,362,a)].
% 1.53/1.78 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = A. [resolve(364,a,363,a)].
% 1.53/1.78 365 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.53/1.78 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(365,a,362,a)].
% 1.53/1.78 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A. [resolve(365,a,363,a)].
% 1.53/1.78 366 class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.53/1.78 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(366,a,362,a)].
% 1.53/1.78 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = B. [resolve(366,a,363,a)].
% 1.53/1.78 367 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.53/1.78 368 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_mult__1_0) # label(axiom). [assumption].
% 1.53/1.78 369 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.53/1.78 370 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.53/1.78 371 class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.53/1.78 372 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.53/1.78 373 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(E,D,A) | -c_lessequals(C,B,A) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 1.53/1.78 374 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(C,B,A) | -c_lessequals(E,D,A) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 1.53/1.78 375 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,C,A) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 1.53/1.78 376 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 1.53/1.78 377 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(E,D,A) | -c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 1.53/1.78 378 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 1.53/1.78 379 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 1.53/1.78 380 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_HOL_Oord__class_Oless(D,E,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 1.53/1.78 381 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,E,A) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 1.53/1.78 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(372,a,373,a)].
% 1.53/1.78 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint). [resolve(372,a,374,a)].
% 1.53/1.78 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(372,a,375,a)].
% 1.53/1.78 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(372,a,376,a)].
% 1.53/1.78 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(A,c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint),tc_Int_Oint). [resolve(372,a,377,a)].
% 1.53/1.78 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(372,a,378,a)].
% 1.53/1.78 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(372,a,379,a)].
% 1.53/1.78 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_HOL_Oord__class_Oless(C,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(372,a,380,a)].
% 1.53/1.78 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,D,tc_Int_Oint). [resolve(372,a,381,a)].
% 1.53/1.78 382 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.53/1.78 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_lessequals(D,C,tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(382,a,373,a)].
% 1.53/1.78 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal) | -c_lessequals(D,C,tc_RealDef_Oreal). [resolve(382,a,374,a)].
% 1.53/1.78 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(382,a,375,a)].
% 1.53/1.78 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(382,a,376,a)].
% 1.53/1.78 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(D,C,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Oplus__class_Oplus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(382,a,377,a)].
% 1.54/1.80 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(382,a,378,a)].
% 1.54/1.80 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(382,a,379,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(382,a,380,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,D,tc_RealDef_Oreal). [resolve(382,a,381,a)].
% 1.54/1.80 383 class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.54/1.80 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ominus__class_Ominus(D,E,tc_Polynomial_Opoly(A)) | c_lessequals(E,D,tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(383,a,373,a)].
% 1.54/1.80 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ominus__class_Ominus(D,E,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)) | -c_lessequals(E,D,tc_Polynomial_Opoly(A)). [resolve(383,a,374,a)].
% 1.54/1.80 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(383,a,375,a)].
% 1.54/1.80 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(383,a,376,a)].
% 1.54/1.80 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(E,D,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(383,a,377,a)].
% 1.54/1.80 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(383,a,378,a)].
% 1.54/1.80 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(383,a,379,a)].
% 1.54/1.80 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ominus__class_Ominus(D,E,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(D,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(383,a,380,a)].
% 1.54/1.80 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ominus__class_Ominus(D,E,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,E,tc_Polynomial_Opoly(A)). [resolve(383,a,381,a)].
% 1.54/1.80 384 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.54/1.80 385 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 1.54/1.80 386 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 1.54/1.80 387 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 1.54/1.80 388 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,C,A),C,A) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 1.54/1.80 389 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 1.54/1.80 390 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(384,a,385,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(384,a,386,a)].
% 1.54/1.80 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),B,tc_Int_Oint) = A. [resolve(384,a,388,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(384,a,389,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),B,tc_Int_Oint) = A. [resolve(384,a,390,a)].
% 1.54/1.80 391 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(391,a,385,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(391,a,386,a)].
% 1.54/1.80 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = A. [resolve(391,a,388,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(391,a,389,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = A. [resolve(391,a,390,a)].
% 1.54/1.80 392 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(392,a,385,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(392,a,386,a)].
% 1.54/1.80 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A. [resolve(392,a,388,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(392,a,389,a)].
% 1.54/1.80 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A. [resolve(392,a,390,a)].
% 1.54/1.80 393 class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Oab__group__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.54/1.80 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(393,a,385,a)].
% 1.54/1.80 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(393,a,386,a)].
