TSTP Solution File: ALG361-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG361-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:54:34 EDT 2022
% Result : Unsatisfiable 1.46s 1.76s
% Output : Refutation 1.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG361-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n029.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 9 03:50:06 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.00/1.24 ============================== Prover9 ===============================
% 1.00/1.24 Prover9 (32) version 2009-11A, November 2009.
% 1.00/1.24 Process 17434 was started by sandbox2 on n029.cluster.edu,
% 1.00/1.24 Thu Jun 9 03:50:07 2022
% 1.00/1.24 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17281_n029.cluster.edu".
% 1.00/1.24 ============================== end of head ===========================
% 1.00/1.24
% 1.00/1.24 ============================== INPUT =================================
% 1.00/1.24
% 1.00/1.24 % Reading from file /tmp/Prover9_17281_n029.cluster.edu
% 1.00/1.24
% 1.00/1.24 set(prolog_style_variables).
% 1.00/1.24 set(auto2).
% 1.00/1.24 % set(auto2) -> set(auto).
% 1.00/1.24 % set(auto) -> set(auto_inference).
% 1.00/1.24 % set(auto) -> set(auto_setup).
% 1.00/1.24 % set(auto_setup) -> set(predicate_elim).
% 1.00/1.24 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.00/1.24 % set(auto) -> set(auto_limits).
% 1.00/1.24 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.00/1.24 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.00/1.24 % set(auto) -> set(auto_denials).
% 1.00/1.24 % set(auto) -> set(auto_process).
% 1.00/1.24 % set(auto2) -> assign(new_constants, 1).
% 1.00/1.24 % set(auto2) -> assign(fold_denial_max, 3).
% 1.00/1.24 % set(auto2) -> assign(max_weight, "200.000").
% 1.00/1.24 % set(auto2) -> assign(max_hours, 1).
% 1.00/1.24 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.00/1.24 % set(auto2) -> assign(max_seconds, 0).
% 1.00/1.24 % set(auto2) -> assign(max_minutes, 5).
% 1.00/1.24 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.00/1.24 % set(auto2) -> set(sort_initial_sos).
% 1.00/1.24 % set(auto2) -> assign(sos_limit, -1).
% 1.00/1.24 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.00/1.24 % set(auto2) -> assign(max_megs, 400).
% 1.00/1.24 % set(auto2) -> assign(stats, some).
% 1.00/1.24 % set(auto2) -> clear(echo_input).
% 1.00/1.24 % set(auto2) -> set(quiet).
% 1.00/1.24 % set(auto2) -> clear(print_initial_clauses).
% 1.00/1.24 % set(auto2) -> clear(print_given).
% 1.00/1.24 assign(lrs_ticks,-1).
% 1.00/1.24 assign(sos_limit,10000).
% 1.00/1.24 assign(order,kbo).
% 1.00/1.24 set(lex_order_vars).
% 1.00/1.24 clear(print_given).
% 1.00/1.24
% 1.00/1.24 % formulas(sos). % not echoed (595 formulas)
% 1.00/1.24
% 1.00/1.24 ============================== end of input ==========================
% 1.00/1.24
% 1.00/1.24 % From the command line: assign(max_seconds, 300).
% 1.00/1.24
% 1.00/1.24 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.00/1.24
% 1.00/1.24 % Formulas that are not ordinary clauses:
% 1.00/1.24
% 1.00/1.24 ============================== end of process non-clausal formulas ===
% 1.00/1.24
% 1.00/1.24 ============================== PROCESS INITIAL CLAUSES ===============
% 1.00/1.24
% 1.00/1.24 ============================== PREDICATE ELIMINATION =================
% 1.00/1.24 1 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.00/1.24 2 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 1.00/1.24 3 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 1.00/1.24 4 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 1.00/1.24 5 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 1.00/1.24 6 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 1.00/1.24 7 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 1.00/1.24 8 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 1.00/1.24 9 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 1.00/1.24 10 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 1.00/1.24 11 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 1.00/1.24 12 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 1.00/1.24 13 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 1.00/1.24 14 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 1.00/1.24 15 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 1.00/1.24 16 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 1.00/1.24 17 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(1,a,2,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,3,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,5,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat). [resolve(1,a,6,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A),tc_nat). [resolve(1,a,7,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,8,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C),tc_nat). [resolve(1,a,9,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B),tc_nat). [resolve(1,a,10,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,11,a)].
% 1.00/1.24 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C),tc_nat). [resolve(1,a,12,a)].
% 1.00/1.24 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B),tc_nat). [resolve(1,a,13,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,14,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(1,a,15,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(1,a,16,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,17,a)].
% 1.00/1.24 18 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(18,a,2,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(18,a,3,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(18,a,5,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal). [resolve(18,a,6,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(18,a,7,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(18,a,8,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C),tc_RealDef_Oreal). [resolve(18,a,9,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal). [resolve(18,a,10,a)].
% 1.00/1.24 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(18,a,11,a)].
% 1.00/1.24 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C),tc_RealDef_Oreal). [resolve(18,a,12,a)].
% 1.00/1.24 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal). [resolve(18,a,13,a)].
% 1.00/1.26 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(18,a,14,a)].
% 1.00/1.26 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(18,a,15,a)].
% 1.00/1.26 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(18,a,16,a)].
% 1.00/1.26 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(18,a,17,a)].
% 1.00/1.26 19 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 1.00/1.26 20 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__le__D2_0) # label(axiom). [assumption].
% 1.00/1.26 21 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(B,C,A) # label(cls_abs__leI_0) # label(axiom). [assumption].
% 1.00/1.26 22 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(B,C,A) # label(cls_abs__le__iff_2) # label(axiom). [assumption].
% 1.00/1.26 23 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = hAPP(c_HOL_Oabs__class_Oabs(A),B) # label(cls_abs__minus__cancel_0) # label(axiom). [assumption].
% 1.00/1.26 24 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_1) # label(axiom). [assumption].
% 1.00/1.26 25 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)) = hAPP(c_HOL_Oabs__class_Oabs(A),B) # label(cls_abs__idempotent_0) # label(axiom). [assumption].
% 1.00/1.26 26 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oabs__class_Oabs(A),B),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__abs__iff_1) # label(axiom). [assumption].
% 1.00/1.26 27 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__nonneg_0) # label(axiom). [assumption].
% 1.00/1.26 28 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_0) # label(axiom). [assumption].
% 1.00/1.26 29 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__neg_0) # label(axiom). [assumption].
% 1.00/1.26 30 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__minus__le__zero_0) # label(axiom). [assumption].
% 1.00/1.26 31 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__le__D1_0) # label(axiom). [assumption].
% 1.00/1.26 32 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_1) # label(axiom). [assumption].
% 1.00/1.26 33 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__pos_0) # label(axiom). [assumption].
% 1.00/1.26 34 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__nonpos_0) # label(axiom). [assumption].
% 1.00/1.26 35 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),B),A) # label(cls_abs__ge__minus__self_0) # label(axiom). [assumption].
% 1.00/1.26 36 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,hAPP(c_HOL_Oabs__class_Oabs(A),B),A) # label(cls_abs__ge__self_0) # label(axiom). [assumption].
% 1.00/1.26 37 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),D,C,A),A) # label(cls_setsum__abs__ge__zero_0) # label(axiom). [assumption].
% 1.00/1.26 38 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__not__less__zero_0) # label(axiom). [assumption].
% 1.00/1.26 39 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_0) # label(axiom). [assumption].
% 1.00/1.26 40 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)),A) # label(cls_zero__less__abs__iff_0) # label(axiom). [assumption].
% 1.00/1.26 41 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oabs__class_Oabs(A),B),A) # label(cls_abs__ge__zero_0) # label(axiom). [assumption].
% 1.00/1.26 42 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),D,C,A)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),D,C,A) # label(cls_abs__setsum__abs_0) # label(axiom). [assumption].
% 1.00/1.26 43 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_Finite__Set_Osetsum(B,C,D,A)),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,D),C,D,A),A) # label(cls_setsum__abs_0) # label(axiom). [assumption].
% 1.00/1.26 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal). [resolve(19,a,20,a)].
% 1.00/1.26 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(19,a,21,a)].
% 1.00/1.26 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A). [resolve(19,a,23,a)].
% 1.00/1.26 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(19,a,24,a)].
% 1.00/1.26 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A)) = hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A). [resolve(19,a,25,a)].
% 1.00/1.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(19,a,26,a)].
% 1.00/1.28 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A) = A | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(19,a,27,a)].
% 1.00/1.28 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(19,a,28,a)].
% 1.00/1.28 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(19,a,29,a)].
% 1.00/1.28 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(19,a,30,a)].
% 1.00/1.28 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal). [resolve(19,a,31,a)].
% 1.00/1.28 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(19,a,32,a)].
% 1.00/1.28 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A) = A | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(19,a,33,a)].
% 1.00/1.28 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(19,a,34,a)].
% 1.00/1.28 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(19,a,35,a)].
% 1.00/1.28 Derived: c_lessequals(A,hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(19,a,36,a)].
% 1.00/1.28 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,B),C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(19,a,37,a)].
% 1.00/1.28 Derived: -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(19,a,38,a)].
% 1.00/1.28 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(19,a,39,a)].
% 1.00/1.28 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(19,a,40,a)].
% 1.00/1.28 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(19,a,41,a)].
% 1.00/1.28 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,B),C,B,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,B),C,B,tc_RealDef_Oreal). [resolve(19,a,42,a)].
% 1.00/1.28 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),c_Finite__Set_Osetsum(A,B,C,tc_RealDef_Oreal)),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,C),B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(19,a,43,a)].
% 1.00/1.28 44 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.00/1.28 45 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 1.00/1.31 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(44,a,45,a)].
% 1.00/1.31 46 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.00/1.31 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),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(46,a,45,a)].
% 1.00/1.31 47 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.00/1.31 48 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 1.00/1.31 49 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 1.00/1.31 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(47,a,49,a)].
% 1.00/1.31 50 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.00/1.31 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),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(50,a,49,a)].
