TSTP Solution File: ALG367-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG367-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:54:36 EDT 2022
% Result : Unsatisfiable 5.47s 5.82s
% Output : Refutation 5.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG367-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 8 13:36:34 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.95/1.33 ============================== Prover9 ===============================
% 0.95/1.33 Prover9 (32) version 2009-11A, November 2009.
% 0.95/1.33 Process 30049 was started by sandbox on n025.cluster.edu,
% 0.95/1.33 Wed Jun 8 13:36:35 2022
% 0.95/1.33 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29895_n025.cluster.edu".
% 0.95/1.33 ============================== end of head ===========================
% 0.95/1.33
% 0.95/1.33 ============================== INPUT =================================
% 0.95/1.33
% 0.95/1.33 % Reading from file /tmp/Prover9_29895_n025.cluster.edu
% 0.95/1.33
% 0.95/1.33 set(prolog_style_variables).
% 0.95/1.33 set(auto2).
% 0.95/1.33 % set(auto2) -> set(auto).
% 0.95/1.33 % set(auto) -> set(auto_inference).
% 0.95/1.33 % set(auto) -> set(auto_setup).
% 0.95/1.33 % set(auto_setup) -> set(predicate_elim).
% 0.95/1.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.95/1.33 % set(auto) -> set(auto_limits).
% 0.95/1.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.95/1.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.95/1.33 % set(auto) -> set(auto_denials).
% 0.95/1.33 % set(auto) -> set(auto_process).
% 0.95/1.33 % set(auto2) -> assign(new_constants, 1).
% 0.95/1.33 % set(auto2) -> assign(fold_denial_max, 3).
% 0.95/1.33 % set(auto2) -> assign(max_weight, "200.000").
% 0.95/1.33 % set(auto2) -> assign(max_hours, 1).
% 0.95/1.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.95/1.33 % set(auto2) -> assign(max_seconds, 0).
% 0.95/1.33 % set(auto2) -> assign(max_minutes, 5).
% 0.95/1.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.95/1.33 % set(auto2) -> set(sort_initial_sos).
% 0.95/1.33 % set(auto2) -> assign(sos_limit, -1).
% 0.95/1.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.95/1.33 % set(auto2) -> assign(max_megs, 400).
% 0.95/1.33 % set(auto2) -> assign(stats, some).
% 0.95/1.33 % set(auto2) -> clear(echo_input).
% 0.95/1.33 % set(auto2) -> set(quiet).
% 0.95/1.33 % set(auto2) -> clear(print_initial_clauses).
% 0.95/1.33 % set(auto2) -> clear(print_given).
% 0.95/1.33 assign(lrs_ticks,-1).
% 0.95/1.33 assign(sos_limit,10000).
% 0.95/1.33 assign(order,kbo).
% 0.95/1.33 set(lex_order_vars).
% 0.95/1.33 clear(print_given).
% 0.95/1.33
% 0.95/1.33 % formulas(sos). % not echoed (965 formulas)
% 0.95/1.33
% 0.95/1.33 ============================== end of input ==========================
% 0.95/1.33
% 0.95/1.33 % From the command line: assign(max_seconds, 300).
% 0.95/1.33
% 0.95/1.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.95/1.33
% 0.95/1.33 % Formulas that are not ordinary clauses:
% 0.95/1.33
% 0.95/1.33 ============================== end of process non-clausal formulas ===
% 0.95/1.33
% 0.95/1.33 ============================== PROCESS INITIAL CLAUSES ===============
% 0.95/1.33
% 0.95/1.33 ============================== PREDICATE ELIMINATION =================
% 0.95/1.33 1 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.95/1.33 2 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.95/1.33 3 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.95/1.33 4 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.95/1.34 5 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.95/1.34 6 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.95/1.34 7 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 0.95/1.34 8 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 0.95/1.34 9 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.95/1.34 10 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.95/1.34 11 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.95/1.34 12 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.95/1.34 13 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.95/1.34 14 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.95/1.34 15 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.95/1.34 16 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.95/1.34 17 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.95/1.34 18 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.95/1.34 19 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.95/1.34 20 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.95/1.34 21 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.95/1.34 22 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.95/1.34 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,2,a)].
% 0.95/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(1,a,5,a)].
% 0.95/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(1,a,6,a)].
% 0.95/1.34 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(1,a,7,a)].
% 0.95/1.34 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(1,a,8,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(1,a,9,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(1,a,10,a)].
% 0.95/1.34 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(1,a,11,a)].
% 0.95/1.34 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat). [resolve(1,a,12,a)].
% 0.95/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(1,a,13,a)].
% 0.95/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(1,a,14,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(1,a,17,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(1,a,18,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(1,a,19,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(1,a,20,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat). [resolve(1,a,21,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(1,a,22,a)].
% 0.95/1.34 23 class_Lattices_Olower__semilattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.95/1.34 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(23,a,2,a)].
% 0.95/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(23,a,5,a)].
% 0.95/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(23,a,6,a)].
% 0.95/1.34 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(23,a,7,a)].
% 0.95/1.34 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(23,a,8,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(23,a,9,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(23,a,10,a)].
% 0.95/1.34 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(23,a,11,a)].
% 0.95/1.34 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(23,a,12,a)].
% 0.95/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(23,a,13,a)].
% 0.95/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(23,a,14,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = B | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(23,a,17,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) != A | c_lessequals(A,B,tc_RealDef_Oreal). [resolve(23,a,18,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = A | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(23,a,19,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_RealDef_Oreal). [resolve(23,a,20,a)].
% 0.95/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal). [resolve(23,a,21,a)].
% 0.95/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_RealDef_Oreal) = A. [resolve(23,a,22,a)].
% 0.95/1.37 24 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 0.95/1.37 25 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 0.95/1.37 26 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 0.95/1.37 27 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 0.95/1.37 28 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 0.95/1.37 29 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_0) # label(axiom). [assumption].
% 0.95/1.37 30 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_1) # label(axiom). [assumption].
% 0.95/1.37 31 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,B,A),A) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 0.95/1.37 32 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 0.95/1.37 33 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 0.95/1.37 34 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 0.95/1.37 35 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 0.95/1.37 36 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 0.95/1.37 37 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 0.95/1.37 38 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 0.95/1.37 39 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 0.95/1.37 40 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 0.95/1.37 41 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),A) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 0.95/1.37 42 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 0.95/1.37 43 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 0.95/1.37 44 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 0.95/1.37 45 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 0.95/1.37 46 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 0.95/1.37 47 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 0.95/1.37 48 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 0.95/1.37 49 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 0.95/1.37 50 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 0.95/1.37 51 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 0.95/1.37 52 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 0.95/1.37 53 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 0.95/1.37 54 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,C,A),c_HOL_Otimes__class_Otimes(B,B,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 0.95/1.37 55 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 0.95/1.37 56 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 0.95/1.37 57 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 0.95/1.37 58 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(D,B,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 0.95/1.37 59 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 0.95/1.37 60 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 0.95/1.37 61 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 0.95/1.37 62 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 0.95/1.37 63 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 0.95/1.37 64 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 0.95/1.37 65 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 0.95/1.37 66 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 0.95/1.37 67 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 0.95/1.37 68 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom). [assumption].
% 0.95/1.37 69 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 0.95/1.37 70 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 0.95/1.37 71 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 0.95/1.37 72 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 0.95/1.37 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,25,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,26,a)].
% 0.95/1.37 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,27,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,28,a)].
% 0.95/1.37 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(24,a,29,a)].
% 0.95/1.37 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(24,a,30,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,31,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(24,a,32,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,33,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,34,a)].
% 0.95/1.37 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,35,a)].
% 0.95/1.37 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,36,a)].
% 0.95/1.37 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,37,a)].
% 0.95/1.37 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,38,a)].
% 0.95/1.37 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,39,a)].
% 0.95/1.37 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,40,a)].
% 0.95/1.37 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,41,a)].
% 0.95/1.37 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,42,a)].
% 0.95/1.37 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,43,a)].
% 0.95/1.37 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,44,a)].
% 0.95/1.37 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,45,a)].
% 0.95/1.37 Derived: -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,46,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(24,a,47,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,48,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,49,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(24,a,50,a)].
% 0.95/1.37 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(24,a,51,a)].
% 0.95/1.37 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,52,a)].
% 0.95/1.37 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,53,a)].
% 0.95/1.37 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,54,a)].
% 0.95/1.37 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,55,a)].
% 0.95/1.37 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(24,a,56,a)].
% 0.95/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(24,a,57,a)].
% 0.95/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,58,a)].
% 0.95/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(24,a,59,a)].
% 0.95/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,61,a)].
% 0.95/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(24,a,62,a)].
% 0.95/1.38 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(24,a,65,a)].
% 0.95/1.38 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,67,a)].
% 0.95/1.38 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(24,a,68,a)].
% 0.95/1.38 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(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,69,a)].
% 0.95/1.38 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(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,70,a)].
% 0.95/1.38 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(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,71,a)].
% 0.95/1.38 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(c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(24,a,72,a)].
% 0.95/1.38 73 class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,25,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,26,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,27,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,28,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(73,a,29,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(73,a,30,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,31,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(73,a,32,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,33,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,34,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,35,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,36,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,37,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,38,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,39,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,40,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,41,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,42,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,43,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,44,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,45,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,46,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(73,a,47,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,48,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,49,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(73,a,50,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(73,a,51,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,52,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,53,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,54,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,55,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(73,a,56,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(73,a,57,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,58,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(73,a,59,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,61,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(73,a,62,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(73,a,65,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,67,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(73,a,68,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,69,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,70,a)].
% 0.95/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,71,a)].
% 0.95/1.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(73,a,72,a)].
% 0.95/1.41 74 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 0.95/1.41 75 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 0.95/1.41 76 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 0.95/1.41 77 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 0.95/1.41 78 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 0.95/1.41 79 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 0.95/1.41 80 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 0.95/1.41 81 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 0.95/1.41 82 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 0.95/1.41 83 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 0.95/1.41 84 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 0.95/1.41 85 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 0.95/1.41 86 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 0.95/1.41 87 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 0.95/1.41 88 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 0.95/1.41 89 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 0.95/1.41 90 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),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(74,a,75,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),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(74,a,76,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),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(74,a,78,a)].
% 0.95/1.41 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),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). [resolve(74,a,79,a)].
% 0.95/1.41 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),c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat). [resolve(74,a,80,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),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(74,a,81,a)].
% 0.95/1.41 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(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(74,a,82,a)].
% 0.95/1.41 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(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat). [resolve(74,a,83,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),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(74,a,84,a)].
% 0.95/1.41 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(74,a,85,a)].
% 0.95/1.41 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat). [resolve(74,a,86,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,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,tc_nat). [resolve(74,a,87,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),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(74,a,88,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),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(74,a,89,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),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(74,a,90,a)].
% 0.95/1.41 91 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(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(91,a,75,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(91,a,76,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(91,a,78,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(91,a,79,a)].
% 0.95/1.41 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(91,a,80,a)].
% 0.95/1.42 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(91,a,81,a)].
% 0.95/1.42 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(91,a,82,a)].
% 0.95/1.42 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(91,a,83,a)].
% 0.95/1.42 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(91,a,84,a)].
% 0.95/1.42 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(91,a,85,a)].
% 0.95/1.42 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(91,a,89,a)].
% 0.95/1.42 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(91,a,90,a)].
% 0.95/1.42 92 class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(92,a,75,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(92,a,76,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(92,a,78,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(92,a,79,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(92,a,80,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(92,a,81,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(92,a,82,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(92,a,83,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(92,a,84,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(92,a,85,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(92,a,89,a)].
% 0.95/1.42 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(92,a,90,a)].
% 0.95/1.46 93 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 0.95/1.46 94 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D2_0) # label(axiom). [assumption].
% 0.95/1.46 95 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),A) # label(cls_abs__triangle__ineq2_0) # label(axiom). [assumption].
% 0.95/1.46 96 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,B,A),A) # label(cls_abs__minus__commute_0) # label(axiom). [assumption].
% 0.95/1.46 97 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__nonneg_0) # label(axiom). [assumption].
% 0.95/1.46 98 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_0) # label(axiom). [assumption].
% 0.95/1.46 99 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__neg_0) # label(axiom). [assumption].
% 0.95/1.46 100 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(B,C,A) # label(cls_abs__leI_0) # label(axiom). [assumption].
% 0.95/1.46 101 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(B,C,A) # label(cls_abs__le__iff_2) # label(axiom). [assumption].
% 0.95/1.46 102 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__minus__cancel_0) # label(axiom). [assumption].
% 0.95/1.46 103 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_1) # label(axiom). [assumption].
% 0.95/1.46 104 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(B,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__minus__le__zero_0) # label(axiom). [assumption].
% 0.95/1.46 105 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D1_0) # label(axiom). [assumption].
% 0.95/1.46 106 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),A) # label(cls_abs__triangle__ineq3_0) # label(axiom). [assumption].
% 0.95/1.46 107 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_1) # label(axiom). [assumption].
% 0.95/1.46 108 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__triangle__ineq_0) # label(axiom). [assumption].
% 0.95/1.46 109 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,E,A),A),A),A) # label(cls_abs__diff__triangle__ineq_0) # label(axiom). [assumption].
% 0.95/1.46 110 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__idempotent_0) # label(axiom). [assumption].
% 0.95/1.46 111 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(B,A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__abs__iff_1) # label(axiom). [assumption].
% 0.95/1.46 112 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__minus__self_0) # label(axiom). [assumption].
% 0.95/1.46 113 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__self_0) # label(axiom). [assumption].
% 0.95/1.46 114 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__pos_0) # label(axiom). [assumption].
% 0.95/1.46 115 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__nonpos_0) # label(axiom). [assumption].
% 0.95/1.46 116 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__not__less__zero_0) # label(axiom). [assumption].
% 0.95/1.46 117 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__triangle__ineq4_0) # label(axiom). [assumption].
% 0.95/1.46 118 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_0) # label(axiom). [assumption].
% 0.95/1.46 119 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A),A) # label(cls_zero__less__abs__iff_0) # label(axiom). [assumption].
% 0.95/1.46 120 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__zero_0) # label(axiom). [assumption].
% 0.95/1.46 121 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_abs__add__abs_0) # label(axiom). [assumption].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(93,a,94,a)].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,95,a)].
% 0.95/1.46 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,96,a)].
% 0.95/1.46 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(93,a,97,a)].
% 0.95/1.46 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,98,a)].
% 0.95/1.46 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,99,a)].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(93,a,100,a)].
% 0.95/1.46 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal). [resolve(93,a,102,a)].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,103,a)].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,104,a)].
% 0.95/1.46 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(93,a,105,a)].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,106,a)].
% 0.95/1.46 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(93,a,107,a)].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,108,a)].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,109,a)].
% 0.95/1.46 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal). [resolve(93,a,110,a)].
% 0.95/1.46 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(93,a,111,a)].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,112,a)].
