TSTP Solution File: SWV595-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV595-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:14:01 EDT 2022
% Result : Timeout 300.05s 300.33s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV595-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 16 00:41:19 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.91/1.19 ============================== Prover9 ===============================
% 0.91/1.19 Prover9 (32) version 2009-11A, November 2009.
% 0.91/1.19 Process 337 was started by sandbox2 on n020.cluster.edu,
% 0.91/1.19 Thu Jun 16 00:41:20 2022
% 0.91/1.19 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32652_n020.cluster.edu".
% 0.91/1.19 ============================== end of head ===========================
% 0.91/1.19
% 0.91/1.19 ============================== INPUT =================================
% 0.91/1.19
% 0.91/1.19 % Reading from file /tmp/Prover9_32652_n020.cluster.edu
% 0.91/1.19
% 0.91/1.19 set(prolog_style_variables).
% 0.91/1.19 set(auto2).
% 0.91/1.19 % set(auto2) -> set(auto).
% 0.91/1.19 % set(auto) -> set(auto_inference).
% 0.91/1.19 % set(auto) -> set(auto_setup).
% 0.91/1.19 % set(auto_setup) -> set(predicate_elim).
% 0.91/1.19 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.91/1.19 % set(auto) -> set(auto_limits).
% 0.91/1.19 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.91/1.19 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.91/1.19 % set(auto) -> set(auto_denials).
% 0.91/1.19 % set(auto) -> set(auto_process).
% 0.91/1.19 % set(auto2) -> assign(new_constants, 1).
% 0.91/1.19 % set(auto2) -> assign(fold_denial_max, 3).
% 0.91/1.19 % set(auto2) -> assign(max_weight, "200.000").
% 0.91/1.19 % set(auto2) -> assign(max_hours, 1).
% 0.91/1.19 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.91/1.19 % set(auto2) -> assign(max_seconds, 0).
% 0.91/1.19 % set(auto2) -> assign(max_minutes, 5).
% 0.91/1.19 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.91/1.19 % set(auto2) -> set(sort_initial_sos).
% 0.91/1.19 % set(auto2) -> assign(sos_limit, -1).
% 0.91/1.19 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.91/1.19 % set(auto2) -> assign(max_megs, 400).
% 0.91/1.19 % set(auto2) -> assign(stats, some).
% 0.91/1.19 % set(auto2) -> clear(echo_input).
% 0.91/1.19 % set(auto2) -> set(quiet).
% 0.91/1.19 % set(auto2) -> clear(print_initial_clauses).
% 0.91/1.19 % set(auto2) -> clear(print_given).
% 0.91/1.19 assign(lrs_ticks,-1).
% 0.91/1.19 assign(sos_limit,10000).
% 0.91/1.19 assign(order,kbo).
% 0.91/1.19 set(lex_order_vars).
% 0.91/1.19 clear(print_given).
% 0.91/1.19
% 0.91/1.19 % formulas(sos). % not echoed (476 formulas)
% 0.91/1.19
% 0.91/1.19 ============================== end of input ==========================
% 0.91/1.19
% 0.91/1.19 % From the command line: assign(max_seconds, 300).
% 0.91/1.19
% 0.91/1.19 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.91/1.19
% 0.91/1.19 % Formulas that are not ordinary clauses:
% 0.91/1.19
% 0.91/1.19 ============================== end of process non-clausal formulas ===
% 0.91/1.19
% 0.91/1.19 ============================== PROCESS INITIAL CLAUSES ===============
% 0.91/1.19
% 0.91/1.19 ============================== PREDICATE ELIMINATION =================
% 0.91/1.19 1 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.91/1.19 2 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 0.91/1.19 3 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_class__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 0.91/1.19 4 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(D,B,A),C,A) # label(cls_dvd__mult__right_0) # label(axiom). [assumption].
% 0.91/1.19 5 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_dvd__mult__left_0) # label(axiom). [assumption].
% 0.91/1.19 6 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mult2_0) # label(axiom). [assumption].
% 0.91/1.19 7 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mult_0) # label(axiom). [assumption].
% 0.91/1.19 8 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__trans_0) # label(axiom). [assumption].
% 0.91/1.19 9 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,B,A) # label(cls_dvd__refl_0) # label(axiom). [assumption].
% 0.91/1.19 10 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Otimes__class_Otimes(D,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),E,A),A) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 0.91/1.19 11 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(D,E,A),A),A) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 0.91/1.19 12 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 0.91/1.19 13 -class_Ring__and__Field_Ocomm__semiring__1(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_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 0.91/1.19 14 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 0.91/1.19 15 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) = c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 0.91/1.19 16 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 0.91/1.19 17 -class_Ring__and__Field_Ocomm__semiring__1(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_dvd__0__left_0) # label(axiom). [assumption].
% 0.91/1.19 18 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A),A) # label(cls_dvd__power_1) # label(axiom). [assumption].
% 0.91/1.19 19 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_dvd__triv__right_0) # label(axiom). [assumption].
% 0.91/1.19 20 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_dvd__triv__left_0) # label(axiom). [assumption].
% 0.91/1.19 21 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,C,A) = c_HOL_Otimes__class_Otimes(C,B,A) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 0.91/1.19 22 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,C,A) = c_HOL_Otimes__class_Otimes(C,B,A) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 0.91/1.19 23 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__power__same_0) # label(axiom). [assumption].
% 0.91/1.19 24 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_dvd__0__right_0) # label(axiom). [assumption].
% 0.91/1.19 25 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 0.91/1.19 26 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 0.91/1.19 27 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 0.91/1.19 28 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,E,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_mult__dvd__mono_0) # label(axiom). [assumption].
% 0.91/1.19 29 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__dvd_0) # label(axiom). [assumption].