% 1.00/1.31 51 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 1.00/1.31 52 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,C,A) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 1.00/1.31 53 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 1.00/1.31 54 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 1.00/1.31 55 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 1.00/1.31 56 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.00/1.31 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),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(51,a,52,a)].
% 1.00/1.31 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),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(51,a,53,a)].
% 1.00/1.32 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),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(51,a,54,a)].
% 1.00/1.32 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),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(51,a,55,a)].
% 1.00/1.32 57 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) # label(axiom). [assumption].
% 1.00/1.32 58 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(c_RealVector_Oof__real(A),C,tc_RealDef_Oreal,A,B),D,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) # label(cls_of__real_OLIM__zero_0) # label(axiom). [assumption].
% 1.00/1.32 59 -class_RealVector_Oreal__algebra__1(A) | hAPP(c_RealVector_Oof__real(A),B) != 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].
% 1.00/1.32 60 -class_RealVector_Oreal__algebra__1(A) | hAPP(c_RealVector_Oof__real(A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__real__0_0) # label(axiom). [assumption].
% 1.00/1.32 61 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | hAPP(c_RealVector_Oof__real(A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__real_Ozero_0) # label(axiom). [assumption].
% 1.00/1.32 62 -class_RealVector_Oreal__algebra__1(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_Oof__real(A),B),A),C) # label(cls_scaleR__conv__of__real_0) # label(axiom). [assumption].
% 1.00/1.32 63 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_Limits_Otendsto(c_COMBB(c_RealVector_Oof__real(A),B,tc_RealDef_Oreal,A,C),hAPP(c_RealVector_Oof__real(A),D),E,C,A) | -c_Limits_Otendsto(B,D,E,C,tc_RealDef_Oreal) # label(cls_of__real_Otendsto_0) # label(axiom). [assumption].
% 1.00/1.32 64 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_Limits_OZfun(c_COMBB(c_RealVector_Oof__real(A),B,tc_RealDef_Oreal,A,C),D,C,A) | -c_Limits_OZfun(B,D,C,tc_RealDef_Oreal) # label(cls_of__real_OZfun_0) # label(axiom). [assumption].
% 1.00/1.32 65 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_SEQ_OZseq(c_COMBB(c_RealVector_Oof__real(A),B,tc_RealDef_Oreal,A,tc_nat),A) | -c_SEQ_OZseq(B,tc_RealDef_Oreal) # label(cls_of__real_OZseq_0) # label(axiom). [assumption].
% 1.00/1.32 66 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_Series_Osums(c_COMBB(c_RealVector_Oof__real(A),B,tc_RealDef_Oreal,A,tc_nat),hAPP(c_RealVector_Oof__real(A),C),A) | -c_Series_Osums(B,C,tc_RealDef_Oreal) # label(cls_of__real_Osums_0) # label(axiom). [assumption].
% 1.00/1.32 67 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_Series_Osummable(c_COMBB(c_RealVector_Oof__real(A),B,tc_RealDef_Oreal,A,tc_nat),A) | -c_Series_Osummable(B,tc_RealDef_Oreal) # label(cls_of__real_Osummable_0) # label(axiom). [assumption].
% 1.00/1.32 68 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(c_RealVector_Oof__real(A),C,tc_RealDef_Oreal,A,B),D,hAPP(c_RealVector_Oof__real(A),E),B,A) | -c_Lim_OLIM(C,D,E,B,tc_RealDef_Oreal) # label(cls_LIM__of__real_0) # label(axiom). [assumption].
% 1.00/1.32 69 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Oof__real(A),B,tc_RealDef_Oreal,A,tc_nat),hAPP(c_RealVector_Oof__real(A),C),A) | -c_SEQ_OLIMSEQ(B,C,tc_RealDef_Oreal) # label(cls_of__real_OLIMSEQ_0) # label(axiom). [assumption].
% 1.00/1.32 70 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | hAPP(c_RealVector_Oof__real(A),c_Finite__Set_Osetsum(B,C,D,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_Oof__real(A),B,tc_RealDef_Oreal,A,D),C,D,A) # label(cls_of__real_Osetsum_0) # label(axiom). [assumption].
% 1.00/1.32 71 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | hAPP(c_RealVector_Oof__real(A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_RealVector_Oof__real(A),B)) # label(cls_of__real_Ominus_0) # label(axiom). [assumption].
% 1.00/1.32 72 -class_RealVector_Oreal__algebra__1(A) | hAPP(c_RealVector_Oof__real(A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_RealVector_Oof__real(A),B)) # label(cls_of__real__minus_0) # label(axiom). [assumption].
% 1.00/1.32 73 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | c_SEQ_OCauchy(c_COMBB(c_RealVector_Oof__real(A),B,tc_RealDef_Oreal,A,tc_nat),A) | -c_SEQ_OCauchy(B,tc_RealDef_Oreal) # label(cls_of__real_OCauchy_0) # label(axiom). [assumption].
% 1.00/1.32 74 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__algebra__1(A) | hAPP(c_RealVector_Oof__real(A),c_Series_Osuminf(B,tc_RealDef_Oreal)) = c_Series_Osuminf(c_COMBB(c_RealVector_Oof__real(A),B,tc_RealDef_Oreal,A,tc_nat),A) | -c_Series_Osummable(B,tc_RealDef_Oreal) # label(cls_of__real_Osuminf_0) # label(axiom). [assumption].
% 1.00/1.32 75 -class_RealVector_Oreal__algebra__1(A) | hAPP(c_RealVector_Oof__real(A),B) != hAPP(c_RealVector_Oof__real(A),C) | B = C # label(cls_of__real__eq__iff_0) # label(axiom). [assumption].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,A),C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_Lim_OLIM(B,C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(57,a,58,b)].
% 1.00/1.32 Derived: hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(57,a,59,a)].
% 1.00/1.32 Derived: hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(57,a,60,a)].
% 1.00/1.32 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B). [resolve(57,a,62,a)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | c_Limits_Otendsto(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,B),hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),C),D,B,tc_RealDef_Oreal) | -c_Limits_Otendsto(A,C,D,B,tc_RealDef_Oreal). [resolve(57,a,63,b)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | c_Limits_OZfun(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,B),C,B,tc_RealDef_Oreal) | -c_Limits_OZfun(A,C,B,tc_RealDef_Oreal). [resolve(57,a,64,b)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | c_SEQ_OZseq(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) | -c_SEQ_OZseq(A,tc_RealDef_Oreal). [resolve(57,a,65,b)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | c_Series_Osums(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_Series_Osums(A,B,tc_RealDef_Oreal). [resolve(57,a,66,b)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | c_Series_Osummable(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) | -c_Series_Osummable(A,tc_RealDef_Oreal). [resolve(57,a,67,b)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,A),C,hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),D),A,tc_RealDef_Oreal) | -c_Lim_OLIM(B,C,D,A,tc_RealDef_Oreal). [resolve(57,a,68,b)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_SEQ_OLIMSEQ(A,B,tc_RealDef_Oreal). [resolve(57,a,69,b)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),c_Finite__Set_Osetsum(A,B,C,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,C),B,C,tc_RealDef_Oreal). [resolve(57,a,70,b)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),A)). [resolve(57,a,71,b)].
% 1.00/1.32 Derived: hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),A)). [resolve(57,a,72,a)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | c_SEQ_OCauchy(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) | -c_SEQ_OCauchy(A,tc_RealDef_Oreal). [resolve(57,a,73,b)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),c_Series_Osuminf(A,tc_RealDef_Oreal)) = c_Series_Osuminf(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) | -c_Series_Osummable(A,tc_RealDef_Oreal). [resolve(57,a,74,b)].
% 1.00/1.32 Derived: hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),A) != hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),B) | A = B. [resolve(57,a,75,a)].
% 1.00/1.32 76 class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) # label(axiom). [assumption].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),B,tc_RealDef_Oreal,tc_Complex_Ocomplex,A),C,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(76,a,58,b)].
% 1.00/1.32 Derived: hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),A) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(76,a,59,a)].
% 1.00/1.32 Derived: hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(76,a,60,a)].
% 1.00/1.32 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),B). [resolve(76,a,62,a)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | c_Limits_Otendsto(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),A,tc_RealDef_Oreal,tc_Complex_Ocomplex,B),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),C),D,B,tc_Complex_Ocomplex) | -c_Limits_Otendsto(A,C,D,B,tc_RealDef_Oreal). [resolve(76,a,63,b)].
% 1.00/1.32 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | c_Limits_OZfun(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),A,tc_RealDef_Oreal,tc_Complex_Ocomplex,B),C,B,tc_Complex_Ocomplex) | -c_Limits_OZfun(A,C,B,tc_RealDef_Oreal). [resolve(76,a,64,b)].
% 1.09/1.35 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | c_SEQ_OZseq(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),A,tc_RealDef_Oreal,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_RealDef_Oreal). [resolve(76,a,65,b)].
% 1.09/1.35 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | c_Series_Osums(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),A,tc_RealDef_Oreal,tc_Complex_Ocomplex,tc_nat),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,B,tc_RealDef_Oreal). [resolve(76,a,66,b)].
% 1.09/1.35 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | c_Series_Osummable(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),A,tc_RealDef_Oreal,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_RealDef_Oreal). [resolve(76,a,67,b)].
% 1.09/1.35 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),B,tc_RealDef_Oreal,tc_Complex_Ocomplex,A),C,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),D),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,C,D,A,tc_RealDef_Oreal). [resolve(76,a,68,b)].
% 1.09/1.35 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),A,tc_RealDef_Oreal,tc_Complex_Ocomplex,tc_nat),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_RealDef_Oreal). [resolve(76,a,69,b)].
% 1.09/1.35 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,B,C,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),A,tc_RealDef_Oreal,tc_Complex_Ocomplex,C),B,C,tc_Complex_Ocomplex). [resolve(76,a,70,b)].
% 1.09/1.35 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),A)). [resolve(76,a,71,b)].
% 1.09/1.35 Derived: hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),A)). [resolve(76,a,72,a)].