% 0.95/1.46 Derived: c_lessequals(A,c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,113,a)].
% 0.95/1.46 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(93,a,114,a)].
% 0.95/1.46 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,115,a)].
% 0.95/1.46 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,116,a)].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,117,a)].
% 0.95/1.46 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(93,a,118,a)].
% 0.95/1.46 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,119,a)].
% 0.95/1.46 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,120,a)].
% 0.95/1.46 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(93,a,121,a)].
% 0.95/1.46 122 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(122,a,94,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,95,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,96,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) = B | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(122,a,97,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,98,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,99,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(122,a,100,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)). [resolve(122,a,102,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,103,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,104,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(122,a,105,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,106,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(122,a,107,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,108,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,109,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)). [resolve(122,a,110,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(122,a,111,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,112,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,113,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) = B | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(122,a,114,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,115,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,116,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,117,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(122,a,118,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,119,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,120,a)].
% 0.95/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(122,a,121,a)].
% 0.95/1.50 123 class_Lattices_Odistrib__lattice(tc_nat) # label(clsarity_nat__Lattices_Odistrib__lattice) # label(axiom). [assumption].
% 0.95/1.50 124 -class_Lattices_Odistrib__lattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__inf__distrib1_0) # label(axiom). [assumption].
% 0.95/1.50 125 -class_Lattices_Odistrib__lattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__inf__distrib2_0) # label(axiom). [assumption].
% 0.95/1.50 126 -class_Lattices_Odistrib__lattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(B,D,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__sup__distrib2_0) # label(axiom). [assumption].
% 0.95/1.50 127 -class_Lattices_Odistrib__lattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__sup__distrib1_0) # label(axiom). [assumption].
% 0.95/1.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat). [resolve(123,a,124,a)].
% 0.95/1.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat). [resolve(123,a,125,a)].
% 0.95/1.50 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(123,a,126,a)].
% 0.95/1.50 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(123,a,127,a)].
% 0.95/1.50 128 class_Lattices_Odistrib__lattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Odistrib__lattice) # label(axiom). [assumption].
% 0.95/1.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(128,a,124,a)].
% 0.95/1.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(128,a,125,a)].
% 0.95/1.50 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(128,a,126,a)].
% 1.34/1.63 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(128,a,127,a)].
% 1.34/1.63 129 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.34/1.63 130 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.34/1.63 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(129,a,130,a)].
% 1.34/1.63 131 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.34/1.63 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(131,a,130,a)].
% 1.34/1.63 132 class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.34/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(132,a,130,a)].
% 1.34/1.63 133 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.34/1.63 134 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 1.34/1.63 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(133,a,134,a)].
% 1.34/1.63 135 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.34/1.63 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(135,a,134,a)].
% 1.34/1.63 136 class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.34/1.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(136,a,134,a)].
% 1.34/1.63 137 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.34/1.63 138 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 1.40/1.71 139 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 1.40/1.71 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(137,a,139,a)].
% 1.40/1.71 140 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.40/1.71 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(140,a,139,a)].
% 1.40/1.71 141 class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.40/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(141,a,139,a)].
% 1.40/1.71 142 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 1.40/1.71 143 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,C,A) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 1.40/1.71 144 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 1.40/1.71 145 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 1.40/1.71 146 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 1.40/1.71 147 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.40/1.71 148 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A) | -c_lessequals(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A),A) # label(cls_le__add__iff2_1) # label(axiom). [assumption].
% 1.40/1.71 149 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,A),E,A),F,A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,A),B,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,A),F,A),A) # label(cls_le__add__iff2_0) # label(axiom). [assumption].
% 1.40/1.71 150 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),F,A) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 1.40/1.71 151 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A),E,A),F,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),E,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,A),F,A),A) # label(cls_le__add__iff1_0) # label(axiom). [assumption].
% 1.40/1.71 152 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A),E,A),F,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),E,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,A),F,A),A) # label(cls_less__add__iff1_0) # label(axiom). [assumption].
% 1.40/1.71 153 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),F,A) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 1.40/1.71 154 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,A),E,A),F,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,A),B,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,A),F,A),A) # label(cls_less__add__iff2_0) # label(axiom). [assumption].
% 1.40/1.71 155 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A),A) # label(cls_less__add__iff2_1) # label(axiom). [assumption].
% 1.40/1.71 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal). [resolve(142,a,143,a)].
% 1.40/1.71 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,A,tc_RealDef_Oreal). [resolve(142,a,144,a)].
% 1.40/1.71 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(142,a,148,a)].
% 1.40/1.71 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(142,a,149,a)].
% 1.40/1.71 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal),B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),E,tc_RealDef_Oreal). [resolve(142,a,150,a)].
% 1.40/1.71 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),E,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(142,a,151,a)].
% 1.40/1.71 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),E,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(142,a,152,a)].
% 1.40/1.71 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal),B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),E,tc_RealDef_Oreal). [resolve(142,a,153,a)].
% 1.40/1.71 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(142,a,154,a)].
% 1.40/1.71 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(142,a,155,a)].
% 1.40/1.71 156 class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 1.40/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)). [resolve(156,a,143,a)].
% 1.40/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,B,tc_Polynomial_Opoly(A)). [resolve(156,a,144,a)].
% 1.40/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(156,a,148,a)].
% 1.40/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(156,a,149,a)].
% 1.40/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)). [resolve(156,a,150,a)].
% 1.40/1.75 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(156,a,151,a)].
% 1.40/1.75 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(156,a,152,a)].
% 1.40/1.75 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)). [resolve(156,a,153,a)].
% 1.40/1.75 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(156,a,154,a)].
% 1.40/1.75 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(156,a,155,a)].
% 1.40/1.75 157 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.40/1.75 158 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_HOL_Ouminus__class_Ouminus(B,A),A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_sup__eq__if_1) # label(axiom). [assumption].
% 1.40/1.75 159 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(C,D,A),A) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,A),c_Orderings_Oord__class_Omax(B,D,A),A) # label(cls_min__max_Osup__inf__distrib1_0) # label(axiom). [assumption].
% 1.40/1.75 160 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,D,A),c_Orderings_Oord__class_Omax(C,D,A),A) # label(cls_min__max_Osup__inf__distrib2_0) # label(axiom). [assumption].
% 1.40/1.75 161 -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].
% 1.40/1.75 162 -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].
% 1.40/1.75 163 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,B,A) = B # label(cls_min__max_Osup__idem_0) # label(axiom). [assumption].
% 1.40/1.75 164 -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].
% 1.40/1.75 165 -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].
% 1.40/1.75 166 -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].
% 1.40/1.75 167 -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].
% 1.40/1.75 168 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,B,A) = B # label(cls_min__max_Oinf__idem_0) # label(axiom). [assumption].
% 1.40/1.75 169 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_0) # label(axiom). [assumption].
% 1.40/1.75 170 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(B,C,A),A) = c_Orderings_Oord__class_Omax(B,C,A) # label(cls_min__max_Osup__left__idem_0) # label(axiom). [assumption].
% 1.40/1.75 171 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(B,C,A),A) = B # label(cls_min__max_Osup__inf__absorb_0) # label(axiom). [assumption].
% 1.40/1.75 172 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,A),c_Orderings_Oord__class_Omin(B,D,A),A),c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(C,D,A),A),A) # label(cls_min__max_Odistrib__inf__le_0) # label(axiom). [assumption].
% 1.40/1.75 173 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = c_Orderings_Oord__class_Omax(C,B,A) # label(cls_min__max_Osup__commute_0) # label(axiom). [assumption].
% 1.40/1.75 174 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Oinf__assoc_0) # label(axiom). [assumption].
% 1.40/1.75 175 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(C,D,A),A) = c_Orderings_Oord__class_Omin(C,c_Orderings_Oord__class_Omin(B,D,A),A) # label(cls_min__max_Oinf__left__commute_0) # label(axiom). [assumption].
% 1.40/1.75 176 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,D,A),c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Oinf__sup__distrib2_0) # label(axiom). [assumption].
% 1.40/1.75 177 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(C,D,A),A) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,A),c_Orderings_Oord__class_Omin(B,D,A),A) # label(cls_min__max_Oinf__sup__distrib1_0) # label(axiom). [assumption].
% 1.40/1.75 178 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__sup__iff_2) # label(axiom). [assumption].
% 1.40/1.75 179 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Osup__least_0) # label(axiom). [assumption].
% 1.40/1.75 180 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__supI_0) # label(axiom). [assumption].
% 1.40/1.75 181 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(B,C,A),A) # label(cls_le__maxI1_0) # label(axiom). [assumption].
% 1.40/1.75 182 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,B,A),A) # label(cls_le__maxI2_0) # label(axiom). [assumption].
% 1.40/1.75 183 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Oinf__greatest_0) # label(axiom). [assumption].
% 1.40/1.75 184 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__inf__iff_2) # label(axiom). [assumption].
% 1.40/1.75 185 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__infI_0) # label(axiom). [assumption].
% 1.40/1.75 186 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),C,A) # label(cls_min__max_Oinf__le2_0) # label(axiom). [assumption].
% 1.40/1.75 187 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),B,A) # label(cls_min__max_Oinf__le1_0) # label(axiom). [assumption].
% 1.40/1.75 188 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_max__less__iff__conj_2) # label(axiom). [assumption].
% 1.40/1.75 189 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__less__iff__conj_2) # label(axiom). [assumption].
% 1.40/1.75 190 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(B,C,A),A) = c_Orderings_Oord__class_Omin(B,C,A) # label(cls_min__max_Oinf__left__idem_0) # label(axiom). [assumption].
% 1.40/1.75 191 -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].
% 1.40/1.75 192 -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].
% 1.40/1.75 193 -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].
% 1.40/1.75 194 -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].
% 1.40/1.75 195 -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].
% 1.40/1.75 196 -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].
% 1.40/1.75 197 -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].
% 1.40/1.75 198 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(B,C,A),A) = B # label(cls_min__max_Oinf__sup__absorb_0) # label(axiom). [assumption].
% 1.40/1.75 199 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_0) # label(axiom). [assumption].
% 1.40/1.75 200 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) != B | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_1) # label(axiom). [assumption].
% 1.40/1.75 201 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_min__max_Oinf__absorb2_0) # label(axiom). [assumption].
% 1.40/1.75 202 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__sup_0) # label(axiom). [assumption].
% 1.40/1.75 203 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) != C | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__sup_1) # label(axiom). [assumption].
% 1.40/1.75 204 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_min__max_Osup__absorb1_0) # label(axiom). [assumption].
% 1.40/1.75 205 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_sup__eq__if_0) # label(axiom). [assumption].
% 1.40/1.75 206 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(B,D,A) | -c_lessequals(B,c_Orderings_Oord__class_Omax(D,C,A),A) # label(cls_le__max__iff__disj_0) # label(axiom). [assumption].
% 1.40/1.75 207 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Ole__infE_0) # label(axiom). [assumption].
% 1.40/1.75 208 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__max_Ole__infE_1) # label(axiom). [assumption].
% 1.40/1.75 209 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__infI1_0) # label(axiom). [assumption].
% 1.40/1.75 210 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_min__max_Ole__infI2_0) # label(axiom). [assumption].
% 1.40/1.75 211 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_min__le__iff__disj_1) # label(axiom). [assumption].
% 1.40/1.75 212 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_min__le__iff__disj_2) # label(axiom). [assumption].
% 1.40/1.75 213 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Ole__inf__iff_0) # label(axiom). [assumption].
% 1.40/1.75 214 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__max_Ole__inf__iff_1) # label(axiom). [assumption].
% 1.40/1.75 215 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(D,C,A) | -c_lessequals(c_Orderings_Oord__class_Omin(D,B,A),C,A) # label(cls_min__le__iff__disj_0) # label(axiom). [assumption].
% 1.40/1.75 216 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_min__max_Ole__supE_0) # label(axiom). [assumption].
% 1.40/1.75 217 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_min__max_Ole__supE_1) # label(axiom). [assumption].
% 1.40/1.75 218 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__supI1_0) # label(axiom). [assumption].
% 1.40/1.75 219 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__supI2_0) # label(axiom). [assumption].
% 1.40/1.75 220 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__max__iff__disj_1) # label(axiom). [assumption].
% 1.40/1.75 221 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__max__iff__disj_2) # label(axiom). [assumption].
% 1.40/1.75 222 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_min__max_Ole__sup__iff_0) # label(axiom). [assumption].
% 1.40/1.75 223 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_min__max_Ole__sup__iff_1) # label(axiom). [assumption].
% 1.40/1.75 224 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(D,C,A),A) # label(cls_less__max__iff__disj_0) # label(axiom). [assumption].
% 1.40/1.75 225 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(D,B,A),C,A) # label(cls_min__less__iff__disj_0) # label(axiom). [assumption].
% 1.40/1.75 226 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_max__less__iff__conj_1) # label(axiom). [assumption].
% 1.40/1.75 227 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_max__less__iff__conj_0) # label(axiom). [assumption].
% 1.40/1.75 228 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__max__iff__disj_2) # label(axiom). [assumption].
% 1.40/1.75 229 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__max__iff__disj_1) # label(axiom). [assumption].
% 1.40/1.75 230 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__supI2_0) # label(axiom). [assumption].
% 1.40/1.75 231 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__max_Oless__supI1_0) # label(axiom). [assumption].
% 1.40/1.75 232 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = c_Orderings_Oord__class_Omin(C,B,A) # label(cls_min__max_Oinf__commute_0) # label(axiom). [assumption].
% 1.40/1.75 233 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__less__iff__disj_2) # label(axiom). [assumption].
% 1.40/1.75 234 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__less__iff__disj_1) # label(axiom). [assumption].
% 1.40/1.75 235 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__less__iff__conj_1) # label(axiom). [assumption].
% 1.40/1.75 236 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__less__iff__conj_0) # label(axiom). [assumption].
% 1.40/1.75 237 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__max_Oless__infI2_0) # label(axiom). [assumption].
% 1.40/1.75 238 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__infI1_0) # label(axiom). [assumption].
% 1.40/1.75 239 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A) = c_Orderings_Oord__class_Omax(C,c_Orderings_Oord__class_Omax(B,D,A),A) # label(cls_min__max_Osup__left__commute_0) # label(axiom). [assumption].
% 1.40/1.75 240 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A) # label(cls_min__max_Osup__assoc_0) # label(axiom). [assumption].
% 1.40/1.75 241 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.40/1.75 242 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_1) # label(axiom). [assumption].
% 1.40/1.75 243 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(C,D,A),A),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,A),c_Orderings_Oord__class_Omax(B,D,A),A),A) # label(cls_min__max_Odistrib__sup__le_0) # label(axiom). [assumption].
% 1.40/1.75 244 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.40/1.76 245 -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].