% 0.91/1.19 30 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_class__semiring_Omul__1_0) # label(axiom). [assumption].
% 0.91/1.19 31 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 0.91/1.19 32 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 0.91/1.19 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(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(1,a,2,a)].
% 0.91/1.19 Derived: c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,C,tc_RealDef_Oreal),c_Power_Opower__class_Opower(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,3,a)].
% 0.91/1.19 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(1,a,4,a)].
% 0.91/1.19 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(1,a,5,a)].
% 0.91/1.19 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(1,a,6,a)].
% 0.91/1.19 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal). [resolve(1,a,7,a)].
% 0.91/1.19 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal). [resolve(1,a,8,a)].
% 0.91/1.19 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_RealDef_Oreal). [resolve(1,a,9,a)].
% 0.91/1.19 Derived: c_HOL_Otimes__class_Otimes(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_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),D,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,10,a)].
% 0.91/1.19 Derived: c_HOL_Otimes__class_Otimes(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_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,11,a)].
% 0.91/1.19 Derived: c_HOL_Otimes__class_Otimes(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_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,12,a)].
% 0.95/1.24 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(1,a,13,a)].
% 0.95/1.24 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(1,a,14,a)].
% 0.95/1.24 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,15,a)].
% 0.95/1.24 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(1,a,17,a)].
% 0.95/1.24 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,18,a)].
% 0.95/1.24 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,19,a)].
% 0.95/1.24 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,20,a)].
% 0.95/1.24 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal). [resolve(1,a,21,a)].
% 0.95/1.24 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),c_Power_Opower__class_Opower(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal). [resolve(1,a,23,a)].
% 0.95/1.24 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,24,a)].
% 0.95/1.24 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(1,a,25,a)].
% 0.95/1.24 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(1,a,26,a)].
% 0.95/1.24 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal). [resolve(1,a,28,a)].
% 0.95/1.24 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(1,a,29,a)].
% 0.95/1.24 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = A. [resolve(1,a,30,a)].
% 0.95/1.24 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(1,a,31,a)].
% 0.95/1.24 33 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 0.95/1.24 34 -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].
% 0.95/1.24 35 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) # label(axiom). [assumption].
% 0.95/1.24 36 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(B,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Oone__class_Oone(A),A) # label(cls_of__real__def_0) # label(axiom). [assumption].
% 0.95/1.24 37 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),A) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(B,A),c_RealVector_Oof__real(C,A),A) # label(cls_of__real__mult_0) # label(axiom). [assumption].
% 0.95/1.24 38 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_of__real__eq__0__iff_0) # label(axiom). [assumption].
% 0.95/1.25 39 -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__0_0) # label(axiom). [assumption].
% 0.95/1.25 40 -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].
% 0.95/1.25 41 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(B,A),A) # label(cls_of__real__minus_0) # label(axiom). [assumption].
% 0.95/1.25 42 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(B,A),A) # label(cls_of__real_Ominus_0) # label(axiom). [assumption].
% 0.95/1.25 43 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(B,A) != c_RealVector_Oof__real(C,A) | B = C # label(cls_of__real__eq__iff_0) # label(axiom). [assumption].
% 0.95/1.25 44 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_OscaleR__class_OscaleR(B,C,A) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(B,A),C,A) # label(cls_scaleR__conv__of__real_0) # label(axiom). [assumption].
% 0.95/1.25 45 -class_RealVector_Oreal__algebra__1(A) | c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__real__1_0) # label(axiom). [assumption].
% 0.95/1.25 Derived: c_RealVector_Oof__real(A,tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(35,a,36,a)].
% 0.95/1.25 Derived: c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(A,tc_RealDef_Oreal),c_RealVector_Oof__real(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(35,a,37,a)].
% 0.95/1.25 Derived: c_RealVector_Oof__real(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(35,a,38,a)].
% 0.95/1.25 Derived: c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(35,a,39,a)].
% 0.95/1.25 Derived: c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(35,a,41,a)].
% 0.95/1.25 Derived: c_RealVector_Oof__real(A,tc_RealDef_Oreal) != c_RealVector_Oof__real(B,tc_RealDef_Oreal) | A = B. [resolve(35,a,43,a)].
% 0.95/1.25 Derived: c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(35,a,44,a)].
% 0.95/1.25 Derived: c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(35,a,45,a)].
% 0.95/1.25 46 class_Int_Onumber__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Int_Onumber__ring) # label(axiom). [assumption].
% 0.95/1.25 47 -class_Int_Onumber__ring(A) | c_HOL_Ouminus__class_Ouminus(B,A) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A),B,A) # label(cls_class__ring_Oneg__mul_0) # label(axiom). [assumption].
% 0.95/1.25 48 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_class__fieldgb_Oinverse__divide_0) # label(axiom). [assumption].
% 0.95/1.25 49 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(C,A),A) # label(cls_class__fieldgb_Odivide__inverse_0) # label(axiom). [assumption].
% 0.95/1.25 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(46,a,47,a)].
% 1.00/1.26 Derived: -class_Ring__and__Field_Ofield(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(46,a,48,b)].
% 1.00/1.26 Derived: -class_Ring__and__Field_Ofield(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,c_HOL_Oinverse__class_Oinverse(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(46,a,49,b)].
% 1.00/1.26 50 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.00/1.26 51 -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].
% 1.00/1.26 52 -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].
% 1.00/1.26 53 -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].
% 1.00/1.26 54 -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].
% 1.00/1.26 55 -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].
% 1.00/1.26 56 -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].
% 1.00/1.26 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(50,a,51,a)].
% 1.00/1.26 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(50,a,52,a)].
% 1.00/1.26 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(50,a,53,a)].
% 1.00/1.26 57 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 1.00/1.26 58 -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].