% 1.09/1.35 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | c_SEQ_OCauchy(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),A,tc_RealDef_Oreal,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(A,tc_RealDef_Oreal). [resolve(76,a,73,b)].
% 1.09/1.35 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_RealDef_Oreal)) = c_Series_Osuminf(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),A,tc_RealDef_Oreal,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_RealDef_Oreal). [resolve(76,a,74,b)].
% 1.09/1.35 Derived: hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),A) != hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),B) | A = B. [resolve(76,a,75,a)].
% 1.09/1.35 77 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.09/1.35 78 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(C,A),D,A,A,B),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__right_OLIM__zero_0) # label(axiom). [assumption].
% 1.09/1.35 79 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(C,A),D,A,A,B),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__mult__right__zero_0) # label(axiom). [assumption].
% 1.09/1.35 80 -class_RealVector_Oreal__normed__algebra(A) | c_RealVector_Obounded__linear(c_HOL_Otimes__class_Otimes(B,A),A,A) # label(cls_mult_Obounded__linear__right_0) # label(axiom). [assumption].
% 1.09/1.35 81 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 1.09/1.35 82 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 1.09/1.35 83 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 1.09/1.35 84 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 1.09/1.35 85 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult_OscaleR__left_0) # label(axiom). [assumption].
% 1.09/1.35 86 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult__left_OscaleR_0) # label(axiom). [assumption].
% 1.09/1.35 87 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult_OscaleR__right_0) # label(axiom). [assumption].
% 1.09/1.35 88 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult__right_OscaleR_0) # label(axiom). [assumption].
% 1.09/1.35 89 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OisUCont(c_HOL_Otimes__class_Otimes(B,A),A,A) # label(cls_mult__right_OisUCont_0) # label(axiom). [assumption].
% 1.09/1.35 90 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OLIM(c_HOL_Otimes__class_Otimes(B,A),C,hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A,A) # label(cls_mult__right_Ocont_0) # label(axiom). [assumption].
% 1.09/1.35 91 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OisCont(c_HOL_Otimes__class_Otimes(B,A),C,A,A) # label(cls_mult__right_OisCont_0) # label(axiom). [assumption].
% 1.09/1.35 92 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 1.09/1.35 93 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 1.09/1.35 94 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 1.09/1.35 95 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 1.09/1.35 96 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,E),D,E,A) # label(cls_mult__right_Osetsum_0) # label(axiom). [assumption].
% 1.09/1.35 97 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(C,A),D,A,A,B),E,hAPP(c_HOL_Otimes__class_Otimes(C,A),F),B,A) | -c_Lim_OLIM(D,E,F,B,A) # label(cls_mult__right_OLIM_0) # label(axiom). [assumption].
% 1.09/1.35 98 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_SEQ_OLIMSEQ(C,D,A) # label(cls_mult__right_OLIMSEQ_0) # label(axiom). [assumption].
% 1.09/1.35 99 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) | -c_Series_Osummable(C,A) # label(cls_summable__mult_0) # label(axiom). [assumption].
% 1.09/1.35 100 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) | -c_Series_Osummable(C,A) # label(cls_mult__right_Osummable_0) # label(axiom). [assumption].
% 1.09/1.35 101 -class_RealVector_Oreal__normed__algebra(A) | c_Limits_OZfun(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,D),E,D,A) | -c_Limits_OZfun(C,E,D,A) # label(cls_mult__right_OZfun_0) # label(axiom). [assumption].
% 1.09/1.35 102 -class_RealVector_Oreal__normed__algebra(A) | c_Limits_OZfun(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,D),E,D,A) | -c_Limits_OZfun(C,E,D,A) # label(cls_Zfun__mult__right_0) # label(axiom). [assumption].
% 1.09/1.35 103 -class_RealVector_Oreal__normed__algebra(A) | c_Limits_Otendsto(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,D),hAPP(c_HOL_Otimes__class_Otimes(B,A),E),F,D,A) | -c_Limits_Otendsto(C,E,F,D,A) # label(cls_mult__right_Otendsto_0) # label(axiom). [assumption].
% 1.09/1.35 104 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) | -c_SEQ_OZseq(C,A) # label(cls_mult__right_OZseq_0) # label(axiom). [assumption].
% 1.09/1.35 105 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) | -c_SEQ_OZseq(C,A) # label(cls_Zseq__mult__right_0) # label(axiom). [assumption].
% 1.09/1.35 106 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_Series_Osums(C,D,A) # label(cls_mult__right_Osums_0) # label(axiom). [assumption].
% 1.09/1.35 107 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_Series_Osums(C,D,A) # label(cls_sums__mult_0) # label(axiom). [assumption].
% 1.09/1.35 108 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OCauchy(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) | -c_SEQ_OCauchy(C,A) # label(cls_mult__right_OCauchy_0) # label(axiom). [assumption].
% 1.09/1.35 109 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) = hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Series_Osuminf(C,A)) | -c_Series_Osummable(C,A) # label(cls_suminf__mult_0) # label(axiom). [assumption].
% 1.09/1.35 110 -class_RealVector_Oreal__normed__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Series_Osuminf(C,A)) = c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,tc_nat),A) | -c_Series_Osummable(C,A) # label(cls_mult__right_Osuminf_0) # label(axiom). [assumption].
% 1.09/1.35 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C,tc_RealDef_Oreal,tc_RealDef_Oreal,A),D,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(77,a,78,a)].
% 1.09/1.35 Derived: c_RealVector_Obounded__linear(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(77,a,80,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)). [resolve(77,a,81,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)). [resolve(77,a,83,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)). [resolve(77,a,85,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)). [resolve(77,a,87,a)].
% 1.09/1.35 Derived: c_Lim_OisUCont(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(77,a,89,a)].
% 1.09/1.35 Derived: c_Lim_OLIM(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(77,a,90,a)].
% 1.09/1.35 Derived: c_Lim_OisCont(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(77,a,91,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,92,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(77,a,94,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),c_Finite__Set_Osetsum(B,C,D,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,D),C,D,tc_RealDef_Oreal). [resolve(77,a,96,a)].
% 1.09/1.35 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C,tc_RealDef_Oreal,tc_RealDef_Oreal,A),D,hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),E),A,tc_RealDef_Oreal) | -c_Lim_OLIM(C,D,E,A,tc_RealDef_Oreal). [resolve(77,a,97,a)].
% 1.09/1.35 Derived: c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal) | -c_SEQ_OLIMSEQ(B,C,tc_RealDef_Oreal). [resolve(77,a,98,a)].
% 1.09/1.35 Derived: c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) | -c_Series_Osummable(B,tc_RealDef_Oreal). [resolve(77,a,99,a)].
% 1.09/1.35 Derived: c_Limits_OZfun(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,C),D,C,tc_RealDef_Oreal) | -c_Limits_OZfun(B,D,C,tc_RealDef_Oreal). [resolve(77,a,101,a)].
% 1.09/1.35 Derived: c_Limits_Otendsto(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,C),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),D),E,C,tc_RealDef_Oreal) | -c_Limits_Otendsto(B,D,E,C,tc_RealDef_Oreal). [resolve(77,a,103,a)].
% 1.09/1.35 Derived: c_SEQ_OZseq(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) | -c_SEQ_OZseq(B,tc_RealDef_Oreal). [resolve(77,a,104,a)].
% 1.09/1.35 Derived: c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal) | -c_Series_Osums(B,C,tc_RealDef_Oreal). [resolve(77,a,106,a)].
% 1.09/1.35 Derived: c_SEQ_OCauchy(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) | -c_SEQ_OCauchy(B,tc_RealDef_Oreal). [resolve(77,a,108,a)].
% 1.09/1.35 Derived: c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),c_Series_Osuminf(B,tc_RealDef_Oreal)) | -c_Series_Osummable(B,tc_RealDef_Oreal). [resolve(77,a,109,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),c_Series_Osuminf(B,tc_RealDef_Oreal)) = c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) | -c_Series_Osummable(B,tc_RealDef_Oreal). [resolve(77,a,110,a)].
% 1.09/1.35 111 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.09/1.35 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(111,a,78,a)].
% 1.09/1.35 Derived: c_RealVector_Obounded__linear(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(111,a,80,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B)). [resolve(111,a,81,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B)). [resolve(111,a,83,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C) = hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C)). [resolve(111,a,85,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_Complex_Ocomplex),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C)). [resolve(111,a,87,a)].
% 1.09/1.35 Derived: c_Lim_OisUCont(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(111,a,89,a)].
% 1.09/1.35 Derived: c_Lim_OLIM(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(111,a,90,a)].
% 1.09/1.35 Derived: c_Lim_OisCont(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(111,a,91,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(111,a,92,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(111,a,94,a)].
% 1.09/1.35 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_Finite__Set_Osetsum(B,C,D,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,D),C,D,tc_Complex_Ocomplex). [resolve(111,a,96,a)].
% 1.09/1.35 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),D,hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),E),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,E,A,tc_Complex_Ocomplex). [resolve(111,a,97,a)].
% 1.09/1.35 Derived: c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,C,tc_Complex_Ocomplex). [resolve(111,a,98,a)].
% 1.09/1.35 Derived: c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex). [resolve(111,a,99,a)].
% 1.09/1.35 Derived: c_Limits_OZfun(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,C),D,C,tc_Complex_Ocomplex) | -c_Limits_OZfun(B,D,C,tc_Complex_Ocomplex). [resolve(111,a,101,a)].
% 1.09/1.35 Derived: c_Limits_Otendsto(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,C),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),D),E,C,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,E,C,tc_Complex_Ocomplex). [resolve(111,a,103,a)].
% 1.09/1.36 Derived: c_SEQ_OZseq(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex). [resolve(111,a,104,a)].
% 1.09/1.36 Derived: c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex) | -c_Series_Osums(B,C,tc_Complex_Ocomplex). [resolve(111,a,106,a)].
% 1.09/1.36 Derived: c_SEQ_OCauchy(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(B,tc_Complex_Ocomplex). [resolve(111,a,108,a)].