% 1.40/1.76 Derived: -class_OrderedGroup_Olordered__ab__group__add(tc_nat) | c_Lattices_Oupper__semilattice__class_Osup(A,c_HOL_Ouminus__class_Ouminus(A,tc_nat),tc_nat) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(157,a,158,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_nat),c_Orderings_Oord__class_Omax(A,C,tc_nat),tc_nat). [resolve(157,a,159,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,C,tc_nat),c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat). [resolve(157,a,160,a)].
% 1.40/1.76 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(157,a,161,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,A,tc_nat) = A. [resolve(157,a,163,a)].
% 1.40/1.76 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(157,a,164,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(A,A,tc_nat) = A. [resolve(157,a,168,a)].
% 1.40/1.76 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | c_HOL_Oabs__class_Oabs(A,tc_nat) = c_HOL_Ouminus__class_Ouminus(A,tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(157,a,169,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Oord__class_Omax(A,B,tc_nat). [resolve(157,a,170,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(A,B,tc_nat),tc_nat) = A. [resolve(157,a,171,a)].
% 1.40/1.76 Derived: c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_nat),c_Orderings_Oord__class_Omin(A,C,tc_nat),tc_nat),c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat),tc_nat). [resolve(157,a,172,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) = c_Orderings_Oord__class_Omax(B,A,tc_nat). [resolve(157,a,173,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(157,a,174,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(A,C,tc_nat),tc_nat). [resolve(157,a,175,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,C,tc_nat),c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(157,a,176,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_nat),c_Orderings_Oord__class_Omin(A,C,tc_nat),tc_nat). [resolve(157,a,177,a)].
% 1.40/1.76 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(157,a,178,a)].
% 1.40/1.76 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(A,B,tc_nat),tc_nat). [resolve(157,a,181,a)].
% 1.40/1.76 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,A,tc_nat),tc_nat). [resolve(157,a,182,a)].
% 1.40/1.76 Derived: c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(157,a,183,a)].
% 1.40/1.76 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),B,tc_nat). [resolve(157,a,186,a)].
% 1.40/1.76 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),A,tc_nat). [resolve(157,a,187,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(157,a,188,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(157,a,189,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Oord__class_Omin(A,B,tc_nat). [resolve(157,a,190,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(157,a,191,a)].
% 1.40/1.76 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(157,a,192,a)].
% 1.40/1.76 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(157,a,194,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(A,B,tc_nat),tc_nat) = A. [resolve(157,a,198,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(157,a,199,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(157,a,200,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(157,a,201,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(157,a,202,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(157,a,203,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(157,a,204,a)].
% 1.40/1.76 Derived: -class_OrderedGroup_Olordered__ab__group__add(tc_nat) | c_Lattices_Oupper__semilattice__class_Osup(A,c_HOL_Ouminus__class_Ouminus(A,tc_nat),tc_nat) = c_HOL_Ouminus__class_Ouminus(A,tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(157,a,205,a)].
% 1.40/1.76 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(A,C,tc_nat) | -c_lessequals(A,c_Orderings_Oord__class_Omax(C,B,tc_nat),tc_nat). [resolve(157,a,206,a)].
% 1.40/1.76 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(157,a,207,a)].
% 1.40/1.76 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Orderings_Oord__class_Omin(C,B,tc_nat),tc_nat). [resolve(157,a,208,a)].
% 1.40/1.76 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(157,a,209,a)].
% 1.40/1.76 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(157,a,210,a)].
% 1.40/1.76 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(C,B,tc_nat) | -c_lessequals(c_Orderings_Oord__class_Omin(C,A,tc_nat),B,tc_nat). [resolve(157,a,215,a)].
% 1.40/1.76 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Orderings_Oord__class_Omax(A,C,tc_nat),B,tc_nat). [resolve(157,a,216,a)].
% 1.40/1.76 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Orderings_Oord__class_Omax(C,A,tc_nat),B,tc_nat). [resolve(157,a,217,a)].
% 1.40/1.76 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(157,a,218,a)].
% 1.40/1.76 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(157,a,219,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(C,B,tc_nat),tc_nat). [resolve(157,a,224,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(C,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(C,A,tc_nat),B,tc_nat). [resolve(157,a,225,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(C,A,tc_nat),B,tc_nat). [resolve(157,a,226,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,C,tc_nat),B,tc_nat). [resolve(157,a,227,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(157,a,228,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(157,a,229,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) = c_Orderings_Oord__class_Omin(B,A,tc_nat). [resolve(157,a,232,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(157,a,233,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(157,a,234,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(C,B,tc_nat),tc_nat). [resolve(157,a,235,a)].
% 1.40/1.76 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(157,a,236,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(A,C,tc_nat),tc_nat). [resolve(157,a,239,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat). [resolve(157,a,240,a)].
% 1.40/1.76 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(157,a,241,a)].
% 1.40/1.76 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | c_HOL_Oabs__class_Oabs(A,tc_nat) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(157,a,242,a)].
% 1.40/1.76 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_nat),c_Orderings_Oord__class_Omax(A,C,tc_nat),tc_nat),tc_nat). [resolve(157,a,243,a)].
% 1.40/1.76 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(157,a,244,a)].
% 1.40/1.76 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(157,a,245,a)].
% 1.40/1.76 246 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 1.40/1.76 Derived: -class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) | c_Lattices_Oupper__semilattice__class_Osup(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,158,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,159,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,160,a)].
% 1.40/1.76 Derived: A = B | -c_lessequals(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(246,a,161,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,A,tc_RealDef_Oreal) = A. [resolve(246,a,163,a)].
% 1.40/1.76 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(246,a,164,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(A,A,tc_RealDef_Oreal) = A. [resolve(246,a,168,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal). [resolve(246,a,170,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(246,a,171,a)].
% 1.40/1.76 Derived: c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,172,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(B,A,tc_RealDef_Oreal). [resolve(246,a,173,a)].
% 1.40/1.76 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,174,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,175,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,C,tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,176,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,177,a)].
% 1.40/1.77 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(246,a,178,a)].
% 1.40/1.77 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,181,a)].
% 1.40/1.77 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,182,a)].
% 1.40/1.77 Derived: c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(246,a,183,a)].
% 1.40/1.77 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(246,a,186,a)].
% 1.40/1.77 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(246,a,187,a)].
% 1.40/1.77 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(246,a,188,a)].
% 1.40/1.77 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(246,a,189,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal). [resolve(246,a,190,a)].
% 1.40/1.77 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal). [resolve(246,a,191,a)].
% 1.40/1.77 Derived: -c_lessequals(A,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,A,tc_RealDef_Oreal). [resolve(246,a,192,a)].
% 1.40/1.77 Derived: -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(246,a,194,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(246,a,198,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal) = A | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(246,a,199,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal) != A | c_lessequals(A,B,tc_RealDef_Oreal). [resolve(246,a,200,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal) = B | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(246,a,201,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal) = B | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(246,a,202,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal) != B | c_lessequals(A,B,tc_RealDef_Oreal). [resolve(246,a,203,a)].
% 1.40/1.77 Derived: c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal) = A | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(246,a,204,a)].
% 1.40/1.77 Derived: -class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) | c_Lattices_Oupper__semilattice__class_Osup(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,205,a)].
% 1.40/1.77 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(A,c_Orderings_Oord__class_Omax(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,206,a)].
% 1.50/1.77 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,207,a)].
% 1.50/1.77 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(A,c_Orderings_Oord__class_Omin(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,208,a)].
% 1.50/1.77 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(246,a,209,a)].
% 1.50/1.77 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(246,a,210,a)].
% 1.50/1.77 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(C,B,tc_RealDef_Oreal) | -c_lessequals(c_Orderings_Oord__class_Omin(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(246,a,215,a)].
% 1.50/1.77 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(246,a,216,a)].
% 1.50/1.77 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_Orderings_Oord__class_Omax(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(246,a,217,a)].
% 1.50/1.77 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(246,a,218,a)].
% 1.50/1.77 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(246,a,219,a)].
% 1.50/1.77 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,224,a)].
% 1.50/1.77 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(246,a,225,a)].
% 1.50/1.77 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(246,a,226,a)].
% 1.50/1.77 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(246,a,227,a)].
% 1.50/1.77 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(246,a,228,a)].
% 1.50/1.77 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(246,a,229,a)].
% 1.50/1.77 Derived: c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(B,A,tc_RealDef_Oreal). [resolve(246,a,232,a)].
% 1.50/1.77 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(246,a,233,a)].
% 1.50/1.77 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(246,a,234,a)].
% 1.50/1.77 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,235,a)].
% 1.50/1.77 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,236,a)].
% 1.50/1.77 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,239,a)].
% 1.50/1.77 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,240,a)].
% 1.50/1.77 Derived: -c_HOL_Oord__class_Oless(A,A,tc_RealDef_Oreal). [resolve(246,a,241,a)].
% 1.50/1.77 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,242,a)].
% 1.50/1.77 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),c_Orderings_Oord__class_Omax(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(246,a,243,a)].
% 1.50/1.77 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal). [resolve(246,a,244,a)].
% 1.50/1.77 Derived: -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(246,a,245,a)].
% 1.50/1.77 247 class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [assumption].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Olordered__ab__group__add(tc_Polynomial_Opoly(A)) | c_Lattices_Oupper__semilattice__class_Osup(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,158,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),c_Orderings_Oord__class_Omax(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,159,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,D,tc_Polynomial_Opoly(A)),c_Orderings_Oord__class_Omax(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,160,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = C | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,161,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(B,B,tc_Polynomial_Opoly(A)) = B. [resolve(247,a,163,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = C | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,164,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(B,B,tc_Polynomial_Opoly(A)) = B. [resolve(247,a,168,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,170,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(247,a,171,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),c_Orderings_Oord__class_Omin(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,172,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omax(C,B,tc_Polynomial_Opoly(A)). [resolve(247,a,173,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,174,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omin(C,c_Orderings_Oord__class_Omin(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,175,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,D,tc_Polynomial_Opoly(A)),c_Orderings_Oord__class_Omin(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,176,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),c_Orderings_Oord__class_Omin(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,177,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(247,a,178,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,181,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,182,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,183,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(247,a,186,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(247,a,187,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(247,a,188,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,189,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,190,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(247,a,191,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,B,tc_Polynomial_Opoly(A)). [resolve(247,a,192,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(247,a,194,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(247,a,198,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)) = B | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,199,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)) != B | c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,200,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)) = C | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(247,a,201,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)) = C | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,202,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)) != C | c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,203,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)) = B | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(247,a,204,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Olordered__ab__group__add(tc_Polynomial_Opoly(A)) | c_Lattices_Oupper__semilattice__class_Osup(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,205,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_Orderings_Oord__class_Omax(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,206,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,207,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_Orderings_Oord__class_Omin(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,208,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(247,a,209,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(247,a,210,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(D,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_Orderings_Oord__class_Omin(D,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(247,a,215,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_Orderings_Oord__class_Omax(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(247,a,216,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_Orderings_Oord__class_Omax(D,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(247,a,217,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,218,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(247,a,219,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,224,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(D,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(247,a,225,a)].
% 1.50/1.78 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(D,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(247,a,226,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(247,a,227,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(247,a,228,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(247,a,229,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omin(C,B,tc_Polynomial_Opoly(A)). [resolve(247,a,232,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)). [resolve(247,a,233,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(247,a,234,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,235,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,236,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omax(C,c_Orderings_Oord__class_Omax(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,239,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,240,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,B,tc_Polynomial_Opoly(A)). [resolve(247,a,241,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(tc_Polynomial_Opoly(A)) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,242,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),c_Orderings_Oord__class_Omax(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(247,a,243,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(247,a,244,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)). [resolve(247,a,245,a)].
% 1.56/1.83 248 class_Int_Onumber__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Int_Onumber__ring) # label(axiom). [assumption].
% 1.56/1.83 249 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A) != c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,E,A),A) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 1.56/1.83 250 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 1.56/1.83 251 -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,C,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_class__ring_Osub__add_0) # label(axiom). [assumption].
% 1.56/1.83 252 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 1.56/1.83 253 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 1.56/1.83 254 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 1.56/1.83 255 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 1.56/1.83 256 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != c_HOL_Oplus__class_Oplus(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 1.56/1.83 257 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 1.56/1.83 258 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 1.56/1.83 259 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | C = D | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(248,a,249,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Ominus__class_Ominus(A,A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(248,a,250,b)].
% 1.56/1.83 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(248,a,251,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(248,a,252,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | B = D | A = C. [resolve(248,a,253,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal) | B = C. [resolve(248,a,255,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | A != c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(248,a,256,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(248,a,257,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(248,a,259,b)].
% 1.56/1.83 260 class_Int_Onumber__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Onumber__ring) # label(axiom). [assumption].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(260,a,249,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(260,a,250,b)].
% 1.56/1.83 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(260,a,251,a)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(260,a,252,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = D | A = C. [resolve(260,a,253,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C. [resolve(260,a,255,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(260,a,256,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(260,a,257,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(260,a,259,b)].
% 1.56/1.83 261 class_Int_Onumber__ring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring__1(A) # label(clsarity_Polynomial__Opoly__Int_Onumber__ring) # label(axiom). [assumption].
% 1.56/1.83 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | D = E | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(261,a,249,b)].
% 1.56/1.83 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Ominus__class_Ominus(B,B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(261,a,250,b)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(261,a,251,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = C. [resolve(261,a,252,b)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = E | B = D. [resolve(261,a,253,b)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)) | C = D. [resolve(261,a,255,b)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | B != c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(261,a,256,b)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(261,a,257,b)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | B = c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(261,a,259,b)].
% 1.56/1.88 262 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) # label(axiom). [assumption].
% 1.56/1.88 263 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,D,A),C,A) # label(cls_divide__less__eq_0) # label(axiom). [assumption].
% 1.56/1.88 264 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_divide__less__eq_6) # label(axiom). [assumption].
% 1.56/1.88 265 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(D,C,A),A) # label(cls_less__divide__eq_0) # label(axiom). [assumption].
% 1.56/1.88 266 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_less__divide__eq_6) # label(axiom). [assumption].
% 1.56/1.88 267 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__imp__div__pos__less_0) # label(axiom). [assumption].
% 1.56/1.88 268 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__imp__less__div__pos_0) # label(axiom). [assumption].
% 1.56/1.88 269 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_zero__less__divide__iff_0) # label(axiom). [assumption].
% 1.56/1.88 270 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(C,B,A),A) # label(cls_zero__less__divide__iff_1) # label(axiom). [assumption].
% 1.56/1.88 271 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_zero__less__divide__iff_2) # label(axiom). [assumption].
% 1.56/1.88 272 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(C,B,A),A) # label(cls_zero__less__divide__iff_3) # label(axiom). [assumption].
% 1.56/1.88 273 -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide__nonneg__neg_0) # label(axiom). [assumption].
% 1.56/1.88 274 -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__nonpos__pos_0) # label(axiom). [assumption].
% 1.56/1.88 275 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_divide__right__mono_0) # label(axiom). [assumption].
% 1.56/1.88 276 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_divide__right__mono__neg_0) # label(axiom). [assumption].