% 1.00/1.26 59 -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].
% 1.00/1.26 60 -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].
% 1.00/1.26 61 -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].
% 1.00/1.26 62 -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].
% 1.00/1.26 63 -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].
% 1.00/1.26 64 -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].
% 1.00/1.26 65 -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].
% 1.00/1.26 66 -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].
% 1.00/1.26 67 -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].
% 1.00/1.26 68 -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].
% 1.00/1.26 69 -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].
% 1.00/1.26 70 -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].
% 1.00/1.26 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(57,a,58,a)].
% 1.00/1.26 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(57,a,60,a)].
% 1.00/1.26 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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(57,a,61,a)].
% 1.00/1.27 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(57,a,62,a)].
% 1.00/1.27 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(57,a,63,a)].
% 1.00/1.27 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),A,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(57,a,64,a)].
% 1.00/1.27 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),A,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(57,a,65,a)].
% 1.00/1.27 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(57,a,66,a)].
% 1.00/1.27 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(57,a,67,a)].
% 1.00/1.27 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),A,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(57,a,68,a)].
% 1.00/1.27 71 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 1.00/1.27 72 -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].
% 1.00/1.27 73 -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].
% 1.00/1.27 74 -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].
% 1.00/1.27 75 -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].
% 1.00/1.27 76 -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].
% 1.00/1.27 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(71,a,75,a)].
% 1.00/1.28 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(71,a,76,a)].
% 1.00/1.28 77 class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) # label(axiom). [assumption].
% 1.00/1.28 78 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(B,A),A) # label(cls_inverse__minus__eq_0) # label(axiom). [assumption].
% 1.00/1.28 79 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),C,A) # label(cls_power__inverse_0) # label(axiom). [assumption].
% 1.00/1.28 80 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_1) # label(axiom). [assumption].
% 1.00/1.28 81 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oinverse__class_Oinverse(C,A) | B = C | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__imp__eq_0) # label(axiom). [assumption].
% 1.00/1.28 82 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oinverse__class_Oinverse(C,A) | B = C # label(cls_inverse__eq__iff__eq_0) # label(axiom). [assumption].
% 1.00/1.28 83 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Oone__class_Oone(A) | c_HOL_Oinverse__class_Oinverse(B,A) = C # label(cls_inverse__unique_0) # label(axiom). [assumption].
% 1.00/1.28 84 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_left__inverse_0) # label(axiom). [assumption].
% 1.00/1.28 85 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(B,A),A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_right__inverse_0) # label(axiom). [assumption].
% 1.00/1.28 86 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(C,A),c_HOL_Oinverse__class_Oinverse(B,A),A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__mult__distrib_0) # label(axiom). [assumption].
% 1.00/1.28 87 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A) = B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__inverse__eq_0) # label(axiom). [assumption].
% 1.00/1.28 88 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A) = B # label(cls_inverse__inverse__eq_0) # label(axiom). [assumption].
% 1.00/1.28 89 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),C,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__inverse_0) # label(axiom). [assumption].
% 1.00/1.28 90 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(B,A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__minus__eq_0) # label(axiom). [assumption].
% 1.00/1.28 91 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_0) # label(axiom). [assumption].
% 1.00/1.28 92 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__zero__imp__zero_0) # label(axiom). [assumption].
% 1.00/1.28 93 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__1_0) # label(axiom). [assumption].
% 1.00/1.28 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(77,a,78,a)].
% 1.00/1.28 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(77,a,79,a)].
% 1.00/1.28 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,80,a)].
% 1.00/1.28 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Oinverse(B,tc_RealDef_Oreal) | A = B | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,81,a)].
% 1.00/1.28 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Oinverse(B,tc_RealDef_Oreal) | A = B. [resolve(77,a,82,a)].
% 1.00/1.28 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal) = B. [resolve(77,a,83,a)].
% 1.00/1.28 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,84,a)].
% 1.00/1.28 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,85,a)].
% 1.00/1.28 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,86,a)].
% 1.00/1.28 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,87,a)].
% 1.00/1.28 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(77,a,88,a)].
% 1.00/1.28 Derived: c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,89,a)].
% 1.00/1.28 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,90,a)].
% 1.00/1.28 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,91,a)].
% 1.00/1.28 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,92,a)].
% 1.00/1.29 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(77,a,93,a)].
% 1.00/1.29 94 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) # label(axiom). [assumption].
% 1.00/1.29 95 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_divide__right__mono__neg_0) # label(axiom). [assumption].
% 1.00/1.29 96 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_divide__right__mono_0) # label(axiom). [assumption].
% 1.00/1.29 97 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__1__iff_1) # label(axiom). [assumption].
% 1.00/1.29 98 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__1__iff_0) # label(axiom). [assumption].
% 1.00/1.29 99 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(B,A),A) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(B,A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__abs__inverse_0) # label(axiom). [assumption].
% 1.00/1.29 100 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__abs__divide_0) # label(axiom). [assumption].
% 1.00/1.29 101 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A) # label(cls_inverse__nonnegative__iff__nonnegative_0) # label(axiom). [assumption].
% 1.00/1.29 102 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_inverse__nonnegative__iff__nonnegative_1) # label(axiom). [assumption].
% 1.00/1.29 103 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oone__class_Oone(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_inverse__le__1__iff_1) # label(axiom). [assumption].
% 1.00/1.29 104 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__divide__1__iff_1) # label(axiom). [assumption].
% 1.00/1.29 105 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),A) # label(cls_zero__le__divide__1__iff_0) # label(axiom). [assumption].
% 1.00/1.29 106 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(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_divide__le__0__iff_5) # label(axiom). [assumption].
% 1.00/1.29 107 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(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_divide__le__0__iff_4) # label(axiom). [assumption].