% 1.09/1.36 Derived: c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_Series_Osuminf(B,tc_Complex_Ocomplex)) | -c_Series_Osummable(B,tc_Complex_Ocomplex). [resolve(111,a,109,a)].
% 1.09/1.36 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),c_Series_Osuminf(B,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex). [resolve(111,a,110,a)].
% 1.09/1.36 112 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Obounded__linear(c_RealVector_OscaleR__class_OscaleR(B,A),A,A) # label(cls_scaleR_Obounded__linear__right_0) # label(axiom). [assumption].
% 1.09/1.36 113 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | -class_RealVector_Ometric__space(C) | c_Lim_OLIM(c_COMBB(D,E,B,A,C),F,c_HOL_Ozero__class_Ozero(A),C,A) | -c_Lim_OLIM(E,F,c_HOL_Ozero__class_Ozero(B),C,B) | -c_RealVector_Obounded__linear(D,B,A) # label(cls_bounded__linear_OLIM__zero_0) # label(axiom). [assumption].
% 1.09/1.36 114 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | hAPP(C,hAPP(c_RealVector_OscaleR__class_OscaleR(D,A),E)) = hAPP(c_RealVector_OscaleR__class_OscaleR(D,B),hAPP(C,E)) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_OscaleR_0) # label(axiom). [assumption].
% 1.09/1.36 115 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OisUCont(C,A,B) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_OisUCont_0) # label(axiom). [assumption].
% 1.09/1.36 116 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OisCont(C,D,A,B) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_OisCont_0) # label(axiom). [assumption].
% 1.09/1.36 117 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(C,D,hAPP(C,D),A,B) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_Ocont_0) # label(axiom). [assumption].
% 1.09/1.36 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(c_RealVector_OscaleR__class_OscaleR(C,A),D,A,A,B),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A). [resolve(112,b,113,f)].
% 1.09/1.36 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)). [resolve(112,b,114,d)].
% 1.09/1.36 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | c_Lim_OisUCont(c_RealVector_OscaleR__class_OscaleR(B,A),A,A). [resolve(112,b,115,d)].
% 1.09/1.37 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | c_Lim_OisCont(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A). [resolve(112,b,116,d)].
% 1.09/1.37 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | c_Lim_OLIM(c_RealVector_OscaleR__class_OscaleR(B,A),C,hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A,A). [resolve(112,b,117,d)].
% 1.09/1.37 118 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | -class_RealVector_Ometric__space(C) | c_Lim_OLIM(c_COMBB(D,E,A,B,C),F,hAPP(D,V6),C,B) | -c_Lim_OLIM(E,F,V6,C,A) | -c_RealVector_Obounded__linear(D,A,B) # label(cls_bounded__linear_OLIM_0) # label(axiom). [assumption].
% 1.09/1.37 119 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_SEQ_OLIMSEQ(c_COMBB(C,D,A,B,tc_nat),hAPP(C,E),B) | -c_SEQ_OLIMSEQ(D,E,A) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_OLIMSEQ_0) # label(axiom). [assumption].
% 1.09/1.37 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A,tc_nat),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D),A) | -c_SEQ_OLIMSEQ(C,D,A) | -class_RealVector_Oreal__normed__vector(A). [resolve(119,e,112,b)].
% 1.09/1.37 120 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_Series_Osummable(c_COMBB(C,D,A,B,tc_nat),B) | -c_Series_Osummable(D,A) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_Osummable_0) # label(axiom). [assumption].
% 1.09/1.37 121 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_Limits_OZfun(c_COMBB(C,D,B,A,E),F,E,A) | -c_Limits_OZfun(D,F,E,B) | -c_RealVector_Obounded__linear(C,B,A) # label(cls_bounded__linear_OZfun_0) # label(axiom). [assumption].
% 1.09/1.37 122 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_Limits_Otendsto(c_COMBB(C,D,B,A,E),hAPP(C,F),V6,E,A) | -c_Limits_Otendsto(D,F,V6,E,B) | -c_RealVector_Obounded__linear(C,B,A) # label(cls_bounded__linear_Otendsto_0) # label(axiom). [assumption].
% 1.09/1.37 123 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_SEQ_OZseq(c_COMBB(C,D,A,B,tc_nat),B) | -c_SEQ_OZseq(D,A) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_OZseq_0) # label(axiom). [assumption].
% 1.09/1.37 124 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_Series_Osums(c_COMBB(C,D,A,B,tc_nat),hAPP(C,E),B) | -c_Series_Osums(D,E,A) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_Osums_0) # label(axiom). [assumption].
% 1.09/1.37 Derived: -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBB(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A,tc_nat),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D),A) | -c_Series_Osums(C,D,A) | -class_RealVector_Oreal__normed__vector(A). [resolve(124,e,112,b)].
% 1.09/1.37 125 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | c_SEQ_OCauchy(c_COMBB(C,D,A,B,tc_nat),B) | -c_SEQ_OCauchy(D,A) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_OCauchy_0) # label(axiom). [assumption].
% 1.09/1.37 126 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(B) | hAPP(C,c_Series_Osuminf(D,A)) = c_Series_Osuminf(c_COMBB(C,D,A,B,tc_nat),B) | -c_Series_Osummable(D,A) | -c_RealVector_Obounded__linear(C,A,B) # label(cls_bounded__linear_Osuminf_0) # label(axiom). [assumption].
% 1.09/1.37 127 c_RealVector_Obounded__linear(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(77,a,80,a)].
% 1.09/1.37 Derived: -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | -class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C,tc_RealDef_Oreal,tc_RealDef_Oreal,A),D,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(127,a,113,f)].
% 1.09/1.38 128 c_RealVector_Obounded__linear(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(111,a,80,a)].
% 1.09/1.38 Derived: -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | -class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(128,a,113,f)].
% 1.09/1.38 129 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 1.09/1.38 130 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),B),A) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 1.09/1.38 131 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 1.09/1.38 132 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 1.09/1.38 133 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 1.09/1.38 134 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 1.09/1.38 135 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 1.09/1.38 136 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(C,A),B),A) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 1.09/1.38 137 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 1.09/1.38 138 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 1.09/1.38 139 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 1.09/1.38 140 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),D),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 1.09/1.38 141 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 1.09/1.38 142 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 1.09/1.38 143 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 1.09/1.38 144 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 1.09/1.38 145 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 1.09/1.38 146 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 1.09/1.38 147 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 1.09/1.38 148 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 1.09/1.38 149 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_lessequals(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 1.09/1.38 150 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 1.09/1.38 151 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 1.09/1.38 152 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 1.09/1.38 153 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | -c_HOL_Oord__class_Oless(D,B,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 1.09/1.38 154 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 1.09/1.38 155 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 1.09/1.38 156 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 1.09/1.38 157 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 1.09/1.38 158 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 1.09/1.38 159 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 1.09/1.38 160 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 1.09/1.38 161 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 1.09/1.38 162 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 1.09/1.38 163 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 1.09/1.38 164 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 1.09/1.38 165 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),D),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 1.09/1.38 166 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,A),B),hAPP(c_HOL_Otimes__class_Otimes(D,A),B),A) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 1.09/1.38 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(129,a,130,a)].
% 1.09/1.38 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),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal). [resolve(129,a,133,a)].
% 1.09/1.38 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),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(129,a,134,a)].
% 1.09/1.38 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),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal). [resolve(129,a,135,a)].
% 1.09/1.38 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),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(129,a,136,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal). [resolve(129,a,137,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(129,a,138,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(129,a,139,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal). [resolve(129,a,140,a)].
% 1.09/1.38 Derived: -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,141,a)].
% 1.09/1.38 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),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(129,a,142,a)].
% 1.09/1.38 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),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(129,a,143,a)].
% 1.09/1.38 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(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,144,a)].
% 1.09/1.38 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(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,145,a)].
% 1.09/1.38 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(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,146,a)].
% 1.09/1.38 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(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,147,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,148,a)].
% 1.09/1.38 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(129,a,149,a)].
% 1.09/1.38 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,151,a)].
% 1.09/1.38 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,152,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,153,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,156,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(129,a,160,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(129,a,162,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(129,a,163,a)].
% 1.09/1.38 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal). [resolve(129,a,164,a)].
% 1.16/1.41 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal). [resolve(129,a,165,a)].
% 1.16/1.41 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(129,a,166,a)].
% 1.16/1.41 167 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.16/1.41 168 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.16/1.41 169 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 1.16/1.41 170 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 1.16/1.41 171 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 1.16/1.41 172 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 1.16/1.41 173 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 1.16/1.41 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(167,a,168,a)].
% 1.16/1.41 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(167,a,169,a)].
% 1.16/1.41 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(167,a,170,a)].
% 1.16/1.41 174 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.16/1.41 175 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.16/1.41 176 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 1.16/1.42 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)). [resolve(175,a,176,a)].
% 1.16/1.42 177 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.16/1.42 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)). [resolve(177,a,176,a)].
% 1.16/1.42 178 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.16/1.42 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C)). [resolve(178,a,176,a)].
% 1.16/1.42 179 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.16/1.42 180 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.16/1.42 181 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.16/1.42 182 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.16/1.42 183 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.16/1.42 184 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.16/1.42 185 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(c_HOL_Otimes__class_Otimes(D,A),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.16/1.42 186 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.16/1.42 187 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),A),hAPP(c_HOL_Otimes__class_Otimes(D,A),E)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A),hAPP(c_HOL_Otimes__class_Otimes(C,A),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.16/1.42 188 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(C,A),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.16/1.43 189 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) = hAPP(c_HOL_Otimes__class_Otimes(C,A),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.16/1.43 190 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 1.16/1.43 191 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 1.16/1.43 192 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat),B). [resolve(179,a,180,a)].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),C). [resolve(179,a,182,a)].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C)). [resolve(179,a,183,a)].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),C),tc_nat),hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),D)). [resolve(179,a,187,a)].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_nat),A). [resolve(179,a,188,a)].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(179,a,190,a)].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(179,a,191,a)].