% 1.56/1.88 277 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) | -c_lessequals(E,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),E,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_frac__less_0) # label(axiom). [assumption].
% 1.56/1.88 278 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),C,A) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_abs__div__pos_0) # label(axiom). [assumption].
% 1.56/1.88 279 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_le__divide__eq_8) # label(axiom). [assumption].
% 1.56/1.88 280 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),B,A) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_divide__le__eq_8) # label(axiom). [assumption].
% 1.56/1.88 281 -class_Ring__and__Field_Oordered__field(A) | c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__imp__le__div__pos_0) # label(axiom). [assumption].
% 1.56/1.88 282 -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__imp__div__pos__le_0) # label(axiom). [assumption].
% 1.56/1.88 283 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_le__divide__eq_6) # label(axiom). [assumption].
% 1.56/1.88 284 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,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),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(D,C,A),B,A) # label(cls_divide__less__eq_2) # label(axiom). [assumption].
% 1.56/1.88 285 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,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),C,A) # label(cls_divide__less__eq_3) # label(axiom). [assumption].
% 1.56/1.88 286 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_divide__less__eq_8) # label(axiom). [assumption].
% 1.56/1.88 287 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_divide__less__eq_9) # label(axiom). [assumption].
% 1.56/1.88 288 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,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),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(D,C,A),A) # label(cls_less__divide__eq_2) # label(axiom). [assumption].
% 1.56/1.88 289 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_less__divide__eq_3) # label(axiom). [assumption].
% 1.56/1.88 290 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_less__divide__eq_8) # label(axiom). [assumption].
% 1.56/1.88 291 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_less__divide__eq_9) # label(axiom). [assumption].
% 1.56/1.88 292 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__neg__neg_0) # label(axiom). [assumption].
% 1.56/1.88 293 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide__pos__pos_0) # label(axiom). [assumption].
% 1.56/1.88 294 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__divide__iff_4) # label(axiom). [assumption].
% 1.56/1.88 295 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__less__divide__iff_5) # label(axiom). [assumption].
% 1.56/1.88 296 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_divide__strict__right__mono_0) # label(axiom). [assumption].
% 1.56/1.88 297 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_divide__strict__right__mono__neg_0) # label(axiom). [assumption].
% 1.56/1.88 298 -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide__nonneg__pos_0) # label(axiom). [assumption].
% 1.56/1.88 299 -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__nonpos__neg_0) # label(axiom). [assumption].
% 1.56/1.88 300 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),B,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_divide__le__eq_5) # label(axiom). [assumption].
% 1.56/1.88 301 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_divide__le__eq_7) # label(axiom). [assumption].
% 1.56/1.88 302 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Otimes__class_Otimes(B,D,A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_le__divide__eq_5) # label(axiom). [assumption].
% 1.56/1.88 303 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_le__divide__eq_7) # label(axiom). [assumption].
% 1.56/1.88 304 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Oinverse__class_Odivide(D,C,A),A) # label(cls_le__divide__eq_0) # label(axiom). [assumption].
% 1.56/1.88 305 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_divide__le__eq_6) # label(axiom). [assumption].
% 1.56/1.88 306 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(B,D,A),C,A) # label(cls_divide__le__eq_0) # label(axiom). [assumption].
% 1.56/1.88 307 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_5) # label(axiom). [assumption].
% 1.56/1.88 308 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide__le__0__iff_4) # label(axiom). [assumption].
% 1.56/1.88 309 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,D,A) # label(cls_divide__left__mono__neg_0) # label(axiom). [assumption].
% 1.56/1.88 310 -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(D,C,A) # label(cls_divide__left__mono_0) # label(axiom). [assumption].
% 1.56/1.88 311 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) | -c_HOL_Oord__class_Oless(E,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),E,A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_frac__less2_0) # label(axiom). [assumption].
% 1.56/1.88 312 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(C,B,A),A) # label(cls_zero__le__divide__iff_3) # label(axiom). [assumption].
% 1.56/1.88 313 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_zero__le__divide__iff_2) # label(axiom). [assumption].
% 1.56/1.88 314 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(C,B,A),A) # label(cls_zero__le__divide__iff_1) # label(axiom). [assumption].
% 1.56/1.88 315 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_zero__le__divide__iff_0) # label(axiom). [assumption].
% 1.56/1.88 316 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__abs__divide_0) # label(axiom). [assumption].
% 1.56/1.88 317 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_0) # label(axiom). [assumption].
% 1.56/1.88 318 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_1) # label(axiom). [assumption].
% 1.56/1.88 319 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_2) # label(axiom). [assumption].
% 1.56/1.88 320 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__le__0__iff_3) # label(axiom). [assumption].
% 1.56/1.88 321 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),D,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),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(D,C,A),B,A) # label(cls_divide__less__eq_1) # label(axiom). [assumption].
% 1.56/1.88 322 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),B,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_divide__less__eq_4) # label(axiom). [assumption].
% 1.56/1.88 323 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),B,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_divide__less__eq_5) # label(axiom). [assumption].
% 1.56/1.88 324 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_divide__less__eq_7) # label(axiom). [assumption].
% 1.56/1.88 325 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Oinverse__class_Odivide(B,D,A),A) # label(cls_less__divide__eq_1) # label(axiom). [assumption].
% 1.56/1.88 326 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Otimes__class_Otimes(B,D,A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_less__divide__eq_4) # label(axiom). [assumption].
% 1.56/1.88 327 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Otimes__class_Otimes(B,D,A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_less__divide__eq_5) # label(axiom). [assumption].
% 1.56/1.88 328 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_less__divide__eq_7) # label(axiom). [assumption].
% 1.56/1.88 329 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_abs__divide_0) # label(axiom). [assumption].
% 1.56/1.88 330 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__iff_3) # label(axiom). [assumption].
% 1.56/1.88 331 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,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_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__iff_2) # label(axiom). [assumption].
% 1.56/1.88 332 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__iff_1) # label(axiom). [assumption].
% 1.56/1.88 333 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__iff_0) # label(axiom). [assumption].
% 1.56/1.88 334 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_le__divide__eq_9) # label(axiom). [assumption].
% 1.56/1.88 335 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_le__divide__eq_3) # label(axiom). [assumption].
% 1.56/1.88 336 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Oinverse__class_Odivide(D,C,A),A) # label(cls_le__divide__eq_2) # label(axiom). [assumption].
% 1.56/1.88 337 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),B,A) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_divide__le__eq_9) # label(axiom). [assumption].
% 1.56/1.88 338 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_divide__le__eq_3) # label(axiom). [assumption].
% 1.56/1.88 339 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(D,C,A),B,A) # label(cls_divide__le__eq_2) # label(axiom). [assumption].
% 1.56/1.88 340 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__divide__iff_4) # label(axiom). [assumption].
% 1.56/1.88 341 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__divide__iff_5) # label(axiom). [assumption].
% 1.56/1.88 342 -class_Ring__and__Field_Oordered__field(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) | -c_lessequals(E,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),E,A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_frac__le_0) # label(axiom). [assumption].
% 1.56/1.88 343 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_divide__strict__left__mono_0) # label(axiom). [assumption].
% 1.56/1.88 344 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_divide__strict__left__mono__neg_0) # label(axiom). [assumption].
% 1.56/1.88 345 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),D,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),C,A) | -c_lessequals(c_HOL_Oinverse__class_Odivide(D,C,A),B,A) # label(cls_divide__le__eq_1) # label(axiom). [assumption].
% 1.56/1.88 346 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),B,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_divide__le__eq_4) # label(axiom). [assumption].
% 1.56/1.88 347 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,c_HOL_Oinverse__class_Odivide(B,D,A),A) # label(cls_le__divide__eq_1) # label(axiom). [assumption].
% 1.56/1.88 348 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Otimes__class_Otimes(B,D,A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_le__divide__eq_4) # label(axiom). [assumption].
% 1.56/1.88 349 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__neg__pos_0) # label(axiom). [assumption].
% 1.56/1.88 350 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide__pos__neg_0) # label(axiom). [assumption].
% 1.56/1.88 351 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide__less__0__iff_4) # label(axiom). [assumption].
% 1.56/1.88 352 -class_Ring__and__Field_Oordered__field(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__iff_5) # label(axiom). [assumption].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,263,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,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_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,264,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,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_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,265,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,266,a)].
% 1.56/1.88 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,267,a)].
% 1.56/1.88 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,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(262,a,268,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,269,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,270,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,271,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,272,a)].
% 1.56/1.88 Derived: c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,273,a)].
% 1.56/1.88 Derived: c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),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_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,274,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(262,a,275,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,A,tc_RealDef_Oreal). [resolve(262,a,276,a)].
% 1.56/1.88 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(D,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,277,a)].
% 1.56/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,278,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,279,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,280,a)].
% 1.56/1.89 Derived: c_lessequals(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,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(262,a,281,a)].
% 1.56/1.89 Derived: c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,282,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(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_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(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,284,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,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,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,285,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(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_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,288,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(262,a,289,a)].
% 1.56/1.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,292,a)].
% 1.56/1.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,293,a)].
% 1.56/1.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(262,a,296,a)].
% 1.56/1.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,A,tc_RealDef_Oreal). [resolve(262,a,297,a)].
% 1.56/1.89 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,298,a)].
% 1.56/1.89 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,299,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,300,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,301,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(262,a,302,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,303,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,304,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,306,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,307,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,308,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(262,a,309,a)].
% 1.56/1.89 Derived: c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal). [resolve(262,a,310,a)].
% 1.56/1.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(D,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,311,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,313,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,314,a)].
% 1.56/1.89 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(262,a,316,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,318,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,319,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,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),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,321,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,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_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,322,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,323,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,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,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,324,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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,c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,325,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(262,a,326,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(262,a,327,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,328,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,329,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(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(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,330,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,331,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,332,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,333,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,334,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(262,a,335,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_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),B,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,336,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,337,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | c_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),B,tc_RealDef_Oreal). [resolve(262,a,338,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_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),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,339,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,340,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,341,a)].
% 1.56/1.89 Derived: c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(D,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,342,a)].
% 1.56/1.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal). [resolve(262,a,343,a)].
% 1.56/1.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(262,a,344,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,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),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,345,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(262,a,346,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(262,a,347,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(262,a,348,a)].
% 1.56/1.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),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(262,a,349,a)].
% 1.63/1.94 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(262,a,350,a)].
% 1.63/1.94 353 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.63/1.94 354 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 1.63/1.94 355 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 1.63/1.94 356 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 1.63/1.94 357 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 1.63/1.94 358 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 1.63/1.94 359 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 1.63/1.94 360 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 1.63/1.94 361 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 1.63/1.94 362 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 1.63/1.94 363 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 1.63/1.94 364 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 1.63/1.94 365 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 1.63/1.94 366 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 1.63/1.94 367 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.63/1.94 368 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 1.63/1.94 369 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 1.63/1.94 370 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 1.63/1.94 371 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 1.63/1.94 372 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 1.63/1.94 373 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 1.63/1.94 374 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 1.63/1.94 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),B,tc_nat). [resolve(353,a,354,a)].
% 1.63/1.94 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),B,tc_nat). [resolve(353,a,355,a)].
% 1.63/1.94 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(353,a,356,a)].
% 1.63/1.94 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(353,a,357,a)].
% 1.63/1.94 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(353,a,360,a)].
% 1.63/1.94 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(353,a,361,a)].
% 1.63/1.94 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(353,a,362,a)].
% 1.63/1.94 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(353,a,363,a)].
% 1.63/1.94 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(353,a,364,a)].
% 1.63/1.94 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(353,a,367,a)].
% 1.63/1.94 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat). [resolve(353,a,368,a)].
% 1.63/1.94 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat). [resolve(353,a,369,a)].
% 1.63/1.94 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(353,a,370,a)].
% 1.63/1.94 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat). [resolve(353,a,371,a)].
% 1.63/1.94 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(353,a,372,a)].
% 1.63/1.94 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(353,a,373,a)].
% 1.63/1.94 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(353,a,374,a)].
% 1.63/1.94 375 class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.63/1.94 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(375,a,354,a)].
% 1.63/1.94 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(375,a,355,a)].
% 1.63/1.94 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(375,a,356,a)].
% 1.63/1.94 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(375,a,357,a)].
% 1.70/2.03 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(375,a,360,a)].
% 1.70/2.03 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(375,a,361,a)].
% 1.70/2.03 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(375,a,362,a)].
% 1.70/2.03 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(375,a,363,a)].
% 1.70/2.03 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(375,a,364,a)].
% 1.70/2.03 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_RealDef_Oreal) = A. [resolve(375,a,367,a)].
% 1.70/2.03 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(375,a,368,a)].
% 1.70/2.03 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(375,a,369,a)].
% 1.70/2.03 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_RealDef_Oreal). [resolve(375,a,370,a)].
% 1.70/2.03 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal). [resolve(375,a,371,a)].
% 1.70/2.03 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = B | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(375,a,372,a)].
% 1.70/2.03 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) != B | c_lessequals(A,B,tc_RealDef_Oreal). [resolve(375,a,373,a)].
% 1.70/2.03 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal) = A | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(375,a,374,a)].
% 1.70/2.03 376 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.70/2.03 377 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,E,A) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 1.70/2.03 378 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_HOL_Oord__class_Oless(D,E,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 1.70/2.03 379 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(C,B,A) | -c_lessequals(E,D,A) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 1.70/2.03 380 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(E,D,A) | -c_lessequals(C,B,A) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 1.70/2.03 381 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__le__0__iff__le_1) # label(axiom). [assumption].
% 1.70/2.03 382 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__le__0__iff__le_0) # label(axiom). [assumption].
% 1.70/2.03 383 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_neg__less__iff__less_1) # label(axiom). [assumption].
% 1.70/2.03 384 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__less__iff__less_0) # label(axiom). [assumption].
% 1.70/2.03 385 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__0__le__iff__le_0) # label(axiom). [assumption].
% 1.70/2.03 386 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__le__iff__le_1) # label(axiom). [assumption].
% 1.70/2.03 387 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__le__iff__le_0) # label(axiom). [assumption].
% 1.70/2.03 388 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,B,A) # label(cls_le__imp__neg__le_0) # label(axiom). [assumption].
% 1.70/2.03 389 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),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].
% 1.70/2.03 390 -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(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__less__0__iff__less_0) # label(axiom). [assumption].
% 1.70/2.03 391 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,D,A),A) # label(cls_max__diff__distrib__left_0) # label(axiom). [assumption].
% 1.70/2.03 392 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,D,A),A) # label(cls_min__diff__distrib__left_0) # label(axiom). [assumption].
% 1.70/2.03 393 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__less__iff_1) # label(axiom). [assumption].
% 1.70/2.03 394 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__less__iff_0) # label(axiom). [assumption].
% 1.70/2.03 395 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__minus__iff_1) # label(axiom). [assumption].