% 1.00/1.29 108 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(C,B,A),A) # label(cls_zero__le__divide__iff_3) # label(axiom). [assumption].
% 1.00/1.29 109 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(B,C,A),A) # label(cls_zero__le__divide__iff_2) # label(axiom). [assumption].
% 1.00/1.29 110 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(C,B,A),A) # label(cls_zero__le__divide__iff_1) # label(axiom). [assumption].
% 1.00/1.29 111 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(B,C,A),A) # label(cls_zero__le__divide__iff_0) # label(axiom). [assumption].
% 1.00/1.29 112 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oone__class_Oone(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oone__class_Oone(A),A) # label(cls_inverse__le__1__iff_0) # label(axiom). [assumption].
% 1.00/1.29 113 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_inverse__nonpositive__iff__nonpositive_1) # label(axiom). [assumption].
% 1.00/1.29 114 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_inverse__nonpositive__iff__nonpositive_0) # label(axiom). [assumption].
% 1.00/1.29 115 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(B,A),A) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__inverse_0) # label(axiom). [assumption].
% 1.00/1.29 116 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_abs__divide_0) # label(axiom). [assumption].
% 1.00/1.29 117 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_le__divide__eq_9) # label(axiom). [assumption].
% 1.00/1.29 118 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),B,A) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_divide__le__eq_9) # label(axiom). [assumption].
% 1.00/1.29 119 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_0) # label(axiom). [assumption].
% 1.00/1.29 120 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_1) # label(axiom). [assumption].
% 1.00/1.29 121 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_2) # label(axiom). [assumption].
% 1.00/1.29 122 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_3) # label(axiom). [assumption].
% 1.00/1.29 123 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_inverse__le__1__iff_2) # label(axiom). [assumption].
% 1.00/1.29 124 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Oinverse__class_Oinverse(B,A),A) # label(cls_one__le__inverse__iff_1) # label(axiom). [assumption].
% 1.00/1.29 125 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(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__divide__iff_4) # label(axiom). [assumption].
% 1.00/1.29 126 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(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__divide__iff_5) # label(axiom). [assumption].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(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(94,a,95,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(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(94,a,96,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,97,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,98,a)].
% 1.00/1.29 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(94,a,99,a)].
% 1.00/1.29 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(94,a,100,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | 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_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,101,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(94,a,102,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,103,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(94,a,104,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | 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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,105,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(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(94,a,106,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(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(94,a,107,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,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) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,108,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | 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_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,109,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | 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_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,110,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,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) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,111,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,112,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),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(94,a,113,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,114,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,115,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,116,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(94,a,117,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,118,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,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) | -c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,119,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | 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_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,120,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | 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_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,121,a)].
% 1.00/1.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,122,a)].
% 1.00/1.32 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(94,a,123,a)].
% 1.00/1.32 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(94,a,124,a)].
% 1.00/1.32 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(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(94,a,125,a)].
% 1.00/1.32 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(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(94,a,126,a)].
% 1.00/1.32 127 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.00/1.32 128 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 1.00/1.32 129 -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].
% 1.00/1.32 130 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.00/1.32 131 -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].
% 1.00/1.32 132 -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].
% 1.00/1.32 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(130,a,131,a)].
% 1.00/1.32 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(130,a,132,a)].
% 1.00/1.32 133 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.00/1.32 134 -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].
% 1.00/1.32 135 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 1.00/1.32 136 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(B,A),A) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_norm__sgn_1) # label(axiom). [assumption].
% 1.00/1.32 137 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(B,A),A) # label(cls_sgn__minus_0) # label(axiom). [assumption].
% 1.00/1.32 138 -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].
% 1.00/1.32 139 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(C,A),tc_RealDef_Oreal) # label(cls_norm__scaleR_0) # label(axiom). [assumption].
% 1.00/1.32 140 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(B,A),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(B,A) # label(cls_abs__norm__cancel_0) # label(axiom). [assumption].
% 1.00/1.32 141 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR_Ominus__right_0) # label(axiom). [assumption].
% 1.00/1.32 142 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),C,A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR_Ominus__left_0) # label(axiom). [assumption].
% 1.00/1.32 143 -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].
% 1.00/1.32 144 -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].
% 1.00/1.32 145 -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].
% 1.00/1.32 146 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR_Ozero__right_0) # label(axiom). [assumption].
% 1.00/1.32 147 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR_Ozero__left_0) # label(axiom). [assumption].
% 1.00/1.32 148 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__zero__iff_0) # label(axiom). [assumption].
% 1.00/1.32 149 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_RealVector_Onorm__class_Onorm(B,A) # label(cls_norm__minus__cancel_0) # label(axiom). [assumption].
% 1.00/1.32 150 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR_OscaleR__right_0) # label(axiom). [assumption].
% 1.00/1.32 151 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR__right_OscaleR_0) # label(axiom). [assumption].
% 1.00/1.32 152 -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].
% 1.00/1.32 153 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__zero_0) # label(axiom). [assumption].
% 1.00/1.32 154 -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].
% 1.00/1.32 155 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_norm__sgn_0) # label(axiom). [assumption].
% 1.00/1.32 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(135,a,136,a)].
% 1.00/1.32 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(135,a,137,a)].
% 1.00/1.32 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(135,a,138,a)].
% 1.00/1.32 Derived: c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(135,a,139,a)].
% 1.00/1.32 Derived: c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal). [resolve(135,a,140,a)].
% 1.00/1.32 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(135,a,141,a)].
% 1.00/1.32 Derived: c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(135,a,142,a)].
% 1.00/1.32 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(135,a,143,a)].
% 1.00/1.32 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(135,a,144,a)].
% 1.00/1.32 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(135,a,145,a)].
% 1.00/1.32 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(135,a,146,a)].