% 1.16/1.43 193 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),B). [resolve(193,a,180,a)].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),C). [resolve(193,a,182,a)].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C)). [resolve(193,a,183,a)].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),C),tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),D)). [resolve(193,a,187,a)].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),A). [resolve(193,a,188,a)].
% 1.16/1.43 194 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.16/1.43 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex),B). [resolve(194,a,180,a)].
% 1.16/1.45 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),C). [resolve(194,a,182,a)].
% 1.16/1.45 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C)). [resolve(194,a,183,a)].
% 1.16/1.45 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(C,tc_Complex_Ocomplex),D)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),C),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),D)). [resolve(194,a,187,a)].
% 1.16/1.45 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B) = hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),A). [resolve(194,a,188,a)].
% 1.16/1.45 195 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 1.16/1.45 196 -class_OrderedGroup_Oordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 1.16/1.45 197 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__eq__neg__nonpos_0) # label(axiom). [assumption].
% 1.16/1.45 198 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__eq__neg__nonpos_1) # label(axiom). [assumption].
% 1.16/1.45 199 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A) # label(cls_neg__less__eq__nonneg_0) # label(axiom). [assumption].
% 1.16/1.45 200 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__eq__nonneg_1) # label(axiom). [assumption].
% 1.16/1.45 201 -class_OrderedGroup_Oordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 1.16/1.45 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) != A | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(195,a,196,a)].
% 1.16/1.45 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(195,a,197,a)].
% 1.16/1.45 Derived: c_lessequals(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(195,a,198,a)].
% 1.16/1.45 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),A,tc_RealDef_Oreal). [resolve(195,a,199,a)].
% 1.16/1.45 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(195,a,200,a)].
% 1.16/1.45 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(195,a,201,a)].
% 1.16/1.45 202 class_Ring__and__Field_Oidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.16/1.45 203 -class_Ring__and__Field_Oidom(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),B) # label(cls_square__eq__iff_1) # label(axiom). [assumption].
% 1.23/1.47 204 -class_Ring__and__Field_Oidom(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),B) != hAPP(c_HOL_Otimes__class_Otimes(C,A),C) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_square__eq__iff_0) # label(axiom). [assumption].
% 1.23/1.47 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A). [resolve(202,a,203,a)].
% 1.23/1.47 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A) != hAPP(c_HOL_Otimes__class_Otimes(B,tc_RealDef_Oreal),B) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B) | A = B. [resolve(202,a,204,a)].
% 1.23/1.47 205 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.23/1.47 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),A). [resolve(205,a,203,a)].
% 1.23/1.47 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),A) != hAPP(c_HOL_Otimes__class_Otimes(B,tc_Complex_Ocomplex),B) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B) | A = B. [resolve(205,a,204,a)].
% 1.23/1.47 206 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.23/1.47 207 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),C) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 1.23/1.47 208 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 1.23/1.47 209 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 1.23/1.47 210 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C) = hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 1.23/1.47 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B). [resolve(206,a,207,a)].
% 1.23/1.47 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)). [resolve(206,a,208,a)].
% 1.23/1.47 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B). [resolve(206,a,209,a)].
% 1.23/1.47 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)). [resolve(206,a,210,a)].
% 1.23/1.47 211 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.23/1.47 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B). [resolve(211,a,207,a)].
% 1.23/1.47 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(211,a,208,a)].
% 1.23/1.49 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),B). [resolve(211,a,209,a)].
% 1.23/1.49 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A),tc_Complex_Ocomplex),B) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(211,a,210,a)].
% 1.23/1.49 212 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.23/1.49 213 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 1.23/1.49 214 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 1.23/1.49 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(212,a,213,a)].
% 1.23/1.49 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_nat),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(212,a,214,a)].
% 1.23/1.49 215 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.23/1.49 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D),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(215,a,213,a)].
% 1.23/1.49 Derived: c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D),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(215,a,214,a)].
% 1.23/1.49 216 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.23/1.49 217 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__0__le__iff__le_0) # label(axiom). [assumption].
% 1.23/1.49 218 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__le__iff__le_1) # label(axiom). [assumption].
% 1.23/1.49 219 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__le__0__iff__le_1) # label(axiom). [assumption].
% 1.23/1.49 220 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__le__0__iff__le_0) # label(axiom). [assumption].
% 1.23/1.49 221 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__0__iff__less_1) # label(axiom). [assumption].
% 1.23/1.49 222 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__less__0__iff__less_0) # label(axiom). [assumption].
% 1.23/1.49 223 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__0__less__iff__less_0) # label(axiom). [assumption].
% 1.23/1.49 224 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__less__iff__less_1) # label(axiom). [assumption].
% 1.23/1.49 225 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_neg__less__iff__less_1) # label(axiom). [assumption].
% 1.23/1.49 226 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__less__iff__less_0) # label(axiom). [assumption].
% 1.23/1.49 227 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__le__iff__le_0) # label(axiom). [assumption].
% 1.23/1.49 228 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_lessequals(C,B,A) # label(cls_le__imp__neg__le_0) # label(axiom). [assumption].
% 1.23/1.49 229 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__less__iff_1) # label(axiom). [assumption].
% 1.23/1.49 230 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__less__iff_0) # label(axiom). [assumption].
% 1.23/1.49 231 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_HOL_Oord__class_Oless(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__minus__iff_1) # label(axiom). [assumption].
% 1.23/1.49 232 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_HOL_Oord__class_Oless(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__minus__iff_0) # label(axiom). [assumption].
% 1.23/1.49 233 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__le__iff_1) # label(axiom). [assumption].
% 1.23/1.49 234 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__le__iff_0) # label(axiom). [assumption].
% 1.23/1.49 235 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_lessequals(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_le__minus__iff_1) # label(axiom). [assumption].
% 1.23/1.49 236 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_lessequals(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_le__minus__iff_0) # label(axiom). [assumption].
% 1.23/1.49 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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(216,a,217,a)].
% 1.23/1.49 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(216,a,218,a)].
% 1.23/1.49 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),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). [resolve(216,a,219,a)].
% 1.23/1.49 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(216,a,220,a)].
% 1.23/1.49 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(216,a,221,a)].
% 1.23/1.49 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(216,a,222,a)].
% 1.23/1.49 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(216,a,223,a)].
% 1.23/1.49 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(216,a,224,a)].
% 1.23/1.49 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(216,a,225,a)].
% 1.23/1.49 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(216,a,226,a)].
% 1.23/1.49 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(216,a,227,a)].
% 1.23/1.49 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(216,a,228,a)].
% 1.23/1.49 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),A,tc_RealDef_Oreal). [resolve(216,a,229,a)].
% 1.23/1.49 Derived: c_HOL_Oord__class_Oless(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(216,a,231,a)].
% 1.23/1.49 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),A,tc_RealDef_Oreal). [resolve(216,a,233,a)].
% 1.23/1.49 Derived: c_lessequals(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),tc_RealDef_Oreal) | -c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(216,a,235,a)].
% 1.26/1.50 237 class_RealVector_Oreal__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__vector) # label(axiom). [assumption].
% 1.26/1.50 238 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C) != 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].
% 1.26/1.50 239 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D)) # label(cls_scaleR__left__commute_0) # label(axiom). [assumption].
% 1.26/1.50 240 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)) # label(cls_scaleR__minus__right_0) # label(axiom). [assumption].
% 1.26/1.50 241 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),A),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)) # label(cls_scaleR__minus__left_0) # label(axiom). [assumption].
% 1.26/1.50 242 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B),A),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C)) # label(cls_scaleR__left_Ominus_0) # label(axiom). [assumption].
% 1.26/1.50 243 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR__eq__0__iff_2) # label(axiom). [assumption].
% 1.26/1.50 244 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR__eq__0__iff_1) # label(axiom). [assumption].
% 1.26/1.50 245 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A),B) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A),C) # label(cls_scaleR__cancel__left_1) # label(axiom). [assumption].
% 1.26/1.50 246 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_HOL_Ozero__class_Ozero(A)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),c_HOL_Ozero__class_Ozero(A)) # label(cls_scaleR__cancel__right_1) # label(axiom). [assumption].
% 1.26/1.50 247 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C) != hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),D) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | C = D # label(cls_scaleR__cancel__left_0) # label(axiom). [assumption].
% 1.26/1.50 248 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C) != hAPP(c_RealVector_OscaleR__class_OscaleR(D,A),C) | C = c_HOL_Ozero__class_Ozero(A) | B = D # label(cls_scaleR__cancel__right_0) # label(axiom). [assumption].
% 1.26/1.51 249 -class_RealVector_Oreal__vector(A) | hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A,E),D,E,A) # label(cls_scaleR__right_Osetsum_0) # label(axiom). [assumption].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B) != 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(237,a,238,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C)). [resolve(237,a,239,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)). [resolve(237,a,240,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B)). [resolve(237,a,241,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(237,a,243,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(237,a,244,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),A) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),B). [resolve(237,a,245,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(237,a,246,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B) != hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),C) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = C. [resolve(237,a,247,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B) != hAPP(c_RealVector_OscaleR__class_OscaleR(C,tc_RealDef_Oreal),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = C. [resolve(237,a,248,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),c_Finite__Set_Osetsum(B,C,D,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,D),C,D,tc_RealDef_Oreal). [resolve(237,a,249,a)].
% 1.26/1.51 250 class_RealVector_Oreal__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__vector) # label(axiom). [assumption].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(250,a,238,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_Complex_Ocomplex),C)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_Complex_Ocomplex),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),C)). [resolve(250,a,239,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B)). [resolve(250,a,240,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_Complex_Ocomplex),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B)). [resolve(250,a,241,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(250,a,243,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(250,a,244,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex),A) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex),B). [resolve(250,a,245,a)].
% 1.26/1.51 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(250,a,246,a)].
% 1.29/1.54 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B) != hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),C) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = C. [resolve(250,a,247,a)].
% 1.29/1.54 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B) != hAPP(c_RealVector_OscaleR__class_OscaleR(C,tc_Complex_Ocomplex),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = C. [resolve(250,a,248,a)].