% 1.70/2.03 396 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__minus__iff_0) # label(axiom). [assumption].
% 1.70/2.03 397 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__le__iff_1) # label(axiom). [assumption].
% 1.70/2.03 398 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__le__iff_0) # label(axiom). [assumption].
% 1.70/2.03 399 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__iff_1) # label(axiom). [assumption].
% 1.70/2.03 400 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__iff_0) # label(axiom). [assumption].
% 1.70/2.03 401 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,C,A) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 1.70/2.03 402 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 1.70/2.03 403 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 1.70/2.03 404 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 1.70/2.03 405 -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),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__0__less__iff__less_0) # label(axiom). [assumption].
% 1.70/2.03 406 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),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].
% 1.70/2.03 407 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(E,D,A) | -c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 1.70/2.03 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,D,tc_RealDef_Oreal). [resolve(376,a,377,a)].
% 1.70/2.03 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(C,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(376,a,378,a)].
% 1.70/2.03 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal) | -c_lessequals(D,C,tc_RealDef_Oreal). [resolve(376,a,379,a)].
% 1.70/2.03 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ominus__class_Ominus(C,D,tc_RealDef_Oreal) | c_lessequals(D,C,tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(376,a,380,a)].
% 1.70/2.03 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(376,a,381,a)].
% 1.70/2.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,382,a)].
% 1.70/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(376,a,383,a)].
% 1.70/2.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,384,a)].
% 1.70/2.03 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,385,a)].
% 1.70/2.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,386,a)].
% 1.70/2.03 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,387,a)].
% 1.70/2.03 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(376,a,388,a)].
% 1.70/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),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(376,a,389,a)].
% 1.70/2.03 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_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,390,a)].
% 1.70/2.03 Derived: c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,391,a)].
% 1.70/2.03 Derived: c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,392,a)].
% 1.70/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(376,a,393,a)].
% 1.70/2.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,395,a)].
% 1.70/2.03 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(376,a,397,a)].
% 1.70/2.03 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,399,a)].
% 1.70/2.03 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(376,a,401,a)].
% 1.70/2.03 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,402,a)].
% 1.70/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(376,a,403,a)].
% 1.70/2.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,404,a)].
% 1.70/2.03 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),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,405,a)].
% 1.70/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,406,a)].
% 1.70/2.03 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(D,C,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Oplus__class_Oplus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(376,a,407,a)].
% 1.70/2.04 408 class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ominus__class_Ominus(D,E,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,E,tc_Polynomial_Opoly(A)). [resolve(408,a,377,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ominus__class_Ominus(D,E,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(D,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(408,a,378,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ominus__class_Ominus(D,E,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)) | -c_lessequals(E,D,tc_Polynomial_Opoly(A)). [resolve(408,a,379,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ominus__class_Ominus(D,E,tc_Polynomial_Opoly(A)) | c_lessequals(E,D,tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(408,a,380,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(408,a,381,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,382,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)). [resolve(408,a,383,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,384,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,385,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,386,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,387,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(408,a,388,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(408,a,389,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,390,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Ominus__class_Ominus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,391,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Ominus__class_Ominus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,392,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(408,a,393,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,395,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(408,a,397,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,399,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(408,a,401,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,402,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(408,a,403,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,404,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,405,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,406,a)].
% 1.70/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(E,D,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(408,a,407,a)].
% 1.80/2.07 409 class_Ring__and__Field_Odvd(tc_nat) # label(clsarity_nat__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 1.80/2.07 410 -class_Ring__and__Field_Odvd(A) | -class_Ring__and__Field_Ocomm__ring(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(C,c_HOL_Otimes__class_Otimes(D,E,A),A),F,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(C,F,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,E,A) # label(cls_inf__period_I4_J_0) # label(axiom). [assumption].
% 1.80/2.07 411 -class_Ring__and__Field_Odvd(A) | -class_Ring__and__Field_Ocomm__ring(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(C,c_HOL_Otimes__class_Otimes(E,F,A),A),D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,F,A) # label(cls_inf__period_I4_J_1) # label(axiom). [assumption].
% 1.80/2.07 412 -class_Ring__and__Field_Odvd(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_dvdI_0) # label(axiom). [assumption].
% 1.80/2.07 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat),E,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,E,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_nat). [resolve(409,a,410,a)].
% 1.80/2.07 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,c_HOL_Otimes__class_Otimes(D,E,tc_nat),tc_nat),C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_nat). [resolve(409,a,411,a)].
% 1.80/2.07 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). [resolve(409,a,412,a)].
% 1.80/2.07 413 class_Ring__and__Field_Odvd(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 1.80/2.07 Derived: -class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_RealDef_Oreal). [resolve(413,a,410,a)].
% 1.80/2.07 Derived: -class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,c_HOL_Otimes__class_Otimes(D,E,tc_RealDef_Oreal),tc_RealDef_Oreal),C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_RealDef_Oreal). [resolve(413,a,411,a)].
% 1.80/2.07 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(413,a,412,a)].
% 1.80/2.07 414 class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 1.80/2.07 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),E,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,E,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_Complex_Ocomplex). [resolve(414,a,410,a)].
% 1.80/2.07 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,c_HOL_Otimes__class_Otimes(D,E,tc_Complex_Ocomplex),tc_Complex_Ocomplex),C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_Complex_Ocomplex). [resolve(414,a,411,a)].
% 1.82/2.10 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(414,a,412,a)].
% 1.82/2.10 415 class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 1.82/2.10 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(A)) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(C,c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(C,F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,E,tc_Polynomial_Opoly(A)). [resolve(415,a,410,a)].
% 1.82/2.10 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(A)) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(C,c_HOL_Otimes__class_Otimes(E,F,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,F,tc_Polynomial_Opoly(A)). [resolve(415,a,411,a)].
% 1.82/2.10 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(415,a,412,a)].
% 1.82/2.10 416 class_Orderings_Oorder(tc_nat) # label(clsarity_nat__Orderings_Oorder) # label(axiom). [assumption].
% 1.82/2.10 417 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | B = C | -c_lessequals(B,C,A) # label(cls_order__less__le_2) # label(axiom). [assumption].
% 1.82/2.10 418 -class_Orderings_Oorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_order__le__less_0) # label(axiom). [assumption].
% 1.82/2.10 419 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | B = C | -c_lessequals(B,C,A) # label(cls_order__le__neq__trans_0) # label(axiom). [assumption].
% 1.82/2.10 420 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) | B = C # label(cls_order__neq__le__trans_0) # label(axiom). [assumption].
% 1.82/2.10 421 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) | C = B # label(cls_xt1_I12_J_0) # label(axiom). [assumption].
% 1.82/2.10 422 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | -c_lessequals(B,C,A) # label(cls_xt1_I11_J_0) # label(axiom). [assumption].
% 1.82/2.10 423 -class_Orderings_Oorder(A) | B = C | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) # label(cls_order__antisym__conv_0) # label(axiom). [assumption].
% 1.82/2.10 424 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__eq__iff_2) # label(axiom). [assumption].
% 1.82/2.10 425 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__antisym_0) # label(axiom). [assumption].
% 1.82/2.10 426 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_xt1_I10_J_0) # label(axiom). [assumption].
% 1.82/2.10 427 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__le_1) # label(axiom). [assumption].
% 1.82/2.10 428 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_order__le__less_1) # label(axiom). [assumption].
% 1.82/2.10 429 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__iff_0) # label(axiom). [assumption].
% 1.82/2.11 430 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I8_J_0) # label(axiom). [assumption].
% 1.82/2.11 431 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_xt1_I7_J_0) # label(axiom). [assumption].
% 1.82/2.11 432 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I6_J_0) # label(axiom). [assumption].
% 1.82/2.11 433 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_xt1_I9_J_0) # label(axiom). [assumption].
% 1.82/2.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,B,tc_nat) | B = A. [resolve(416,a,421,a)].
% 1.82/2.11 Derived: A = B | -c_lessequals(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(416,a,423,a)].
% 1.82/2.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(416,a,426,a)].
% 1.82/2.11 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(416,a,428,a)].
% 1.82/2.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(416,a,430,a)].
% 1.82/2.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(416,a,431,a)].
% 1.82/2.11 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(416,a,432,a)].
% 1.82/2.11 434 class_Orderings_Oorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Oorder) # label(axiom). [assumption].
% 1.82/2.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal) | B = A. [resolve(434,a,421,a)].
% 1.82/2.11 Derived: A = B | -c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(434,a,423,a)].
% 1.82/2.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal). [resolve(434,a,426,a)].
% 1.82/2.11 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(434,a,428,a)].
% 1.82/2.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal). [resolve(434,a,430,a)].
% 1.82/2.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal). [resolve(434,a,431,a)].
% 1.82/2.11 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal). [resolve(434,a,432,a)].
% 1.82/2.11 435 class_Orderings_Oorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Oorder) # label(axiom). [assumption].
% 1.82/2.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | C = B. [resolve(435,a,421,a)].
% 1.82/2.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = C | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(435,a,423,a)].
% 1.82/2.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)). [resolve(435,a,426,a)].
% 1.82/2.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(435,a,428,a)].
% 1.82/2.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)). [resolve(435,a,430,a)].
% 1.82/2.11 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)). [resolve(435,a,431,a)].
% 1.88/2.17 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)). [resolve(435,a,432,a)].
% 1.88/2.17 436 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.88/2.17 437 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.88/2.17 438 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 1.88/2.17 439 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 1.88/2.17 440 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 1.88/2.17 441 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 1.88/2.17 442 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 1.88/2.17 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),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(436,a,437,a)].
% 1.88/2.17 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),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(436,a,438,a)].
% 1.88/2.17 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),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(436,a,439,a)].
% 1.88/2.17 443 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.88/2.17 444 class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.88/2.17 445 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.88/2.17 446 -class_OrderedGroup_Oab__semigroup__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 1.88/2.17 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(445,a,446,a)].
% 1.88/2.17 447 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.88/2.20 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(447,a,446,a)].
% 1.88/2.20 448 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.88/2.20 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(448,a,446,a)].
% 1.88/2.20 449 class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.88/2.20 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(449,a,446,a)].
% 1.88/2.20 450 class_Lattices_Olattice(tc_nat) # label(clsarity_nat__Lattices_Olattice) # label(axiom). [assumption].
% 1.88/2.20 451 -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__sup__ord_I2_J_0) # label(axiom). [assumption].
% 1.88/2.20 452 -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__sup__ord_I1_J_0) # label(axiom). [assumption].
% 1.88/2.20 453 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = B # label(cls_inf__sup__absorb_0) # label(axiom). [assumption].
% 1.88/2.20 454 -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A),A) # label(cls_distrib__sup__le_0) # label(axiom). [assumption].
% 1.88/2.20 455 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__sup__aci_I3_J_0) # label(axiom). [assumption].
% 1.88/2.20 456 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__sup__aci_I2_J_0) # label(axiom). [assumption].
% 1.88/2.20 457 -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A),c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A),A) # label(cls_distrib__inf__le_0) # label(axiom). [assumption].
% 1.88/2.20 458 -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_inf__sup__ord_I3_J_0) # label(axiom). [assumption].
% 1.88/2.20 459 -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_inf__sup__ord_I4_J_0) # label(axiom). [assumption].
% 1.88/2.20 460 -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_inf__sup__aci_I7_J_0) # label(axiom). [assumption].
% 1.88/2.20 461 -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_inf__sup__aci_I6_J_0) # label(axiom). [assumption].
% 1.88/2.20 462 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__sup__aci_I1_J_0) # label(axiom). [assumption].
% 1.96/2.23 463 -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_inf__sup__aci_I5_J_0) # label(axiom). [assumption].
% 1.96/2.23 464 -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_inf__sup__aci_I8_J_0) # label(axiom). [assumption].
% 1.96/2.23 465 -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = B # label(cls_sup__inf__absorb_0) # label(axiom). [assumption].
% 1.96/2.23 466 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__sup__aci_I4_J_0) # label(axiom). [assumption].
% 1.96/2.23 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = A. [resolve(450,a,453,a)].
% 1.96/2.23 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat),tc_nat). [resolve(450,a,454,a)].
% 1.96/2.23 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat),tc_nat). [resolve(450,a,457,a)].
% 1.96/2.23 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = A. [resolve(450,a,465,a)].
% 1.96/2.23 467 class_Lattices_Olattice(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Lattices_Olattice) # label(axiom). [assumption].
% 1.96/2.23 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(467,a,453,a)].
% 1.96/2.23 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(467,a,454,a)].
% 1.96/2.23 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(467,a,457,a)].
% 1.96/2.23 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(467,a,465,a)].
% 1.96/2.23 468 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.96/2.23 469 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 1.96/2.23 470 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 1.96/2.23 471 -class_Ring__and__Field_Oring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Otimes__class_Otimes(B,C,A) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 1.96/2.23 472 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,B,A),C,A),E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A) # label(cls_eq__add__iff2_1) # label(axiom). [assumption].
% 1.96/2.23 473 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),A) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 1.96/2.23 474 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 1.96/2.23 475 -class_Ring__and__Field_Oring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A) | D = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 1.96/2.23 476 -class_Ring__and__Field_Oring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 1.96/2.23 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(468,a,469,a)].
% 1.96/2.23 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(468,a,470,a)].
% 1.96/2.23 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal). [resolve(468,a,471,a)].
% 1.96/2.23 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),D,tc_RealDef_Oreal). [resolve(468,a,472,a)].
% 1.96/2.23 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal),B,tc_RealDef_Oreal),C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(468,a,473,a)].
% 1.96/2.23 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_RealDef_Oreal),B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = E. [resolve(468,a,474,a)].
% 1.96/2.23 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_RealDef_Oreal),E,tc_RealDef_Oreal) | C = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),E,tc_RealDef_Oreal). [resolve(468,a,475,a)].
% 1.96/2.23 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(468,a,476,a)].
% 1.96/2.23 477 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.96/2.24 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(477,a,469,a)].
% 1.96/2.24 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(477,a,470,a)].
% 1.96/2.24 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex). [resolve(477,a,471,a)].
% 1.96/2.24 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex). [resolve(477,a,472,a)].
% 1.96/2.24 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(477,a,473,a)].
% 1.96/2.24 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = E. [resolve(477,a,474,a)].
% 1.96/2.24 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex) | C = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex). [resolve(477,a,475,a)].
% 1.96/2.24 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(477,a,476,a)].
% 1.96/2.24 478 class_Ring__and__Field_Oring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.96/2.24 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(478,a,469,a)].
% 1.96/2.24 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(478,a,470,a)].
% 1.96/2.24 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)). [resolve(478,a,471,a)].
% 1.96/2.24 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)). [resolve(478,a,472,a)].
% 1.96/2.24 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(478,a,473,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = F. [resolve(478,a,474,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)) | D = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),F,tc_Polynomial_Opoly(A)). [resolve(478,a,475,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(478,a,476,a)].