% 1.00/1.32 Derived: c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(135,a,147,a)].
% 1.00/1.32 Derived: c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(135,a,148,a)].
% 1.00/1.32 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal). [resolve(135,a,149,a)].
% 1.00/1.32 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_RealVector_OscaleR__class_OscaleR(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(135,a,150,a)].
% 1.00/1.32 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(135,a,152,a)].
% 1.00/1.33 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(135,a,153,a)].
% 1.00/1.33 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(135,a,154,a)].
% 1.00/1.33 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(135,a,155,a)].
% 1.00/1.33 156 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 1.00/1.33 157 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D2_0) # label(axiom). [assumption].
% 1.00/1.33 158 -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].
% 1.00/1.33 159 -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].
% 1.00/1.33 160 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(B,C,A) # label(cls_abs__leI_0) # label(axiom). [assumption].
% 1.00/1.33 161 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(B,C,A) # label(cls_abs__le__iff_2) # label(axiom). [assumption].
% 1.00/1.33 162 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__minus__cancel_0) # label(axiom). [assumption].
% 1.00/1.33 163 -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].
% 1.00/1.33 164 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(B,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__minus__le__zero_0) # label(axiom). [assumption].
% 1.00/1.33 165 -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].
% 1.00/1.33 166 -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].
% 1.00/1.33 167 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__nonpos_0) # label(axiom). [assumption].
% 1.00/1.33 168 -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].
% 1.00/1.33 169 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__minus__self_0) # label(axiom). [assumption].
% 1.00/1.33 170 -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].
% 1.00/1.33 171 -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].
% 1.08/1.34 172 -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].
% 1.08/1.34 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(156,a,157,a)].
% 1.08/1.34 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(156,a,158,a)].
% 1.08/1.34 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(156,a,159,a)].
% 1.08/1.34 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(156,a,160,a)].
% 1.08/1.34 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal). [resolve(156,a,162,a)].
% 1.08/1.34 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(156,a,163,a)].
% 1.08/1.34 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(156,a,164,a)].
% 1.08/1.34 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(156,a,165,a)].
% 1.08/1.34 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(156,a,166,a)].
% 1.08/1.34 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(156,a,167,a)].
% 1.08/1.34 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(156,a,168,a)].
% 1.08/1.34 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(156,a,169,a)].
% 1.08/1.34 Derived: c_lessequals(A,c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(156,a,170,a)].
% 1.08/1.34 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(156,a,171,a)].
% 1.08/1.34 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(156,a,172,a)].
% 1.08/1.34 173 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.08/1.34 174 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__le__0__iff__le_1) # label(axiom). [assumption].
% 1.08/1.34 175 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__le__0__iff__le_0) # label(axiom). [assumption].
% 1.08/1.34 176 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__0__le__iff__le_0) # label(axiom). [assumption].
% 1.08/1.34 177 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__le__iff__le_1) # label(axiom). [assumption].
% 1.08/1.34 178 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__le__iff__le_0) # label(axiom). [assumption].
% 1.08/1.35 179 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,B,A) # label(cls_le__imp__neg__le_0) # label(axiom). [assumption].
% 1.08/1.35 180 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__le__iff_1) # label(axiom). [assumption].
% 1.08/1.35 181 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__le__iff_0) # label(axiom). [assumption].
% 1.08/1.35 182 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__iff_1) # label(axiom). [assumption].
% 1.08/1.35 183 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__iff_0) # label(axiom). [assumption].
% 1.08/1.35 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),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(173,a,174,a)].
% 1.08/1.35 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(173,a,175,a)].
% 1.08/1.35 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),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(173,a,176,a)].
% 1.08/1.35 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(173,a,177,a)].
% 1.08/1.35 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(173,a,178,a)].
% 1.08/1.35 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(173,a,179,a)].
% 1.08/1.35 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(173,a,180,a)].
% 1.08/1.35 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(173,a,182,a)].
% 1.08/1.35 184 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 1.08/1.35 185 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 1.08/1.35 Derived: c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(184,a,185,a)].
% 1.08/1.35 186 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.08/1.35 187 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 1.08/1.36 188 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 1.08/1.36 189 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 1.08/1.36 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(186,a,188,a)].
% 1.08/1.36 Derived: c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(186,a,189,a)].
% 1.08/1.36 190 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.08/1.36 191 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 1.08/1.36 192 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 1.08/1.36 193 -class_Ring__and__Field_Oring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Otimes__class_Otimes(B,C,A) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 1.08/1.36 194 -class_Ring__and__Field_Oring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 1.08/1.36 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(190,a,191,a)].
% 1.08/1.36 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(190,a,192,a)].
% 1.08/1.36 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal). [resolve(190,a,193,a)].
% 1.08/1.36 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(190,a,194,a)].
% 1.08/1.36 195 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 1.08/1.36 196 -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].
% 1.08/1.36 197 -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].
% 1.08/1.36 198 -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].
% 1.08/1.36 199 -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].
% 1.08/1.37 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(195,a,196,a)].
% 1.08/1.37 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(195,a,197,a)].
% 1.08/1.37 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(195,a,198,a)].
% 1.08/1.37 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(195,a,199,a)].
% 1.08/1.37 200 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 1.08/1.37 201 -class_Ring__and__Field_Oordered__idom(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) # label(cls_abs__mult_0) # label(axiom). [assumption].
% 1.08/1.37 202 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(B,A),A) = c_HOL_Osgn__class_Osgn(B,A) # label(cls_sgn__sgn_0) # label(axiom). [assumption].
% 1.08/1.37 203 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Osgn__class_Osgn(B,A),A) # label(cls_abs__sgn_0) # label(axiom). [assumption].