% 1.29/1.54 Derived: hAPP(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),c_Finite__Set_Osetsum(B,C,D,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,D),C,D,tc_Complex_Ocomplex). [resolve(250,a,249,a)].
% 1.29/1.54 251 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra) # label(axiom). [assumption].
% 1.29/1.54 252 -class_RealVector_Oreal__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),C),A),D) = hAPP(c_RealVector_OscaleR__class_OscaleR(B,A),hAPP(c_HOL_Otimes__class_Otimes(C,A),D)) # label(cls_mult__scaleR__left_0) # label(axiom). [assumption].
% 1.29/1.54 253 -class_RealVector_Oreal__algebra(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),D)) = hAPP(c_RealVector_OscaleR__class_OscaleR(C,A),hAPP(c_HOL_Otimes__class_Otimes(B,A),D)) # label(cls_mult__scaleR__right_0) # label(axiom). [assumption].
% 1.29/1.54 254 class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) # label(axiom). [assumption].
% 1.29/1.54 255 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.29/1.54 256 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_le__minus__self__iff_0) # label(axiom). [assumption].
% 1.29/1.54 257 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__minus__self__iff_1) # label(axiom). [assumption].
% 1.29/1.54 258 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A) # label(cls_minus__le__self__iff_0) # label(axiom). [assumption].
% 1.29/1.54 259 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_minus__le__self__iff_1) # label(axiom). [assumption].
% 1.29/1.54 260 class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 1.29/1.54 261 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_abs__less__iff_2) # label(axiom). [assumption].
% 1.29/1.54 262 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)) # label(cls_abs__mult_0) # label(axiom). [assumption].
% 1.29/1.54 263 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__less__iff_1) # label(axiom). [assumption].
% 1.29/1.54 264 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)),hAPP(c_HOL_Otimes__class_Otimes(D,A),E),A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),C),E,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),D,A) # label(cls_abs__mult__less_0) # label(axiom). [assumption].
% 1.29/1.54 265 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__less__iff_0) # label(axiom). [assumption].
% 1.29/1.54 266 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),B)) = hAPP(c_HOL_Otimes__class_Otimes(B,A),B) # label(cls_abs__mult__self_0) # label(axiom). [assumption].
% 1.29/1.54 267 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),C) = hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_abs__mult__pos_0) # label(axiom). [assumption].
% 1.29/1.54 268 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__minus__self__iff_0) # label(axiom). [assumption].
% 1.29/1.54 269 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__minus__self__iff_1) # label(axiom). [assumption].
% 1.29/1.54 270 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 1.29/1.54 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(260,a,261,a)].
% 1.29/1.54 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),B)). [resolve(260,a,262,a)].
% 1.29/1.54 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal). [resolve(260,a,263,a)].
% 1.29/1.54 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(C,tc_RealDef_Oreal),D),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),B),D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),C,tc_RealDef_Oreal). [resolve(260,a,264,a)].
% 1.29/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),B,tc_RealDef_Oreal). [resolve(260,a,265,a)].
% 1.29/1.54 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A)) = hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),A). [resolve(260,a,266,a)].
% 1.29/1.54 Derived: hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),tc_RealDef_Oreal),B) = hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(260,a,267,a)].
% 1.29/1.54 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal). [resolve(260,a,268,a)].
% 1.29/1.54 Derived: c_HOL_Oord__class_Oless(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(260,a,269,a)].
% 1.29/1.54 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | B = A. [resolve(260,a,270,a)].
% 1.29/1.57 271 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 1.29/1.57 272 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_3) # label(axiom). [assumption].
% 1.29/1.57 273 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_2) # label(axiom). [assumption].
% 1.29/1.57 274 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_1) # label(axiom). [assumption].
% 1.29/1.57 275 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_0) # label(axiom). [assumption].
% 1.29/1.57 276 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.29/1.57 277 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom). [assumption].
% 1.29/1.57 278 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom). [assumption].
% 1.29/1.57 279 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) # label(cls_neg__0__equal__iff__equal_1) # label(axiom). [assumption].
% 1.29/1.57 280 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom). [assumption].
% 1.29/1.57 281 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom). [assumption].
% 1.29/1.57 282 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_minus__equation__iff_1) # label(axiom). [assumption].
% 1.29/1.57 283 -class_OrderedGroup_Ogroup__add(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_equation__minus__iff_1) # label(axiom). [assumption].
% 1.29/1.57 284 -class_OrderedGroup_Ogroup__add(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_equation__minus__iff_0) # label(axiom). [assumption].
% 1.29/1.57 285 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_minus__minus_0) # label(axiom). [assumption].
% 1.29/1.57 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(276,a,277,a)].
% 1.29/1.57 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(276,a,278,a)].
% 1.29/1.57 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(276,a,279,a)].
% 1.29/1.59 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),B) | A = B. [resolve(276,a,281,a)].
% 1.29/1.59 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)) = A. [resolve(276,a,282,a)].
% 1.29/1.59 Derived: A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A)). [resolve(276,a,283,a)].
% 1.29/1.59 286 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.29/1.59 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(286,a,277,a)].
% 1.29/1.59 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(286,a,278,a)].
% 1.29/1.59 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(286,a,279,a)].
% 1.29/1.59 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(286,a,280,a)].
% 1.29/1.59 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B) | A = B. [resolve(286,a,281,a)].
% 1.29/1.59 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)) = A. [resolve(286,a,282,a)].
% 1.29/1.59 Derived: A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)). [resolve(286,a,283,a)].
% 1.29/1.59 287 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].
% 1.29/1.59 288 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 1.29/1.59 289 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 1.29/1.59 290 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 1.29/1.59 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B) != 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(287,a,288,a)].
% 1.29/1.59 291 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.29/1.59 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(291,a,288,a)].
% 1.29/1.59 292 class_Ring__and__Field_Ono__zero__divisors(tc_nat) # label(clsarity_nat__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.29/1.59 293 -class_Ring__and__Field_Ono__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != 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].
% 1.29/1.59 294 -class_Ring__and__Field_Ono__zero__divisors(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),C) != 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].
% 1.29/1.62 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),B) != c_HOL_Ozero__class_Ozero(tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(292,a,293,a)].
% 1.29/1.62 295 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.29/1.62 296 class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.29/1.62 297 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 1.29/1.62 298 -class_Ring__and__Field_Oabs__if(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_0) # label(axiom). [assumption].
% 1.29/1.62 299 -class_Ring__and__Field_Oabs__if(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_1) # label(axiom). [assumption].
% 1.29/1.62 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(297,a,299,a)].
% 1.29/1.62 300 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.29/1.62 301 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_0) # label(axiom). [assumption].
% 1.29/1.62 302 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_1) # label(axiom). [assumption].
% 1.29/1.62 303 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.29/1.62 304 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.29/1.62 305 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.29/1.62 306 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.29/1.62 307 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.29/1.62 308 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.29/1.62 309 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.29/1.62 310 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.29/1.62 311 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.29/1.62 312 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.29/1.62 313 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.29/1.62 314 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.29/1.62 315 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.39/1.64 316 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.39/1.64 317 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.39/1.64 318 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.39/1.64 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | hAPP(c_HOL_Oabs__class_Oabs(tc_nat),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_nat),A) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(300,a,301,a)].
% 1.39/1.64 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | hAPP(c_HOL_Oabs__class_Oabs(tc_nat),A) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(300,a,302,a)].
% 1.39/1.64 Derived: -c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(300,a,303,a)].
% 1.39/1.64 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(300,a,304,a)].
% 1.39/1.64 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(B,A,tc_nat) | B = A. [resolve(300,a,310,a)].
% 1.39/1.64 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(300,a,314,a)].
% 1.39/1.64 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(300,a,316,a)].
% 1.39/1.64 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(300,a,317,a)].
% 1.39/1.64 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(300,a,318,a)].
% 1.39/1.64 319 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 1.39/1.64 Derived: -c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(319,a,303,a)].
% 1.39/1.64 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal). [resolve(319,a,304,a)].
% 1.39/1.64 Derived: A = B | -c_lessequals(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(319,a,314,a)].
% 1.39/1.64 Derived: -c_HOL_Oord__class_Oless(A,A,tc_RealDef_Oreal). [resolve(319,a,316,a)].
% 1.39/1.64 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal). [resolve(319,a,317,a)].
% 1.39/1.64 Derived: -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(319,a,318,a)].
% 1.39/1.64 320 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.39/1.64 321 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),D),hAPP(c_HOL_Otimes__class_Otimes(C,A),D),A) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 1.39/1.64 322 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(D,A),B),hAPP(c_HOL_Otimes__class_Otimes(D,A),C),A) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 1.39/1.64 323 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.39/1.64 324 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) # label(axiom). [assumption].
% 1.39/1.64 325 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Otimes__class_Otimes(B,A),C)),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(A),B),A),hAPP(c_HOL_Oabs__class_Oabs(A),C)),A) # label(cls_abs__le__mult_0) # label(axiom). [assumption].
% 1.39/1.64 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),hAPP(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),B)),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),A),tc_RealDef_Oreal),hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),B)),tc_RealDef_Oreal). [resolve(324,a,325,a)].
% 1.39/1.66 326 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.39/1.66 327 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(B,A),C),hAPP(c_HOL_Otimes__class_Otimes(B,A),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 1.39/1.66 328 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.39/1.66 329 class_Ring__and__Field_Omult__zero(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.39/1.66 330 -class_Ring__and__Field_Omult__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),A),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__left_0) # label(axiom). [assumption].
% 1.39/1.66 331 -class_Ring__and__Field_Omult__zero(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__right_0) # label(axiom). [assumption].
% 1.39/1.66 332 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.39/1.66 333 class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.39/1.66 334 class_SEQ_Obanach(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__SEQ_Obanach) # label(axiom). [assumption].