% 1.96/2.27 479 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.96/2.27 480 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A) # label(cls_mult__frac__frac_0) # label(axiom). [assumption].
% 1.96/2.27 481 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(C,B,A),B,A) # label(cls_eq__divide__imp_0) # label(axiom). [assumption].
% 1.96/2.27 482 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(C,B,A),B,A) = C # label(cls_divide__eq__imp_0) # label(axiom). [assumption].
% 1.96/2.27 483 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom). [assumption].
% 1.96/2.27 484 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom). [assumption].
% 1.96/2.27 485 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_diff__divide__distrib_0) # label(axiom). [assumption].
% 1.96/2.27 486 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__divide__right_0) # label(axiom). [assumption].
% 1.96/2.27 487 -class_Ring__and__Field_Ofield(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__divide__left_0) # label(axiom). [assumption].
% 1.96/2.27 488 -class_Ring__and__Field_Ofield(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A),c_HOL_Otimes__class_Otimes(C,E,A),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__frac__eq_0) # label(axiom). [assumption].
% 1.96/2.27 489 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(D,C,A),A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom). [assumption].
% 1.96/2.27 490 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(C,c_HOL_Otimes__class_Otimes(B,D,A),A),D,A) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom). [assumption].
% 1.96/2.27 491 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oinverse__class_Odivide(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__divide_0) # label(axiom). [assumption].
% 1.96/2.27 492 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom). [assumption].
% 1.96/2.27 493 -class_Ring__and__Field_Ofield(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__right_0) # label(axiom). [assumption].
% 1.96/2.27 494 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oinverse__class_Odivide(B,C,A) # label(cls_minus__divide__divide_0) # label(axiom). [assumption].
% 1.96/2.27 495 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),B,A) # label(cls_eq__divide__eq_4) # label(axiom). [assumption].
% 1.96/2.27 496 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A),c_HOL_Otimes__class_Otimes(C,E,A),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom). [assumption].
% 1.96/2.27 497 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom). [assumption].
% 1.96/2.27 498 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom). [assumption].
% 1.96/2.27 499 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom). [assumption].
% 1.96/2.27 500 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom). [assumption].
% 1.96/2.27 501 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom). [assumption].
% 1.96/2.27 502 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) = c_HOL_Oinverse__class_Odivide(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom). [assumption].
% 1.96/2.27 503 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oinverse__class_Odivide(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom). [assumption].
% 1.96/2.27 504 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_mult__frac__num_0) # label(axiom). [assumption].
% 1.96/2.27 505 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_eq__divide__eq_2) # label(axiom). [assumption].
% 1.96/2.27 506 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oinverse__class_Odivide(D,E,A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | c_HOL_Otimes__class_Otimes(B,E,A) = c_HOL_Otimes__class_Otimes(D,C,A) # label(cls_frac__eq__eq_0) # label(axiom). [assumption].
% 1.96/2.27 507 -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Otimes__class_Otimes(D,E,A) | C = c_HOL_Ozero__class_Ozero(A) | E = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,E,A) = c_HOL_Oinverse__class_Odivide(D,C,A) # label(cls_frac__eq__eq_1) # label(axiom). [assumption].
% 1.96/2.27 508 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom). [assumption].
% 1.96/2.27 509 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_add__divide__distrib_0) # label(axiom). [assumption].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(479,a,480,a)].
% 1.96/2.27 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(479,a,481,a)].
% 1.96/2.27 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,A,tc_RealDef_Oreal),A,tc_RealDef_Oreal) = B. [resolve(479,a,482,a)].
% 1.96/2.27 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(479,a,485,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(479,a,486,a)].
% 1.96/2.27 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(479,a,487,a)].
% 1.96/2.27 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,D,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,488,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,489,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal),C,tc_RealDef_Oreal) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,490,a)].
% 1.96/2.27 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,491,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,492,a)].
% 1.96/2.27 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,493,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal). [resolve(479,a,494,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(479,a,495,a)].
% 1.96/2.27 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,496,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | A = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,497,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = A | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,498,a)].
% 1.96/2.27 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,499,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,500,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,502,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,503,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(479,a,504,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(479,a,505,a)].
% 1.96/2.27 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(C,D,tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Otimes__class_Otimes(A,D,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal). [resolve(479,a,506,a)].
% 1.96/2.27 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | D = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,D,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(C,B,tc_RealDef_Oreal). [resolve(479,a,507,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(479,a,508,a)].
% 1.96/2.27 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(A,C,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(479,a,509,a)].
% 1.96/2.27 510 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(510,a,480,a)].
% 1.96/2.27 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,A,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(510,a,481,a)].
% 1.96/2.27 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,A,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = B. [resolve(510,a,482,a)].
% 1.96/2.27 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(510,a,485,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(510,a,486,a)].
% 1.96/2.27 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(510,a,487,a)].
% 1.96/2.27 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,D,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,488,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,489,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,490,a)].
% 1.96/2.27 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,491,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,492,a)].
% 1.96/2.27 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,493,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex). [resolve(510,a,494,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(510,a,495,a)].
% 1.96/2.27 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,496,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | A = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,497,a)].
% 1.96/2.27 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,498,a)].
% 1.96/2.27 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,499,a)].
% 2.03/2.31 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,500,a)].
% 2.03/2.31 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,502,a)].
% 2.03/2.31 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,503,a)].
% 2.03/2.31 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(510,a,504,a)].
% 2.03/2.31 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(510,a,505,a)].
% 2.03/2.31 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(A,D,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex). [resolve(510,a,506,a)].
% 2.03/2.31 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(C,D,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,D,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(C,B,tc_Complex_Ocomplex). [resolve(510,a,507,a)].
% 2.03/2.31 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(510,a,508,a)].
% 2.03/2.31 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(510,a,509,a)].
% 2.03/2.31 511 class_Divides_Osemiring__div(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ofield(A) # label(clsarity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom). [assumption].
% 2.03/2.31 Derived: class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(511,b,479,a)].
% 2.03/2.31 Derived: class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(511,b,510,a)].
% 2.03/2.31 512 class_Divides_Oring__div(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ofield(A) # label(clsarity_Polynomial__Opoly__Divides_Oring__div) # label(axiom). [assumption].
% 2.03/2.31 Derived: class_Divides_Oring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(512,b,479,a)].
% 2.03/2.31 Derived: class_Divides_Oring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(512,b,510,a)].
% 2.03/2.31 513 class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 2.03/2.31 514 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_3) # label(axiom). [assumption].
% 2.03/2.31 515 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_2) # label(axiom). [assumption].
% 2.03/2.31 516 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_1) # label(axiom). [assumption].
% 2.03/2.31 517 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_0) # label(axiom). [assumption].
% 2.03/2.31 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(513,a,514,a)].
% 2.03/2.31 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(513,a,515,a)].
% 2.03/2.31 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(513,a,516,a)].
% 2.03/2.31 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(513,a,517,a)].
% 2.03/2.31 518 class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 2.03/2.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(518,a,514,a)].
% 2.03/2.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(518,a,515,a)].
% 2.03/2.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(518,a,516,a)].
% 2.03/2.34 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)),c_HOL_Oabs__class_Oabs(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(518,a,517,a)].
% 2.03/2.34 519 class_RealVector_Oreal__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__vector) # label(axiom). [assumption].
% 2.03/2.34 520 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ominus__class_Ominus(C,D,A),A) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(B,C,A),c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR__right_Odiff_0) # label(axiom). [assumption].
% 2.03/2.34 521 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR__minus__right_0) # label(axiom). [assumption].
% 2.03/2.34 522 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR__left__commute_0) # label(axiom). [assumption].
% 2.03/2.34 523 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR__eq__0__iff_2) # label(axiom). [assumption].
% 2.03/2.34 524 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_scaleR__cancel__right_1) # label(axiom). [assumption].
% 2.03/2.34 525 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,C,A) != c_RealVector_OscaleR__class_OscaleR(D,C,A) | C = c_HOL_Ozero__class_Ozero(A) | B = D # label(cls_scaleR__cancel__right_0) # label(axiom). [assumption].
% 2.03/2.34 526 -class_RealVector_Oreal__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(B,C,A),c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR__right_Oadd_0) # label(axiom). [assumption].
% 2.03/2.34 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal),c_RealVector_OscaleR__class_OscaleR(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(519,a,520,a)].
% 2.03/2.34 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(519,a,521,a)].
% 2.03/2.34 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_RealVector_OscaleR__class_OscaleR(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(519,a,522,a)].
% 2.03/2.34 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(519,a,523,a)].
% 2.03/2.34 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(519,a,524,a)].
% 2.11/2.37 Derived: c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal) != c_RealVector_OscaleR__class_OscaleR(C,B,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = C. [resolve(519,a,525,a)].
% 2.11/2.37 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal),c_RealVector_OscaleR__class_OscaleR(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(519,a,526,a)].
% 2.11/2.37 527 class_RealVector_Oreal__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__vector) # label(axiom). [assumption].
% 2.11/2.37 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(A,B,tc_Complex_Ocomplex),c_RealVector_OscaleR__class_OscaleR(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(527,a,520,a)].
% 2.11/2.37 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(527,a,521,a)].
% 2.11/2.37 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_RealVector_OscaleR__class_OscaleR(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(527,a,522,a)].
% 2.11/2.37 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(527,a,523,a)].
% 2.11/2.37 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(527,a,524,a)].
% 2.11/2.37 Derived: c_RealVector_OscaleR__class_OscaleR(A,B,tc_Complex_Ocomplex) != c_RealVector_OscaleR__class_OscaleR(C,B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = C. [resolve(527,a,525,a)].
% 2.11/2.37 Derived: c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(A,B,tc_Complex_Ocomplex),c_RealVector_OscaleR__class_OscaleR(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(527,a,526,a)].
% 2.11/2.37 528 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 2.11/2.37 529 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ominus__class_Ominus(C,D,A),A) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(B,C,A),c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR_Odiff__right_0) # label(axiom). [assumption].
% 2.11/2.37 530 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(B,C,A),A) # label(cls_scaleR_Ominus__right_0) # label(axiom). [assumption].
% 2.11/2.37 531 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR_OscaleR__right_0) # label(axiom). [assumption].
% 2.11/2.37 532 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR__right_OscaleR_0) # label(axiom). [assumption].
% 2.11/2.37 533 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_scaleR_Ozero__right_0) # label(axiom). [assumption].
% 2.17/2.44 534 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(B,C,A),c_RealVector_OscaleR__class_OscaleR(B,D,A),A) # label(cls_scaleR_Oadd__right_0) # label(axiom). [assumption].
% 2.17/2.44 535 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 2.17/2.44 536 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.17/2.44 537 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom). [assumption].
% 2.17/2.44 538 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom). [assumption].
% 2.17/2.44 539 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 2.17/2.44 540 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 2.17/2.44 541 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 2.17/2.44 542 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ouminus__class_Ouminus(B,A) # label(cls_group__add__class_Odiff__0_0) # label(axiom). [assumption].
% 2.17/2.44 543 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_diff__minus_0) # label(axiom). [assumption].
% 2.17/2.44 544 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Ouminus__class_Ouminus(B,A) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom). [assumption].
% 2.17/2.44 545 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ouminus__class_Ouminus(B,A) = C # label(cls_minus__unique_0) # label(axiom). [assumption].
% 2.17/2.44 546 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ouminus__class_Ouminus(C,A) # label(cls_eq__neg__iff__add__eq__0_1) # label(axiom). [assumption].
% 2.17/2.44 547 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__neg__iff__add__eq__0_0) # label(axiom). [assumption].
% 2.17/2.44 548 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus_0) # label(axiom). [assumption].
% 2.17/2.44 549 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_left__minus_0) # label(axiom). [assumption].
% 2.17/2.44 550 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 2.17/2.44 551 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oplus__class_Oplus(B,C,A) # label(cls_diff__minus__eq__add_0) # label(axiom). [assumption].
% 2.17/2.44 552 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__equation__iff_1) # label(axiom). [assumption].
% 2.17/2.44 553 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_1) # label(axiom). [assumption].
% 2.17/2.44 554 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_0) # label(axiom). [assumption].
% 2.17/2.44 555 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__minus_0) # label(axiom). [assumption].
% 2.17/2.44 556 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__equal__iff__equal_1) # label(axiom). [assumption].
% 2.17/2.44 557 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom). [assumption].
% 2.17/2.44 558 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(B,C,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_minus__add_0) # label(axiom). [assumption].
% 2.17/2.44 559 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Oplus__class_Oplus(B,C,A),A) = C # label(cls_minus__add__cancel_0) # label(axiom). [assumption].
% 2.17/2.44 560 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),C,A),A) = C # label(cls_add__minus__cancel_0) # label(axiom). [assumption].
% 2.17/2.44 561 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,C,A),C,A) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 2.17/2.44 562 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 2.17/2.44 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal) | A = B. [resolve(536,a,537,a)].
% 2.17/2.44 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(536,a,538,a)].
% 2.17/2.44 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(536,a,539,a)].
% 2.17/2.44 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(536,a,540,a)].
% 2.17/2.44 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal). [resolve(536,a,542,a)].
% 2.17/2.44 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(536,a,544,a)].
% 2.17/2.44 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) = B. [resolve(536,a,545,a)].
% 2.17/2.44 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal). [resolve(536,a,546,a)].
% 2.17/2.44 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(536,a,547,a)].
% 2.17/2.44 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(536,a,548,a)].
% 2.17/2.44 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(536,a,550,a)].
% 2.17/2.44 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal). [resolve(536,a,551,a)].
% 2.17/2.44 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(536,a,552,a)].
% 2.17/2.44 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(536,a,553,a)].
% 2.17/2.44 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(536,a,556,a)].
% 2.17/2.44 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(536,a,557,a)].
% 2.17/2.45 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(536,a,558,a)].
% 2.17/2.45 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = B. [resolve(536,a,559,a)].
% 2.17/2.45 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal),tc_RealDef_Oreal) = B. [resolve(536,a,560,a)].
% 2.17/2.45 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = A. [resolve(536,a,561,a)].
% 2.17/2.45 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = A. [resolve(536,a,562,a)].
% 2.17/2.45 563 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.17/2.45 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex) | A = B. [resolve(563,a,537,a)].
% 2.17/2.45 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(563,a,538,a)].
% 2.17/2.45 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(563,a,539,a)].
% 2.17/2.45 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(563,a,540,a)].
% 2.17/2.45 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex). [resolve(563,a,542,a)].
% 2.17/2.45 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(563,a,544,a)].
% 2.17/2.45 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) = B. [resolve(563,a,545,a)].
% 2.17/2.45 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex). [resolve(563,a,546,a)].
% 2.17/2.45 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(563,a,547,a)].
% 2.17/2.45 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(563,a,548,a)].
% 2.17/2.45 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(563,a,550,a)].
% 2.17/2.45 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex). [resolve(563,a,551,a)].
% 2.17/2.45 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(563,a,552,a)].
% 2.17/2.45 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(563,a,553,a)].