% 1.54/1.80 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = B. [resolve(393,a,388,a)].
% 1.54/1.80 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = C. [resolve(393,a,389,a)].
% 1.54/1.80 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = B. [resolve(393,a,390,a)].
% 1.57/1.84 394 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.57/1.84 395 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.57/1.84 396 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 1.57/1.84 397 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 1.57/1.84 398 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 1.57/1.84 399 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 1.57/1.84 400 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 1.57/1.84 401 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.57/1.84 402 class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.57/1.84 403 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.57/1.84 404 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 1.57/1.84 405 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 1.57/1.84 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(403,a,404,a)].
% 1.57/1.84 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(403,a,405,a)].
% 1.57/1.84 406 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.57/1.87 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(406,a,404,a)].
% 1.57/1.87 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(406,a,405,a)].
% 1.57/1.87 407 class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.57/1.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(407,a,404,a)].
% 1.57/1.87 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(407,a,405,a)].
% 1.57/1.87 408 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.57/1.87 409 -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].
% 1.57/1.87 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C. [resolve(408,a,409,a)].
% 1.57/1.87 410 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.57/1.87 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal) | B = C. [resolve(410,a,409,a)].
% 1.57/1.87 411 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.57/1.87 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C. [resolve(411,a,409,a)].
% 1.57/1.87 412 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocancel__comm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.57/1.87 Derived: -class_OrderedGroup_Ocancel__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)) | C = D. [resolve(412,a,409,a)].
% 1.57/1.87 413 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.57/1.87 414 -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].
% 1.57/1.87 415 -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].
% 1.65/1.92 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint) | A = C. [resolve(413,a,415,a)].
% 1.65/1.92 416 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.65/1.92 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal) | A = C. [resolve(416,a,415,a)].
% 1.65/1.92 417 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.65/1.92 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(C,B,tc_Complex_Ocomplex) | A = C. [resolve(417,a,415,a)].
% 1.65/1.92 418 class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocancel__comm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.65/1.92 Derived: -class_OrderedGroup_Ocancel__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)) | B = D. [resolve(418,a,415,a)].
% 1.65/1.92 419 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.65/1.92 420 -class_RealVector_Oreal__normed__algebra__1(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) # label(cls_norm__one_0) # label(axiom). [assumption].
% 1.65/1.92 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(419,a,420,a)].
% 1.65/1.92 421 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.65/1.92 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(421,a,420,a)].
% 1.65/1.92 422 class_Ring__and__Field_Oabs__if(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 1.65/1.92 423 -class_Ring__and__Field_Oabs__if(A) | c_HOL_Oabs__class_Oabs(B,A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_1) # label(axiom). [assumption].
% 1.65/1.92 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(422,a,423,a)].
% 1.65/1.92 424 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 1.65/1.92 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(424,a,423,a)].
% 1.65/1.92 425 class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 1.65/1.92 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(425,a,423,a)].
% 1.65/1.92 426 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].
% 1.65/1.92 427 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 1.65/1.92 428 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.65/1.93 429 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.65/1.93 430 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.65/1.93 431 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A) | D = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 1.65/1.93 432 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 1.65/1.93 433 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),A) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 1.65/1.93 434 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,A),A),A) # label(cls_left__diff__distrib__number__of_0) # label(axiom). [assumption].
% 1.65/1.93 435 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ominus__class_Ominus(C,D,A),A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A) # label(cls_right__diff__distrib__number__of_0) # label(axiom). [assumption].
% 1.65/1.93 436 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,B,A),C,A),E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A) # label(cls_eq__add__iff2_1) # label(axiom). [assumption].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint) | C = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),B,tc_Int_Oint),E,tc_Int_Oint). [resolve(430,a,431,a)].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint) = E. [resolve(430,a,432,a)].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint),tc_Int_Oint). [resolve(430,a,433,a)].
% 1.65/1.93 Derived: -class_Int_Onumber(tc_Int_Oint) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(430,a,434,a)].
% 1.65/1.93 Derived: -class_Int_Onumber(tc_Int_Oint) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),C,tc_Int_Oint),tc_Int_Oint). [resolve(430,a,435,a)].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,A,tc_Int_Oint),B,tc_Int_Oint),D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),D,tc_Int_Oint). [resolve(430,a,436,a)].
% 1.65/1.93 437 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal) | C = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),E,tc_RealDef_Oreal). [resolve(437,a,431,a)].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal),B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = E. [resolve(437,a,432,a)].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal),B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(437,a,433,a)].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),D,tc_RealDef_Oreal). [resolve(437,a,436,a)].