% 1.39/1.66 335 -class_SEQ_Obanach(A) | c_Series_Osummable(B,A) | -c_Series_Osummable(C,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(A),hAPP(B,c_Series_Osko__Series__Xsummable__comparison__test__1__1(B,C,D,A))),hAPP(C,c_Series_Osko__Series__Xsummable__comparison__test__1__1(B,C,D,A)),tc_RealDef_Oreal) # label(cls_summable__comparison__test_1) # label(axiom). [assumption].
% 1.39/1.66 336 -class_SEQ_Obanach(A) | c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(A),c_Series_Osuminf(B,A)),c_Series_Osuminf(c_COMBB(c_RealVector_Onorm__class_Onorm(A),B,A,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(A),B,A,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) # label(cls_summable__norm_0) # label(axiom). [assumption].
% 1.39/1.66 337 -class_SEQ_Obanach(A) | c_Series_Osummable(B,A) | -c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(A),B,A,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) # label(cls_summable__norm__cancel_0) # label(axiom). [assumption].
% 1.39/1.66 338 -class_SEQ_Obanach(A) | c_Series_Osummable(B,A) | -c_Series_Osummable(C,tc_RealDef_Oreal) | c_lessequals(D,c_Series_Osko__Series__Xsummable__comparison__test__1__1(B,C,D,A),tc_nat) # label(cls_summable__comparison__test_0) # label(axiom). [assumption].
% 1.39/1.66 Derived: c_Series_Osummable(A,tc_RealDef_Oreal) | -c_Series_Osummable(B,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),hAPP(A,c_Series_Osko__Series__Xsummable__comparison__test__1__1(A,B,C,tc_RealDef_Oreal))),hAPP(B,c_Series_Osko__Series__Xsummable__comparison__test__1__1(A,B,C,tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(334,a,335,a)].
% 1.39/1.67 Derived: c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),c_Series_Osuminf(A,tc_RealDef_Oreal)),c_Series_Osuminf(c_COMBB(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal). [resolve(334,a,336,a)].
% 1.39/1.67 Derived: c_Series_Osummable(A,tc_RealDef_Oreal) | -c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal). [resolve(334,a,337,a)].
% 1.39/1.67 Derived: c_Series_Osummable(A,tc_RealDef_Oreal) | -c_Series_Osummable(B,tc_RealDef_Oreal) | c_lessequals(C,c_Series_Osko__Series__Xsummable__comparison__test__1__1(A,B,C,tc_RealDef_Oreal),tc_nat). [resolve(334,a,338,a)].
% 1.39/1.68 339 class_SEQ_Obanach(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__SEQ_Obanach) # label(axiom). [assumption].
% 1.39/1.68 Derived: c_Series_Osummable(A,tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_RealDef_Oreal) | -c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(A,c_Series_Osko__Series__Xsummable__comparison__test__1__1(A,B,C,tc_Complex_Ocomplex))),hAPP(B,c_Series_Osko__Series__Xsummable__comparison__test__1__1(A,B,C,tc_Complex_Ocomplex)),tc_RealDef_Oreal). [resolve(339,a,335,a)].
% 1.39/1.68 Derived: c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),c_Series_Osuminf(c_COMBB(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal). [resolve(339,a,336,a)].
% 1.39/1.68 Derived: c_Series_Osummable(A,tc_Complex_Ocomplex) | -c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal). [resolve(339,a,337,a)].
% 1.39/1.68 Derived: c_Series_Osummable(A,tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_RealDef_Oreal) | c_lessequals(C,c_Series_Osko__Series__Xsummable__comparison__test__1__1(A,B,C,tc_Complex_Ocomplex),tc_nat). [resolve(339,a,338,a)].
% 1.39/1.68 340 -class_RealVector_Ometric__space(A) | -class_RealVector_Ometric__space(B) | c_Lim_OisCont(C,D,A,B) | -c_Lim_OisUCont(C,A,B) # label(cls_isUCont__isCont_0) # label(axiom). [assumption].
% 1.39/1.68 341 -class_RealVector_Oreal__normed__vector(A) | c_Lim_OisUCont(c_RealVector_OscaleR__class_OscaleR(B,A),A,A) # label(cls_scaleR__right_OisUCont_0) # label(axiom). [assumption].
% 1.39/1.68 342 -class_RealVector_Ometric__space(A) | -class_RealVector_Ometric__space(B) | c_SEQ_OCauchy(c_COMBB(C,D,A,B,tc_nat),B) | -c_SEQ_OCauchy(D,A) | -c_Lim_OisUCont(C,A,B) # label(cls_isUCont__Cauchy_0) # label(axiom). [assumption].
% 1.39/1.68 Derived: -class_RealVector_Ometric__space(A) | -class_RealVector_Ometric__space(A) | c_SEQ_OCauchy(c_COMBB(c_RealVector_OscaleR__class_OscaleR(B,A),C,A,A,tc_nat),A) | -c_SEQ_OCauchy(C,A) | -class_RealVector_Oreal__normed__vector(A). [resolve(342,e,341,b)].
% 1.39/1.68 343 c_Lim_OisUCont(c_Complex_OIm,tc_Complex_Ocomplex,tc_RealDef_Oreal) # label(cls_Im_OisUCont_0) # label(axiom). [assumption].
% 1.39/1.68 Derived: -class_RealVector_Ometric__space(tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(tc_RealDef_Oreal) | c_Lim_OisCont(c_Complex_OIm,A,tc_Complex_Ocomplex,tc_RealDef_Oreal). [resolve(343,a,340,d)].
% 1.39/1.68 Derived: -class_RealVector_Ometric__space(tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(tc_RealDef_Oreal) | c_SEQ_OCauchy(c_COMBB(c_Complex_OIm,A,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) | -c_SEQ_OCauchy(A,tc_Complex_Ocomplex). [resolve(343,a,342,e)].
% 1.39/1.68 344 c_Lim_OisUCont(c_Complex_ORe,tc_Complex_Ocomplex,tc_RealDef_Oreal) # label(cls_Re_OisUCont_0) # label(axiom). [assumption].
% 1.39/1.68 345 c_Lim_OisUCont(c_HOL_Otimes__class_Otimes(A,tc_RealDef_Oreal),tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(77,a,89,a)].
% 1.39/1.68 346 c_Lim_OisUCont(c_HOL_Otimes__class_Otimes(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(111,a,89,a)].
% 1.39/1.68 347 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Oreal__normed__vector(A) | c_Lim_OisUCont(c_RealVector_OscaleR__class_OscaleR(B,A),A,A). [resolve(112,b,115,d)].
% 1.39/1.68 348 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.39/1.68 349 -class_Ring__and__Field_Osemiring__0(A) | hAPP(c_HOL_Otimes__class_Otimes(B,A),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(B,A),C,A,A,E),D,E,A) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 1.46/1.70 Derived: hAPP(c_HOL_Otimes__class_Otimes(A,tc_nat),c_Finite__Set_Osetsum(B,C,D,tc_nat)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(A,tc_nat),B,tc_nat,tc_nat,D),C,D,tc_nat). [resolve(348,a,349,a)].
% 1.46/1.70 350 class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.46/1.70 351 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.46/1.70 352 c_SEQ_Osubseq(c_SEQ_Osko__SEQ__Xseq__monosub__1__1(A)) # label(cls_seq__monosub_0) # label(axiom). [assumption].
% 1.46/1.70 353 -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(c_Fun_Ocomp(B,C,tc_nat,A,tc_nat),D,A) | -c_SEQ_Osubseq(C) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__subseq__LIMSEQ_0) # label(axiom). [assumption].
% 1.46/1.70 354 -class_RealVector_Ometric__space(A) | c_SEQ_OCauchy(c_Fun_Ocomp(B,C,tc_nat,A,tc_nat),A) | -c_SEQ_Osubseq(C) | -c_SEQ_OCauchy(B,A) # label(cls_Cauchy__subseq__Cauchy_0) # label(axiom). [assumption].
% 1.46/1.70 Derived: -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(c_Fun_Ocomp(B,c_SEQ_Osko__SEQ__Xseq__monosub__1__1(C),tc_nat,A,tc_nat),D,A) | -c_SEQ_OLIMSEQ(B,D,A). [resolve(352,a,353,c)].
% 1.46/1.70 Derived: -class_RealVector_Ometric__space(A) | c_SEQ_OCauchy(c_Fun_Ocomp(B,c_SEQ_Osko__SEQ__Xseq__monosub__1__1(C),tc_nat,A,tc_nat),A) | -c_SEQ_OCauchy(B,A). [resolve(352,a,354,c)].
% 1.46/1.70 355 c_lessequals(A,hAPP(B,A),tc_nat) | -c_SEQ_Osubseq(B) # label(cls_seq__suble_0) # label(axiom). [assumption].
% 1.46/1.70 Derived: c_lessequals(A,hAPP(c_SEQ_Osko__SEQ__Xseq__monosub__1__1(B),A),tc_nat). [resolve(355,b,352,a)].
% 1.46/1.70 356 c_HOL_Oord__class_Oless(hAPP(A,B),hAPP(A,C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_SEQ_Osubseq(A) # label(cls_subseq__def_0) # label(axiom). [assumption].
% 1.46/1.70 Derived: c_HOL_Oord__class_Oless(hAPP(c_SEQ_Osko__SEQ__Xseq__monosub__1__1(A),B),hAPP(c_SEQ_Osko__SEQ__Xseq__monosub__1__1(A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(356,c,352,a)].
% 1.46/1.70 357 v_thesis____ | -c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,A,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) | -c_SEQ_Osubseq(A) # label(cls_that_0) # label(axiom). [assumption].
% 1.46/1.70 Derived: v_thesis____ | -c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,c_SEQ_Osko__SEQ__Xseq__monosub__1__1(A),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)). [resolve(357,c,352,a)].
% 1.46/1.70 358 c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)) # label(cls_CHAINED_0) # label(axiom). [assumption].
% 1.46/1.70 Derived: -class_RealVector_Ometric__space(A) | c_SEQ_OLIMSEQ(c_Fun_Ocomp(B,v_sko__CHAINED__1(v_s),tc_nat,A,tc_nat),C,A) | -c_SEQ_OLIMSEQ(B,C,A). [resolve(358,a,353,c)].