% 2.17/2.45 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(563,a,556,a)].
% 2.17/2.45 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(563,a,557,a)].
% 2.17/2.45 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(563,a,558,a)].
% 2.17/2.45 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = B. [resolve(563,a,559,a)].
% 2.17/2.45 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = B. [resolve(563,a,560,a)].
% 2.17/2.45 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A. [resolve(563,a,561,a)].
% 2.17/2.45 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A. [resolve(563,a,562,a)].
% 2.17/2.45 564 class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Oab__group__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) != c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)) | B = C. [resolve(564,a,537,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(564,a,538,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(564,a,539,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(564,a,540,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)). [resolve(564,a,542,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(564,a,543,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(564,a,544,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) = C. [resolve(564,a,545,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)). [resolve(564,a,546,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(564,a,547,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(564,a,548,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = C. [resolve(564,a,550,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)). [resolve(564,a,551,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(564,a,552,a)].
% 2.17/2.45 Derived: -class_OrderedGroup_Oab__group__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(564,a,553,a)].
% 2.17/2.48 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(564,a,556,a)].
% 2.17/2.48 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(564,a,557,a)].
% 2.17/2.48 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(564,a,558,a)].
% 2.17/2.48 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = C. [resolve(564,a,559,a)].
% 2.17/2.48 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = C. [resolve(564,a,560,a)].
% 2.17/2.48 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = B. [resolve(564,a,561,a)].
% 2.17/2.48 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = B. [resolve(564,a,562,a)].
% 2.17/2.48 565 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.17/2.48 566 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 2.17/2.48 567 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 2.17/2.48 568 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 2.17/2.48 569 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 2.17/2.48 570 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 2.17/2.48 571 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 2.17/2.48 572 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 2.17/2.48 573 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.17/2.48 574 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 2.17/2.48 575 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 2.17/2.48 576 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 2.17/2.48 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(565,a,566,a)].
% 2.17/2.48 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(565,a,567,a)].
% 2.17/2.48 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(565,a,568,a)].
% 2.17/2.48 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(565,a,569,a)].
% 2.17/2.48 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(565,a,570,a)].
% 2.17/2.48 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(565,a,571,a)].
% 2.17/2.48 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(565,a,572,a)].
% 2.17/2.48 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),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(565,a,573,a)].
% 2.17/2.48 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(565,a,574,a)].
% 2.17/2.48 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(565,a,576,a)].
% 2.17/2.48 577 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.17/2.49 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(577,a,566,a)].
% 2.17/2.49 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(577,a,567,a)].
% 2.17/2.49 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(577,a,568,a)].
% 2.17/2.49 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(577,a,569,a)].
% 2.17/2.49 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(577,a,570,a)].
% 2.17/2.49 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(577,a,571,a)].
% 2.17/2.49 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(577,a,572,a)].
% 2.17/2.49 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(577,a,573,a)].
% 2.17/2.49 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(577,a,574,a)].
% 2.17/2.49 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(577,a,576,a)].
% 2.17/2.49 578 class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.17/2.49 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(578,a,566,a)].
% 2.26/2.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(578,a,567,a)].
% 2.26/2.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(578,a,568,a)].
% 2.26/2.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(578,a,569,a)].
% 2.26/2.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(578,a,570,a)].
% 2.26/2.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(578,a,571,a)].
% 2.26/2.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(578,a,572,a)].
% 2.26/2.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(578,a,573,a)].
% 2.26/2.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(578,a,574,a)].
% 2.26/2.52 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(578,a,576,a)].
% 2.26/2.52 579 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].
% 2.26/2.56 580 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 2.26/2.56 581 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 2.26/2.56 582 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 2.26/2.56 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(579,a,580,a)].
% 2.26/2.56 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(579,a,581,a)].
% 2.26/2.56 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(579,a,582,a)].
% 2.26/2.56 583 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].
% 2.26/2.56 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(583,a,580,a)].
% 2.26/2.56 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(583,a,581,a)].
% 2.26/2.56 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(583,a,582,a)].
% 2.26/2.56 584 class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.26/2.56 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(584,a,580,a)].
% 2.26/2.56 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(584,a,581,a)].
% 2.26/2.56 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(584,a,582,a)].
% 2.26/2.56 585 class_Ring__and__Field_Ono__zero__divisors(tc_nat) # label(clsarity_nat__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 2.26/2.56 586 -class_Ring__and__Field_Ono__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divisors_0) # label(axiom). [assumption].
% 2.26/2.56 587 -class_Ring__and__Field_Ono__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divirors__neq0_0) # label(axiom). [assumption].
% 2.26/2.56 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(585,a,586,a)].
% 2.26/2.56 588 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 2.26/2.56 589 class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 2.33/2.63 590 class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 2.33/2.63 591 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 2.33/2.63 592 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_divide_Odiff_0) # label(axiom). [assumption].
% 2.33/2.63 593 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_divide_Ominus_0) # label(axiom). [assumption].
% 2.33/2.63 594 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_divide_OscaleR_0) # label(axiom). [assumption].
% 2.33/2.63 595 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom). [assumption].
% 2.33/2.63 596 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_divide_Oadd_0) # label(axiom). [assumption].
% 2.33/2.63 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(591,a,593,a)].
% 2.33/2.63 Derived: c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Oinverse__class_Odivide(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(591,a,594,a)].
% 2.33/2.63 597 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 2.33/2.63 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(597,a,593,a)].
% 2.33/2.63 Derived: c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(597,a,594,a)].
% 2.33/2.63 598 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 2.33/2.63 599 -class_Ring__and__Field_Oabs__if(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_0) # label(axiom). [assumption].
% 2.33/2.63 600 -class_Ring__and__Field_Oabs__if(A) | c_HOL_Oabs__class_Oabs(B,A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_1) # label(axiom). [assumption].
% 2.33/2.63 Derived: c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(598,a,600,a)].
% 2.33/2.63 601 class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 2.33/2.63 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,tc_Polynomial_Opoly(A)) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(601,a,600,a)].
% 2.42/2.70 602 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.42/2.70 603 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 2.42/2.70 604 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 2.42/2.70 605 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.42/2.70 606 class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.42/2.70 607 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 2.42/2.70 608 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 2.42/2.70 609 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__eq__neg__nonpos_0) # label(axiom). [assumption].
% 2.42/2.70 610 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__eq__neg__nonpos_1) # label(axiom). [assumption].
% 2.42/2.70 611 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) # label(cls_neg__less__eq__nonneg_0) # label(axiom). [assumption].
% 2.42/2.70 612 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__eq__nonneg_1) # label(axiom). [assumption].
% 2.42/2.70 613 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 2.42/2.70 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != A | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(607,a,608,a)].
% 2.42/2.70 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(607,a,609,a)].
% 2.42/2.70 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(607,a,610,a)].
% 2.42/2.70 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(607,a,611,a)].
% 2.42/2.70 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(607,a,612,a)].
% 2.42/2.70 614 class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 2.42/2.70 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) != B | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(614,a,608,a)].
% 2.42/2.70 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(614,a,609,a)].
% 2.46/2.73 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(614,a,610,a)].
% 2.46/2.73 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(614,a,611,a)].
% 2.46/2.73 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(614,a,612,a)].
% 2.46/2.73 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(614,a,613,a)].
% 2.46/2.73 615 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 2.46/2.73 616 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 2.46/2.73 617 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 2.46/2.73 618 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 2.46/2.73 619 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 2.46/2.73 620 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_OscaleR__left_0) # label(axiom). [assumption].
% 2.46/2.73 621 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_OscaleR_0) # label(axiom). [assumption].
% 2.46/2.73 622 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_OscaleR__right_0) # label(axiom). [assumption].
% 2.46/2.73 623 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,E,A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,D,A),E,A),A),c_HOL_Otimes__class_Otimes(D,c_HOL_Ominus__class_Ominus(C,E,A),A),A) # label(cls_mult_Oprod__diff__prod_0) # label(axiom). [assumption].
% 2.46/2.73 624 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_OscaleR_0) # label(axiom). [assumption].
% 2.46/2.73 625 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 2.46/2.73 626 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 2.46/2.73 627 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ominus__class_Ominus(C,D,A),A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_Odiff_0) # label(axiom). [assumption].
% 2.46/2.73 628 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ominus__class_Ominus(C,D,A),A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_Odiff__right_0) # label(axiom). [assumption].
% 2.46/2.73 629 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_Odiff__left_0) # label(axiom). [assumption].
% 2.46/2.73 630 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_Odiff_0) # label(axiom). [assumption].
% 2.46/2.73 631 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 2.46/2.73 632 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 2.46/2.73 633 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_Oadd__left_0) # label(axiom). [assumption].
% 2.46/2.73 634 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_Oadd_0) # label(axiom). [assumption].
% 2.46/2.73 635 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_Oadd__right_0) # label(axiom). [assumption].
% 2.46/2.73 636 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_Oadd_0) # label(axiom). [assumption].
% 2.46/2.73 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(615,a,616,a)].
% 2.46/2.73 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(615,a,618,a)].
% 2.46/2.73 Derived: c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(615,a,620,a)].
% 2.46/2.73 Derived: c_HOL_Otimes__class_Otimes(A,c_RealVector_OscaleR__class_OscaleR(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(615,a,622,a)].
% 2.46/2.73 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),D,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(615,a,623,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ominus__class_Ominus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(615,a,627,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(615,a,629,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(615,a,633,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(615,a,635,a)].
% 2.48/2.74 637 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(637,a,616,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(637,a,618,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(637,a,620,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(A,c_RealVector_OscaleR__class_OscaleR(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(637,a,622,a)].
% 2.48/2.74 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(637,a,623,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(637,a,627,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(637,a,629,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(637,a,633,a)].
% 2.48/2.74 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(637,a,635,a)].
% 2.48/2.83 638 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.48/2.83 639 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 2.48/2.83 640 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 2.48/2.83 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),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(638,a,639,a)].
% 2.48/2.83 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),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(638,a,640,a)].
% 2.48/2.83 641 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.48/2.83 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(641,a,639,a)].
% 2.48/2.83 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(641,a,640,a)].
% 2.48/2.83 642 class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.48/2.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(642,a,639,a)].
% 2.48/2.83 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(642,a,640,a)].
% 2.48/2.83 643 class_Divides_Oring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(512,b,479,a)].
% 2.48/2.83 644 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(B,C,A),A),C,A) # label(cls_mod__minus__eq_0) # label(axiom). [assumption].
% 2.48/2.83 645 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(B,D,A),c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__diff__eq_0) # label(axiom). [assumption].
% 2.48/2.83 646 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A) # label(cls_mod__diff__left__eq_0) # label(axiom). [assumption].
% 2.48/2.83 647 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__diff__right__eq_0) # label(axiom). [assumption].
% 2.48/2.83 648 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(D,A),C,A) # label(cls_mod__minus__cong_0) # label(axiom). [assumption].
% 2.48/2.83 649 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(E,B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(F,D,A),C,A) # label(cls_mod__diff__cong_0) # label(axiom). [assumption].
% 2.48/2.83 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(A,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(643,a,644,a)].
% 2.48/2.83 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(643,a,645,a)].
% 2.48/2.83 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(643,a,646,a)].
% 2.48/2.83 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(643,a,647,a)].
% 2.48/2.83 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(A,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(643,a,648,a)].
% 2.48/2.83 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Divides_Odiv__class_Omod(D,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) != c_Divides_Odiv__class_Omod(E,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(D,A,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(E,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(643,a,649,a)].
% 2.57/2.84 650 class_Divides_Oring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(512,b,510,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(650,a,644,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(650,a,645,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(650,a,646,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(650,a,647,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(650,a,648,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(D,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(E,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(D,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(E,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(650,a,649,a)].
% 2.57/2.84 651 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 2.57/2.84 652 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__imp__mod__0_0) # label(axiom). [assumption].
% 2.57/2.84 653 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_HOL_Ozero__class_Ozero(A) | c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__eq__mod__eq__0_1) # label(axiom). [assumption].
% 2.57/2.84 654 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) # label(cls_dvd__mod__imp__dvd_0) # label(axiom). [assumption].
% 2.57/2.84 655 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mod__iff_1) # label(axiom). [assumption].
% 2.57/2.84 656 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mod__iff_0) # label(axiom). [assumption].
% 2.57/2.84 657 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mod_0) # label(axiom). [assumption].
% 2.57/2.84 658 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_zmod__simps_I4_J_0) # label(axiom). [assumption].
% 2.57/2.84 659 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__0_0) # label(axiom). [assumption].
% 2.57/2.84 660 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mod__trivial_0) # label(axiom). [assumption].
% 2.57/2.84 661 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_mod__by__0_0) # label(axiom). [assumption].
% 2.57/2.84 662 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__self_0) # label(axiom). [assumption].
% 2.57/2.84 663 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__mult__eq_0) # label(axiom). [assumption].
% 2.57/2.84 664 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(F,D,A),C,A) # label(cls_mod__mult__cong_0) # label(axiom). [assumption].
% 2.57/2.84 665 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__mult__right__eq_0) # label(axiom). [assumption].
% 2.57/2.84 666 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A) # label(cls_mod__mult__left__eq_0) # label(axiom). [assumption].
% 2.57/2.84 667 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mult__self2_0) # label(axiom). [assumption].
% 2.57/2.84 668 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),D,A) = c_Divides_Odiv__class_Omod(B,D,A) # label(cls_mod__mult__self1_0) # label(axiom). [assumption].
% 2.57/2.84 669 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),D,A) = c_Divides_Odiv__class_Omod(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) # label(cls_mod__mod__cancel_0) # label(axiom). [assumption].
% 2.57/2.84 670 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self1__is__0_0) # label(axiom). [assumption].
% 2.57/2.84 671 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self2__is__0_0) # label(axiom). [assumption].
% 2.57/2.84 672 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,A),A) # label(cls_mod__mult__mult1_0) # label(axiom). [assumption].
% 2.57/2.84 673 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),C,A) # label(cls_mod__mult__mult2_0) # label(axiom). [assumption].
% 2.57/2.84 674 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(F,D,A),C,A) # label(cls_mod__add__cong_0) # label(axiom). [assumption].
% 2.57/2.84 675 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_zmod__simps_I1_J_0) # label(axiom). [assumption].
% 2.57/2.84 676 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_zmod__simps_I2_J_0) # label(axiom). [assumption].
% 2.57/2.84 677 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__add__self2_0) # label(axiom). [assumption].
% 2.57/2.84 678 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),B,A) = c_Divides_Odiv__class_Omod(C,B,A) # label(cls_mod__add__self1_0) # label(axiom). [assumption].
% 2.57/2.84 679 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,A),c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__add__eq_0) # label(axiom). [assumption].
% 2.57/2.84 680 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__add__right__eq_0) # label(axiom). [assumption].
% 2.57/2.84 681 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A) # label(cls_mod__add__left__eq_0) # label(axiom). [assumption].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(651,a,652,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(651,a,653,a)].