% 1.08/1.37 204 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),C,A) | -c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__left__le__one__le_0) # label(axiom). [assumption].
% 1.08/1.37 205 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),B,A) | -c_lessequals(C,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__right__le__one__le_0) # label(axiom). [assumption].
% 1.08/1.37 206 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),C,A),A) # label(cls_zero__le__power__abs_0) # label(axiom). [assumption].
% 1.08/1.37 207 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power__iff_1) # label(axiom). [assumption].
% 1.08/1.37 208 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Oabs__class_Oabs(B,A),A) = B # label(cls_mult__sgn__abs_0) # label(axiom). [assumption].
% 1.08/1.37 209 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_3) # label(axiom). [assumption].
% 1.08/1.37 210 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_power__abs_0) # label(axiom). [assumption].
% 1.08/1.37 211 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__0__0_0) # label(axiom). [assumption].
% 1.08/1.37 212 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Otimes__class_Otimes(B,B,A) # label(cls_abs__mult__self_0) # label(axiom). [assumption].
% 1.08/1.37 213 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(B,A),C,A),A) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(B,C,A),A) # label(cls_abs__power__minus_0) # label(axiom). [assumption].
% 1.08/1.37 214 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),C,A) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_abs__mult__pos_0) # label(axiom). [assumption].
% 1.08/1.37 215 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__dvd__iff_0) # label(axiom). [assumption].
% 1.08/1.37 216 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_abs__dvd__iff_1) # label(axiom). [assumption].
% 1.08/1.37 217 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_dvd__abs__iff_0) # label(axiom). [assumption].
% 1.08/1.37 218 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oabs__class_Oabs(C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__abs__iff_1) # label(axiom). [assumption].
% 1.08/1.37 219 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__0__0_1) # label(axiom). [assumption].
% 1.08/1.37 220 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Osgn__class_Osgn(C,A),A) # label(cls_sgn__times_0) # label(axiom). [assumption].
% 1.08/1.37 221 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,A) != c_HOL_Oabs__class_Oabs(C,A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__if__abs__eq_0) # label(axiom). [assumption].
% 1.08/1.37 222 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_abs__one_0) # label(axiom). [assumption].
% 1.08/1.37 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). [resolve(200,a,201,a)].
% 1.08/1.37 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal). [resolve(200,a,202,a)].
% 1.08/1.37 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(200,a,203,a)].
% 1.08/1.37 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -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). [resolve(200,a,204,a)].
% 1.08/1.37 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Oone__class_Oone(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(200,a,205,a)].
% 1.08/1.37 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(200,a,206,a)].
% 1.08/1.37 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(200,a,207,a)].
% 1.08/1.37 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(200,a,208,a)].
% 1.08/1.37 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(200,a,209,a)].
% 1.08/1.37 Derived: c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(200,a,210,a)].
% 1.08/1.37 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal). [resolve(200,a,212,a)].
% 1.08/1.37 Derived: c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(200,a,213,a)].
% 1.08/1.37 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(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). [resolve(200,a,214,a)].
% 1.08/1.37 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(200,a,215,a)].
% 1.08/1.37 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(200,a,216,a)].
% 1.08/1.37 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(200,a,217,a)].
% 1.08/1.37 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(200,a,218,a)].
% 1.08/1.37 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal),c_HOL_Osgn__class_Osgn(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(200,a,220,a)].
% 1.08/1.37 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) != c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal) | c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(200,a,221,a)].
% 1.08/1.37 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(200,a,222,a)].
% 1.08/1.37 223 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.08/1.37 224 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(C,c_HOL_Ozero__class_Ozero(A),A),A) # label(cls_dvd__mult__cancel__right_1) # label(axiom). [assumption].
% 1.08/1.37 225 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A) # label(cls_dvd__mult__cancel__left_1) # label(axiom). [assumption].
% 1.08/1.38 226 -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Otimes__class_Otimes(B,B,A) # label(cls_square__eq__iff_1) # label(axiom). [assumption].
% 1.08/1.38 227 -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,B,A) != c_HOL_Otimes__class_Otimes(C,C,A) | B = c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_square__eq__iff_0) # label(axiom). [assumption].
% 1.08/1.38 228 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_dvd__mult__cancel__right_0) # label(axiom). [assumption].
% 1.08/1.38 229 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_dvd__mult__cancel__left_0) # label(axiom). [assumption].
% 1.08/1.38 230 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,A) # label(cls_dvd__mult__cancel__left_2) # label(axiom). [assumption].
% 1.08/1.38 231 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mult__cancel__right_2) # label(axiom). [assumption].
% 1.08/1.38 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(223,a,224,a)].
% 1.08/1.38 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(223,a,225,a)].
% 1.08/1.38 Derived: c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal) | A = c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal) | A = B. [resolve(223,a,227,a)].
% 1.08/1.38 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(223,a,228,a)].
% 1.08/1.38 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(223,a,229,a)].
% 1.08/1.38 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_RealDef_Oreal). [resolve(223,a,230,a)].
% 1.08/1.38 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_RealDef_Oreal). [resolve(223,a,231,a)].
% 1.08/1.38 232 class_Orderings_Oorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Oorder) # label(axiom). [assumption].
% 1.08/1.38 233 -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].
% 1.08/1.38 234 -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].
% 1.08/1.38 235 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__antisym_0) # label(axiom). [assumption].
% 1.08/1.38 236 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__iff_0) # label(axiom). [assumption].
% 1.12/1.40 237 -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].
% 1.12/1.40 Derived: A = B | -c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(232,a,233,a)].
% 1.12/1.40 Derived: c_lessequals(A,A,tc_RealDef_Oreal). [resolve(232,a,236,a)].
% 1.12/1.40 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal). [resolve(232,a,237,a)].