% 1.65/1.93 438 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex) | C = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex). [resolve(438,a,431,a)].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = E. [resolve(438,a,432,a)].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(438,a,433,a)].
% 1.65/1.93 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex). [resolve(438,a,436,a)].
% 1.65/1.93 439 class_Ring__and__Field_Oring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.65/1.97 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)) | D = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)). [resolve(439,a,431,a)].
% 1.65/1.97 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = F. [resolve(439,a,432,a)].
% 1.65/1.97 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(439,a,433,a)].
% 1.65/1.97 Derived: -class_Ring__and__Field_Ocomm__ring(A) | -class_Int_Onumber(tc_Polynomial_Opoly(A)) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(439,a,434,a)].
% 1.65/1.97 Derived: -class_Ring__and__Field_Ocomm__ring(A) | -class_Int_Onumber(tc_Polynomial_Opoly(A)) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),c_HOL_Ominus__class_Ominus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(439,a,435,a)].
% 1.65/1.97 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)). [resolve(439,a,436,a)].
% 1.65/1.97 440 class_RealVector_Odist__norm(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Odist__norm) # label(axiom). [assumption].
% 1.65/1.97 441 -class_RealVector_Odist__norm(A) | c_RealVector_Odist__class_Odist(B,C,A) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(B,C,A),A) # label(cls_dist__norm_0) # label(axiom). [assumption].
% 1.65/1.97 Derived: c_RealVector_Odist__class_Odist(A,B,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(440,a,441,a)].
% 1.65/1.97 442 class_RealVector_Odist__norm(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Odist__norm) # label(axiom). [assumption].
% 1.65/1.97 Derived: c_RealVector_Odist__class_Odist(A,B,tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(442,a,441,a)].
% 1.65/1.97 443 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 1.65/1.97 444 -class_RealVector_Oreal__normed__div__algebra(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(B,A),c_RealVector_Onorm__class_Onorm(C,A),tc_RealDef_Oreal) # label(cls_norm__mult_0) # label(axiom). [assumption].
% 2.05/2.32 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(443,a,444,a)].
% 2.05/2.32 445 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 2.05/2.32 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(B,tc_Complex_Ocomplex),tc_RealDef_Oreal). [resolve(445,a,444,a)].
% 2.05/2.32 446 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.05/2.32 447 -class_OrderedGroup_Oab__semigroup__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 2.05/2.32 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(446,a,447,a)].
% 2.05/2.32 448 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.05/2.32 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(448,a,447,a)].
% 2.05/2.32 449 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.05/2.32 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(449,a,447,a)].
% 2.05/2.32 450 class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.05/2.32 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(450,a,447,a)].
% 2.05/2.32
% 2.05/2.32 ============================== end predicate elimination =============
% 2.05/2.32
% 2.05/2.32 Auto_denials: (non-Horn, no changes).
% 2.05/2.32
% 2.05/2.32 Term ordering decisions:
% 2.05/2.32 Function symbol KB weights: tc_RealDef_Oreal=1. tc_Int_Oint=1. tc_Complex_Ocomplex=1. v_z=1. v_cs____=1. v_e=1. v_da____=1. v_w____=1. v_m____=1. c_HOL_Oabs__class_Oabs=1. c_Int_Onumber__class_Onumber__of=1. c_RealVector_Onorm__class_Onorm=1. c_RealVector_Oof__real=1. tc_Polynomial_Opoly=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Oone__class_Oone=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ominus__class_Ominus=1. c_RealVector_Odist__class_Odist=1. c_Polynomial_Osmult=1. c_Polynomial_Opoly=1. v_sko__local__XpCons__1=1. v_sko__local__XpCons__Xhyps__1=1.
% 2.05/2.32
% 2.05/2.32 ============================== end of process initial clauses ========
% 2.05/2.32
% 2.05/2.32 ============================== CLAUSES FOR SEARCH ====================
% 2.05/2.32
% 2.05/2.32 ============================== end of clauses for search =============
% 2.05/2.32
% 2.05/2.32 ============================== SEARCH ================================
% 2.05/2.32
% 2.05/2.32 % Starting search at 0.92 seconds.
% 2.05/2.32
% 2.05/2.32 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 34 (0.00 of 1.02 sec).
% 2.05/2.32
% 2.05/2.32 Low Water (keep): wt=33.0Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------