% 1.46/1.70 Derived: -class_RealVector_Ometric__space(A) | c_SEQ_OCauchy(c_Fun_Ocomp(B,v_sko__CHAINED__1(v_s),tc_nat,A,tc_nat),A) | -c_SEQ_OCauchy(B,A). [resolve(358,a,354,c)].
% 1.46/1.70 Derived: c_lessequals(A,hAPP(v_sko__CHAINED__1(v_s),A),tc_nat). [resolve(358,a,355,b)].
% 1.46/1.70 Derived: c_HOL_Oord__class_Oless(hAPP(v_sko__CHAINED__1(v_s),A),hAPP(v_sko__CHAINED__1(v_s),B),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(358,a,356,c)].
% 1.46/1.70 Derived: v_thesis____ | -c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)). [resolve(358,a,357,c)].
% 1.46/1.70 359 c_SEQ_Odecseq(A) | -c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) # label(cls_decseq__eq__incseq_1) # label(axiom). [assumption].
% 1.46/1.70 360 c_lessequals(hAPP(A,B),hAPP(A,C),tc_RealDef_Oreal) | -c_lessequals(C,B,tc_nat) | -c_SEQ_Odecseq(A) # label(cls_decseq__def_0) # label(axiom). [assumption].
% 1.46/1.70 361 c_lessequals(A,hAPP(B,C),tc_RealDef_Oreal) | -c_SEQ_OLIMSEQ(B,A,tc_RealDef_Oreal) | -c_SEQ_Odecseq(B) # label(cls_decseq__le_0) # label(axiom). [assumption].
% 1.46/1.70 362 c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) | -c_SEQ_Odecseq(A) # label(cls_decseq__eq__incseq_0) # label(axiom). [assumption].
% 1.46/1.71 Derived: -c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) | c_lessequals(hAPP(A,B),hAPP(A,C),tc_RealDef_Oreal) | -c_lessequals(C,B,tc_nat). [resolve(359,a,360,c)].
% 1.46/1.71 Derived: -c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) | c_lessequals(B,hAPP(A,C),tc_RealDef_Oreal) | -c_SEQ_OLIMSEQ(A,B,tc_RealDef_Oreal). [resolve(359,a,361,c)].
% 1.46/1.71 363 c_SEQ_Omonoseq(A) | -c_SEQ_Odecseq(A) # label(cls_decseq__imp__monoseq_0) # label(axiom). [assumption].
% 1.46/1.71 Derived: c_SEQ_Omonoseq(A) | -c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)). [resolve(363,b,359,a)].
% 1.46/1.71 364 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.46/1.71 365 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__algebra__1(B) | c_Lim_OisCont(c_COMBB(c_RealVector_Oof__real(B),C,tc_RealDef_Oreal,B,A),D,A,B) | -c_Lim_OisCont(C,D,A,tc_RealDef_Oreal) # label(cls_isCont__of__real_0) # label(axiom). [assumption].
% 1.46/1.71 366 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__algebra__1(B) | C = D | -c_Lim_OLIM(E,F,D,B,A) | -c_Lim_OLIM(E,F,C,B,A) # label(cls_LIM__unique_0) # label(axiom). [assumption].
% 1.46/1.71 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OisCont(c_COMBB(c_RealVector_Oof__real(tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal,A),C,A,tc_RealDef_Oreal) | -c_Lim_OisCont(B,C,A,tc_RealDef_Oreal). [resolve(364,a,365,b)].
% 1.46/1.71 Derived: -class_RealVector_Ometric__space(A) | B = C | -c_Lim_OLIM(D,E,C,tc_RealDef_Oreal,A) | -c_Lim_OLIM(D,E,B,tc_RealDef_Oreal,A). [resolve(364,a,366,b)].
% 1.46/1.71 367 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.46/1.71 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OisCont(c_COMBB(c_RealVector_Oof__real(tc_Complex_Ocomplex),B,tc_RealDef_Oreal,tc_Complex_Ocomplex,A),C,A,tc_Complex_Ocomplex) | -c_Lim_OisCont(B,C,A,tc_RealDef_Oreal). [resolve(367,a,365,b)].
% 1.46/1.71 Derived: -class_RealVector_Ometric__space(A) | B = C | -c_Lim_OLIM(D,E,C,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(D,E,B,tc_Complex_Ocomplex,A). [resolve(367,a,366,b)].
% 1.46/1.71 368 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.46/1.71 369 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,A),C,A) | -c_Deriv_Odifferentiable(B,C,A) # label(cls_differentiable__minus_0) # label(axiom). [assumption].
% 1.46/1.71 370 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBB(B,C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,hAPP(C,D),A) # label(cls_differentiable__compose_0) # label(axiom). [assumption].
% 1.46/1.71 Derived: c_Deriv_Odifferentiable(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_Deriv_Odifferentiable(A,B,tc_RealDef_Oreal). [resolve(368,a,369,a)].
% 1.46/1.71 Derived: c_Deriv_Odifferentiable(c_COMBB(A,B,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_Deriv_Odifferentiable(B,C,tc_RealDef_Oreal) | -c_Deriv_Odifferentiable(A,hAPP(B,C),tc_RealDef_Oreal). [resolve(368,a,370,a)].
% 1.46/1.71 371 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.46/1.71 Derived: c_Deriv_Odifferentiable(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,B,tc_Complex_Ocomplex). [resolve(371,a,369,a)].
% 1.46/1.71 Derived: c_Deriv_Odifferentiable(c_COMBB(A,B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,hAPP(B,C),tc_Complex_Ocomplex). [resolve(371,a,370,a)].
% 1.46/1.76 372 class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 1.46/1.76 373 -class_OrderedGroup_Oab__group__add(A) | c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,C),D,C,A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Finite__Set_Osetsum(B,D,C,A)) # label(cls_setsum__negf_0) # label(axiom). [assumption].
% 1.46/1.76 Derived: c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),A,tc_RealDef_Oreal,tc_RealDef_Oreal,B),C,B,tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_Finite__Set_Osetsum(A,C,B,tc_RealDef_Oreal)). [resolve(372,a,373,a)].
% 1.46/1.76 374 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 1.46/1.76 Derived: c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,B),C,B,tc_Complex_Ocomplex) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,C,B,tc_Complex_Ocomplex)). [resolve(374,a,373,a)].
% 1.46/1.76 375 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.46/1.76 376 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.46/1.76 Derived: A = A. [resolve(375,b,376,a)].
% 1.46/1.76
% 1.46/1.76 ============================== end predicate elimination =============
% 1.46/1.76
% 1.46/1.76 Auto_denials: (non-Horn, no changes).
% 1.46/1.76
% 1.46/1.76 Term ordering decisions:
% 1.46/1.76 Function symbol KB weights: tc_RealDef_Oreal=1. tc_Complex_Ocomplex=1. tc_nat=1. c_Complex_ORe=1. c_Complex_OIm=1. c_Complex_Ocnj=1. v_s=1. tc_bool=1. v_z=1. hAPP=1. c_HOL_Otimes__class_Otimes=1. c_RealVector_OscaleR__class_OscaleR=1. c_Series_Osuminf=1. c_Complex_Ocomplex_OComplex=1. tc_fun=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Ouminus__class_Ouminus=1. c_RealVector_Oof__real=1. c_HOL_Oabs__class_Oabs=1. c_RealVector_Onorm__class_Onorm=1. c_SEQ_Osko__SEQ__Xseq__monosub__1__1=1. v_sko__CHAINED__1=1. c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1=1. c_Finite__Set_Osetsum=1. c_Series_Osko__Series__Xsummable__comparison__test__1__1=1. c_Set_Oimage=1. c_COMBB=1. c_Fun_Ocomp=1.
% 1.46/1.76
% 1.46/1.76 ============================== PROOF =================================
% 1.46/1.76 % SZS status Unsatisfiable
% 1.46/1.76 % SZS output start Refutation
% 1.46/1.76
% 1.46/1.76 % Proof 1 at 0.60 (+ 0.00) seconds.
% 1.46/1.76 % Length of proof is 6.
% 1.46/1.76 % Level of proof is 2.
% 1.46/1.76 % Maximum clause weight is 13.000.
% 1.46/1.76 % Given clauses 0.
% 1.46/1.76
% 1.46/1.76 357 v_thesis____ | -c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,A,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) | -c_SEQ_Osubseq(A) # label(cls_that_0) # label(axiom). [assumption].
% 1.46/1.76 358 c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)) # label(cls_CHAINED_0) # label(axiom). [assumption].
% 1.46/1.76 587 c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) # label(cls_CHAINED_1) # label(axiom). [assumption].
% 1.46/1.76 588 -v_thesis____ # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 1.46/1.76 981 v_thesis____ | -c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)). [resolve(358,a,357,c)].
% 1.46/1.76 982 $F. [copy(981),unit_del(a,588),unit_del(b,587)].
% 1.46/1.76
% 1.46/1.76 % SZS output end Refutation
% 1.46/1.76 ============================== end of proof ==========================
% 1.46/1.76
% 1.46/1.76 ============================== STATISTICS ============================
% 1.46/1.76
% 1.46/1.76 Given=0. Generated=540. Kept=471. proofs=1.
% 1.46/1.76 Usable=0. Sos=0. Demods=80. Limbo=471, Disabled=919. Hints=0.
% 1.46/1.76 Megabytes=1.17.
% 1.46/1.76 User_CPU=0.60, System_CPU=0.00, Wall_clock=1.
% 1.46/1.76
% 1.46/1.76 ============================== end of statistics =====================
% 1.46/1.76
% 1.46/1.76 ============================== end of search =========================
% 1.46/1.76
% 1.46/1.76 THEOREM PROVED
% 1.46/1.76 % SZS status Unsatisfiable
% 1.46/1.76
% 1.46/1.76 Exiting with 1 proof.
% 1.46/1.76
% 1.46/1.76 Process 17434 exit (max_proofs) Thu Jun 9 03:50:08 2022
% 1.46/1.76 Prover9 interrupted
%------------------------------------------------------------------------------