% 1.12/1.40 238 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.12/1.40 239 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom). [assumption].
% 1.12/1.40 240 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom). [assumption].
% 1.12/1.40 241 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Ouminus__class_Ouminus(B,A) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom). [assumption].
% 1.12/1.40 242 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__equation__iff_1) # label(axiom). [assumption].
% 1.12/1.40 243 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_1) # label(axiom). [assumption].
% 1.12/1.40 244 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_0) # label(axiom). [assumption].
% 1.12/1.40 245 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__minus_0) # label(axiom). [assumption].
% 1.12/1.40 246 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__equal__iff__equal_1) # label(axiom). [assumption].
% 1.12/1.40 247 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom). [assumption].
% 1.12/1.40 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal) | A = B. [resolve(238,a,239,a)].
% 1.12/1.40 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(238,a,240,a)].
% 1.12/1.40 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(238,a,241,a)].
% 1.12/1.40 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(238,a,242,a)].
% 1.12/1.40 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(238,a,243,a)].
% 1.12/1.40 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(238,a,246,a)].
% 1.12/1.40 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(238,a,247,a)].
% 1.12/1.40 248 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 1.12/1.40 249 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 1.12/1.40 250 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__eq__neg__nonpos_0) # label(axiom). [assumption].
% 1.12/1.40 251 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__eq__neg__nonpos_1) # label(axiom). [assumption].
% 1.12/1.40 252 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) # label(cls_neg__less__eq__nonneg_0) # label(axiom). [assumption].
% 1.12/1.40 253 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__eq__nonneg_1) # label(axiom). [assumption].
% 1.12/1.40 254 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 1.12/1.40 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != A | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(248,a,249,a)].
% 1.12/1.40 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(248,a,250,a)].
% 1.12/1.40 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(248,a,251,a)].
% 1.12/1.40 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(248,a,252,a)].
% 1.12/1.40 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(248,a,253,a)].
% 1.12/1.40 255 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.12/1.40 256 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 1.12/1.40 257 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 1.12/1.40 258 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 1.12/1.40 259 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 1.12/1.40 260 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_OscaleR__left_0) # label(axiom). [assumption].
% 1.12/1.40 261 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_OscaleR_0) # label(axiom). [assumption].
% 1.12/1.40 262 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_OscaleR__right_0) # label(axiom). [assumption].
% 1.12/1.40 263 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_OscaleR_0) # label(axiom). [assumption].
% 1.12/1.40 264 -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].
% 1.12/1.41 265 -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].
% 1.12/1.41 266 -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].
% 1.12/1.41 267 -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].
% 1.12/1.41 268 -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].
% 1.12/1.41 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(255,a,256,a)].
% 1.12/1.41 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(255,a,258,a)].
% 1.12/1.41 Derived: c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(255,a,260,a)].
% 1.12/1.41 Derived: c_HOL_Otimes__class_Otimes(A,c_RealVector_OscaleR__class_OscaleR(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(255,a,262,a)].
% 1.12/1.41 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(255,a,264,a)].
% 1.12/1.41 269 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.12/1.41 270 -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].
% 1.12/1.41 271 -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].
% 1.12/1.41 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(269,a,270,a)].
% 1.12/1.41 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(269,a,271,a)].
% 1.12/1.41 272 class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 1.12/1.42 273 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_dvd__minus__iff_0) # label(axiom). [assumption].
% 1.12/1.42 274 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__minus__iff_1) # label(axiom). [assumption].
% 1.12/1.42 275 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__dvd__iff_0) # label(axiom). [assumption].
% 1.12/1.42 276 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_minus__dvd__iff_1) # label(axiom). [assumption].
% 1.12/1.42 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(272,a,273,a)].
% 1.12/1.42 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(272,a,274,a)].
% 1.12/1.42 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(272,a,275,a)].
% 1.12/1.42 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_RealDef_Oreal). [resolve(272,a,276,a)].
% 1.12/1.42 277 class_RealVector_Oreal__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__vector) # label(axiom). [assumption].
% 1.12/1.42 278 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,C,A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) # label(cls_scaleR__eq__0__iff_0) # label(axiom). [assumption].
% 1.12/1.42 279 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR__minus__right_0) # label(axiom). [assumption].
% 1.12/1.42 280 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),C,A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR__minus__left_0) # label(axiom). [assumption].
% 1.12/1.42 281 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),C,A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR__left_Ominus_0) # label(axiom). [assumption].
% 1.12/1.42 282 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),D,A) # label(cls_real__vector_Oscale__scale_0) # label(axiom). [assumption].
% 1.12/1.42 283 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR__eq__0__iff_2) # label(axiom). [assumption].
% 1.12/1.42 284 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR__eq__0__iff_1) # label(axiom). [assumption].
% 1.12/1.42 285 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR__left__commute_0) # label(axiom). [assumption].
% 1.12/1.42 286 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,A) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,A) # label(cls_scaleR__cancel__left_1) # label(axiom). [assumption].
% 1.12/1.43 287 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_scaleR__cancel__right_1) # label(axiom). [assumption].
% 1.12/1.43 288 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,C,A) != c_RealVector_OscaleR__class_OscaleR(B,D,A) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | C = D # label(cls_scaleR__cancel__left_0) # label(axiom). [assumption].
% 1.12/1.43 289 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,C,A) != c_RealVector_OscaleR__class_OscaleR(D,C,A) | C = c_HOL_Ozero__class_Ozero(A) | B = D # label(cls_scaleR__cancel__right_0) # label(axiom). [assumption].
% 1.12/1.43 290 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),B,A) = B # label(cls_real__vector_Oscale__one_0) # label(axiom). [assumption].
% 1.12/1.43 Derived: c_RealVector_OscaleR__class_OscaleR(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(277,a,278,a)].
% 1.12/1.43 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_RealVector_OscaleR__class_OscaleR(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(277,a,282,a)].
% 1.12/1.43 Derived: c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(277,a,286,a)].
% 1.12/1.43 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(277,a,287,a)].
% 1.12/1.43 Derived: c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal) != c_RealVector_OscaleR__class_OscaleR(A,C,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = C. [resolve(277,a,288,a)].
% 1.12/1.43 Derived: c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal) != c_RealVector_OscaleR__class_OscaleR(C,B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = C. [resolve(277,a,289,a)].
% 1.12/1.43 Derived: c_RealVector_OscaleR__class_OscaleR(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = A. [resolve(277,a,290,a)].
% 1.12/1.43 291 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra) # label(axiom). [assumption].
% 1.12/1.43 292 -class_RealVector_Oreal__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__scaleR__left_0) # label(axiom). [assumption].
% 1.12/1.43 293 -class_RealVector_Oreal__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__scaleR__right_0) # label(axiom). [assumption].
% 1.12/1.43 294 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.12/1.43 295 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_divide_OscaleR_0) # label(axiom). [assumption].
% 1.12/1.43 296 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_divide_Ominus_0) # label(axiom). [assumption].
% 1.12/1.43 297 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom). [assumption].
% 1.18/1.44 Derived: c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(294,a,295,a)].
% 1.18/1.44 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(294,a,296,a)].
% 1.18/1.44 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(294,a,297,a)].
% 1.18/1.44 298 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.18/1.44 299 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 1.18/1.44 300 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(B,D,A) # label(cls_power__mono_0) # label(axiom). [assumption].
% 1.18/1.44 301 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 1.18/1.44 302 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.18/1.44 303 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.18/1.44 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),c_Power_Opower__class_Opower(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(298,a,300,a)].
% 1.18/1.44 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(298,a,301,a)].
% 1.18/1.44 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(298,a,302,a)].
% 1.18/1.44 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(298,a,303,a)].
% 1.18/1.44 304 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.18/1.44 305 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__self__iff_0) # label(axiom). [assumption].
% 1.18/1.44 306 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__minus__self__iff_1) # label(axiom). [assumption].
% 1.18/1.44 307 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) # label(cls_minus__le__self__iff_0) # label(axiom). [assumption].
% 1.18/1.44 308 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_minus__le__self__iff_1) # label(axiom). [assumption].
% 1.18/1.44 309 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.18/1.44 310 -class_RealVector_Oreal__normed__algebra__1(A) | c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(B,A),A) = c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal) # label(cls_norm__of__real_0) # label(axiom). [assumption].
% 1.20/1.46 311 -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].
% 1.20/1.46 312 -class_RealVector_Oreal__normed__algebra__1(A) | c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_sgn__one_0) # label(axiom). [assumption].
% 1.20/1.46 Derived: c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal). [resolve(309,a,310,a)].
% 1.20/1.46 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(309,a,311,a)].
% 1.20/1.46 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(309,a,312,a)].
% 1.20/1.46 313 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].
% 1.20/1.46 314 -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].
% 1.20/1.46 315 -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].
% 1.20/1.46 316 -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].
% 1.20/1.46 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(313,a,314,a)].
% 1.20/1.46 317 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.20/1.46 318 -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].
% 1.20/1.46 319 -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].
% 1.20/1.46 320 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) # label(axiom). [assumption].
% 1.20/1.46 321 -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].
% 1.20/1.46 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(320,a,321,a)].
% 1.20/1.46 322 class_Ring__and__Field_Odvd(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 1.20/1.46 323 -class_Ring__and__Field_Odvd(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_dvdI_0) # label(axiom). [assumption].
% 1.20/1.46 324 class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 1.20/1.46 325 -class_Ring__and__Field_Oring__1(A) | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A),C,A),c_Power_Opower__class_Opower(B,C,A),A) # label(cls_power__minus_0) # label(axiom). [assumption].
% 1.20/1.48 Derived: c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),B,tc_RealDef_Oreal),c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(324,a,325,a)].
% 1.20/1.48 326 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 1.20/1.48 327 -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].
% 1.20/1.48 328 -class_RealVector_Oreal__normed__div__algebra(A) | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Osgn__class_Osgn(C,A),A) # label(cls_sgn__mult_0) # label(axiom). [assumption].
% 1.20/1.48 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(326,a,327,a)].
% 1.20/1.48 329 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.20/1.48 330 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A) # label(cls_power__commutes_0) # label(axiom). [assumption].
% 1.20/1.48 331 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 1.20/1.48 332 -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].
% 1.20/1.48 333 -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].
% 1.20/1.48 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(329,a,331,a)].
% 1.20/1.48 334 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.20/1.48 335 -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].
% 1.20/1.48 336 -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].
% 1.20/1.48 337 class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.20/1.48 338 -class_Ring__and__Field_Osemiring__1(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Int_Oiszero(B,A) # label(cls_iszero__def_0) # label(axiom). [assumption].
% 1.20/1.48 339 -class_Ring__and__Field_Osemiring__1(A) | c_Int_Oiszero(c_HOL_Ozero__class_Ozero(A),A) # label(cls_iszero__0_0) # label(axiom). [assumption].
% 1.20/1.48 340 -class_Ring__and__Field_Osemiring__1(A) | -c_Int_Oiszero(c_HOL_Oone__class_Oone(A),A) # label(cls_not__iszero__1_0) # label(axiom). [assumption].
% 1.20/1.48 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_Int_Oiszero(A,tc_RealDef_Oreal). [resolve(337,a,338,a)].
% 1.20/1.48 Derived: c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(337,a,339,a)].
% 1.20/1.48 Derived: -c_Int_Oiszero(c_HOL_Oone_Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------