% 2.57/2.84 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat). [resolve(651,a,654,a)].
% 2.57/2.84 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(651,a,655,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_nat),B,tc_nat). [resolve(651,a,658,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(651,a,659,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(651,a,660,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(651,a,661,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(651,a,662,a)].
% 2.57/2.84 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat). [resolve(651,a,663,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(D,A,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,C,tc_nat),B,tc_nat). [resolve(651,a,664,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat). [resolve(651,a,665,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),B,tc_nat),C,tc_nat). [resolve(651,a,666,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(651,a,667,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(A,C,tc_nat). [resolve(651,a,668,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat). [resolve(651,a,669,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(651,a,670,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(651,a,671,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat). [resolve(651,a,672,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),B,tc_nat). [resolve(651,a,673,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(D,A,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,C,tc_nat),B,tc_nat). [resolve(651,a,674,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). [resolve(651,a,675,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat). [resolve(651,a,676,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(651,a,677,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat) = c_Divides_Odiv__class_Omod(B,A,tc_nat). [resolve(651,a,678,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat). [resolve(651,a,679,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat). [resolve(651,a,680,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_nat),B,tc_nat),C,tc_nat). [resolve(651,a,681,a)].
% 2.57/2.87 682 class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(511,b,479,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,652,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,653,a)].
% 2.57/2.87 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,654,a)].
% 2.57/2.87 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,655,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,658,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,659,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,660,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = A. [resolve(682,a,661,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,662,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,663,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Divides_Odiv__class_Omod(D,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) != c_Divides_Odiv__class_Omod(E,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(D,A,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,664,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,665,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,666,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,667,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,668,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,669,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,670,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,671,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,672,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,673,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Divides_Odiv__class_Omod(D,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) != c_Divides_Odiv__class_Omod(E,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(D,A,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,674,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,675,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,676,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,677,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(B,A,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,678,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,679,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,680,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(682,a,681,a)].
% 2.57/2.87 683 class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(511,b,510,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,652,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,653,a)].
% 2.57/2.87 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,654,a)].
% 2.57/2.87 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,655,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,658,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,659,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,660,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A. [resolve(683,a,661,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,662,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,663,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(D,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(E,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(D,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,664,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,665,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,666,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,667,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,668,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,669,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,670,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,671,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,672,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,673,a)].
% 2.57/2.87 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(D,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(E,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(D,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,674,a)].
% 2.57/2.89 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,675,a)].
% 2.57/2.89 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,676,a)].
% 2.57/2.89 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,677,a)].
% 2.57/2.89 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,678,a)].
% 2.57/2.89 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,679,a)].
% 2.57/2.89 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,680,a)].
% 2.57/2.89 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(683,a,681,a)].
% 2.57/2.89 684 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.63/2.89 685 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 2.63/2.89 686 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 2.63/2.89 687 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 2.63/2.89 688 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 2.63/2.89 689 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 2.63/2.89 690 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 2.63/2.89 691 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 2.63/2.89 692 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 2.63/2.89 693 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_min__add__distrib__left_0) # label(axiom). [assumption].
% 2.63/2.89 694 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_max__add__distrib__left_0) # label(axiom). [assumption].
% 2.63/2.89 695 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 2.63/2.89 696 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 2.63/2.89 697 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 2.63/2.89 698 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 2.63/2.89 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(684,a,685,a)].
% 2.63/2.89 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(684,a,686,a)].
% 2.63/2.89 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(684,a,687,a)].
% 2.63/2.89 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(684,a,688,a)].
% 2.63/2.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(684,a,689,a)].
% 2.63/2.89 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(684,a,690,a)].
% 2.63/2.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(684,a,691,a)].
% 2.63/2.89 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat). [resolve(684,a,692,a)].
% 2.63/2.89 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(684,a,693,a)].
% 2.63/2.89 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(684,a,694,a)].
% 2.63/2.89 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(684,a,695,a)].
% 2.63/2.89 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(684,a,696,a)].
% 2.63/2.89 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(684,a,697,a)].
% 2.63/2.89 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat). [resolve(684,a,698,a)].
% 2.63/2.89 699 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.63/2.89 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(699,a,685,a)].
% 2.63/2.89 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(699,a,686,a)].
% 2.63/2.89 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(699,a,687,a)].
% 2.63/2.89 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(699,a,688,a)].
% 2.63/2.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(699,a,689,a)].
% 2.63/2.89 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(699,a,690,a)].
% 2.63/2.89 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(699,a,691,a)].
% 2.63/2.89 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(699,a,692,a)].
% 2.63/2.89 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(699,a,693,a)].
% 2.63/2.89 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(699,a,694,a)].
% 2.63/2.89 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(699,a,695,a)].
% 2.63/2.89 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(699,a,696,a)].
% 2.63/2.89 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(699,a,697,a)].
% 2.63/2.89 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(699,a,698,a)].
% 2.63/2.89 700 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.63/2.89 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(700,a,685,a)].
% 2.63/2.89 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(700,a,686,a)].
% 2.63/2.89 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(700,a,687,a)].
% 2.63/2.89 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(700,a,688,a)].
% 2.63/2.89 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(700,a,689,a)].
% 2.63/2.89 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(700,a,690,a)].
% 2.63/2.89 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)). [resolve(700,a,691,a)].
% 2.63/2.89 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(700,a,692,a)].
% 2.63/2.89 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(700,a,693,a)].
% 2.70/2.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(700,a,694,a)].
% 2.70/2.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(700,a,695,a)].
% 2.70/2.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(700,a,696,a)].
% 2.70/2.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(700,a,697,a)].
% 2.70/2.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(D,B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(700,a,698,a)].
% 2.70/2.97 701 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) # label(axiom). [assumption].
% 2.70/2.97 702 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__le__mult_0) # label(axiom). [assumption].
% 2.70/2.97 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(701,a,702,a)].
% 2.70/2.97 703 class_Orderings_Opreorder(tc_nat) # label(clsarity_nat__Orderings_Opreorder) # label(axiom). [assumption].
% 2.70/2.97 704 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_order__less__trans_0) # label(axiom). [assumption].
% 2.70/2.97 705 -class_Orderings_Opreorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_less__le__not__le_1) # label(axiom). [assumption].
% 2.70/2.97 706 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__irrefl_0) # label(axiom). [assumption].
% 2.70/2.97 707 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_less__le__not__le_2) # label(axiom). [assumption].
% 2.70/2.97 708 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_order__less__imp__le_0) # label(axiom). [assumption].
% 2.70/2.97 709 -class_Orderings_Opreorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__refl_0) # label(axiom). [assumption].
% 2.70/2.97 710 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__le__less__trans_0) # label(axiom). [assumption].
% 2.70/2.97 711 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_order__less__le__trans_0) # label(axiom). [assumption].
% 2.70/2.97 712 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_lessequals(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__trans_0) # label(axiom). [assumption].
% 2.70/2.97 713 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_H_0) # label(axiom). [assumption].
% 2.78/3.08 714 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_0) # label(axiom). [assumption].
% 2.78/3.08 715 class_Orderings_Opreorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Opreorder) # label(axiom). [assumption].
% 2.78/3.08 716 class_Orderings_Opreorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Opreorder) # label(axiom). [assumption].
% 2.78/3.08 717 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra) # label(axiom). [assumption].
% 2.78/3.08 718 -class_RealVector_Oreal__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__scaleR__left_0) # label(axiom). [assumption].
% 2.78/3.08 719 -class_RealVector_Oreal__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__scaleR__right_0) # label(axiom). [assumption].
% 2.78/3.08 720 class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) # label(axiom). [assumption].
% 2.78/3.08 721 class_RealVector_Oreal__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__field) # label(axiom). [assumption].
% 2.78/3.08 722 -class_RealVector_Oreal__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A),F,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(C,E,A),F,A),A),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,D,A),F,A),E,A),A) # label(cls_DERIV__mult__lemma_0) # label(axiom). [assumption].
% 2.78/3.08 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal),E,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,D,tc_RealDef_Oreal),E,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,C,tc_RealDef_Oreal),E,tc_RealDef_Oreal),D,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(721,a,722,a)].
% 2.78/3.08 723 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 2.78/3.08 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),E,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),E,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(723,a,722,a)].
% 2.78/3.08 724 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 2.78/3.08 725 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 2.78/3.08 726 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].
% 2.78/3.08 727 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 2.78/3.12 728 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.78/3.12 729 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 2.78/3.12 730 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 2.78/3.12 731 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 2.78/3.12 732 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 2.78/3.12 733 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 2.78/3.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(728,a,729,a)].
% 2.78/3.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(728,a,730,a)].
% 2.78/3.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(728,a,733,a)].
% 2.78/3.12 734 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.78/3.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(734,a,729,a)].
% 2.78/3.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(734,a,730,a)].
% 2.78/3.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(734,a,733,a)].
% 2.78/3.12 735 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.78/3.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(735,a,729,a)].
% 2.78/3.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(735,a,730,a)].
% 2.94/3.20 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(735,a,733,a)].
% 2.94/3.20 736 class_Ring__and__Field_Omult__zero(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 2.94/3.20 737 -class_Ring__and__Field_Omult__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__left_0) # label(axiom). [assumption].
% 2.94/3.20 738 -class_Ring__and__Field_Omult__zero(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__right_0) # label(axiom). [assumption].
% 2.94/3.20 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(736,a,737,a)].
% 2.94/3.20 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(736,a,738,a)].
% 2.94/3.20 739 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 2.94/3.20 740 class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 2.94/3.20 741 class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 2.94/3.20 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(741,a,737,a)].
% 2.94/3.20 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(741,a,738,a)].
% 2.94/3.20 742 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.94/3.20 743 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 2.94/3.20 744 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 2.94/3.20 745 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 2.94/3.20 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(742,a,743,a)].
% 2.94/3.20 746 class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.94/3.20 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(C,D,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(746,a,743,a)].
% 2.94/3.20 747 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.94/3.20 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(747,a,743,a)].
% 3.03/3.30 748 class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet) # label(axiom). [assumption].
% 3.03/3.30 749 -class_OrderedGroup_Olordered__ab__group__add__meet(A) | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__inf__distrib__right_0) # label(axiom). [assumption].
% 3.03/3.30 750 -class_OrderedGroup_Olordered__ab__group__add__meet(A) | c_HOL_Oplus__class_Oplus(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_add__inf__distrib__left_0) # label(axiom). [assumption].
% 3.03/3.30 Derived: c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(748,a,749,a)].
% 3.03/3.30 Derived: c_HOL_Oplus__class_Oplus(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(748,a,750,a)].
% 3.03/3.30 751 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.03/3.30 752 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(D,C,A) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 3.03/3.30 753 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 3.03/3.30 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C. [resolve(751,a,752,a)].
% 3.03/3.30 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(A,C,tc_nat) | B = C. [resolve(751,a,753,a)].
% 3.03/3.30 754 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.03/3.30 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal) | A = C. [resolve(754,a,752,a)].
% 3.03/3.30 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal) | B = C. [resolve(754,a,753,a)].
% 3.03/3.30 755 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.03/3.30 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(C,B,tc_Complex_Ocomplex) | A = C. [resolve(755,a,752,a)].
% 3.03/3.30 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C. [resolve(755,a,753,a)].
% 3.03/3.30 756 class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocancel__comm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.03/3.30 Derived: -class_OrderedGroup_Ocancel__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)) | B = D. [resolve(756,a,752,a)].
% 3.03/3.30 Derived: -class_OrderedGroup_Ocancel__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)) | C = D. [resolve(756,a,753,a)].
% 3.03/3.30 757 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.03/3.30 758 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 3.10/3.41 759 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.10/3.41 760 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.10/3.41 761 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocancel__comm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.10/3.41 762 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.10/3.41 763 -class_Ring__and__Field_Ocomm__semiring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 3.10/3.41 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(762,a,763,a)].
% 3.10/3.41 764 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.10/3.41 765 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.10/3.41 766 class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.10/3.41 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(766,a,763,a)].
% 3.10/3.41 767 class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join) # label(axiom). [assumption].
% 3.10/3.41 768 -class_OrderedGroup_Olordered__ab__group__add__join(A) | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__sup__distrib__right_0) # label(axiom). [assumption].
% 3.10/3.41 769 -class_OrderedGroup_Olordered__ab__group__add__join(A) | c_HOL_Oplus__class_Oplus(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_add__sup__distrib__left_0) # label(axiom). [assumption].
% 3.10/3.41 Derived: c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(767,a,768,a)].
% 3.10/3.41 Derived: c_HOL_Oplus__class_Oplus(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(767,a,769,a)].
% 3.10/3.41 770 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 3.10/3.41 771 -class_OrderedGroup_Oab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 3.22/3.49 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(770,a,771,a)].
% 3.22/3.49 772 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 3.22/3.49 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(772,a,771,a)].
% 3.22/3.49 773 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 3.22/3.49 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(773,a,771,a)].
% 3.22/3.49 774 class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 3.22/3.49 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(774,a,771,a)].
% 3.22/3.49 775 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 3.22/3.49 776 -class_Ring__and__Field_Osemiring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,A),C,A),E,A) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 3.22/3.49 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_nat),D,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat),D,tc_nat). [resolve(775,a,776,a)].
% 3.22/3.49 777 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 3.22/3.49 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),D,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal),D,tc_RealDef_Oreal). [resolve(777,a,776,a)].
% 3.22/3.49 778 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 3.22/3.49 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex). [resolve(778,a,776,a)].
% 3.22/3.49 779 class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 3.22/3.49 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)). [resolve(779,a,776,a)].
% 3.22/3.49 780 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 3.22/3.49 781 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 5.07/5.33 782 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 5.07/5.33 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(780,a,781,a)].
% 5.07/5.33 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = A. [resolve(780,a,782,a)].
% 5.07/5.33 783 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 5.07/5.33 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(783,a,781,a)].
% 5.07/5.33 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = A. [resolve(783,a,782,a)].
% 5.07/5.33 784 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 5.07/5.33 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(784,a,781,a)].
% 5.07/5.33 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A. [resolve(784,a,782,a)].
% 5.07/5.33 785 class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 5.07/5.33 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(785,a,781,a)].
% 5.07/5.33 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = B. [resolve(785,a,782,a)].
% 5.07/5.33
% 5.07/5.33 ============================== end predicate elimination =============
% 5.07/5.33
% 5.07/5.33 Auto_denials: (non-Horn, no changes).
% 5.07/5.33
% 5.07/5.33 Term ordering decisions:
% 5.07/5.33 Function symbol KB weights: tc_RealDef_Oreal=1. tc_nat=1. tc_Complex_Ocomplex=1. v_p=1. v_z=1. c_HOL_Ouminus__class_Ouminus=1. c_HOL_Oabs__class_Oabs=1. c_Polynomial_Odegree=1. v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1=1. tc_Polynomial_Opoly=1. c_HOL_Ozero__class_Ozero=1. c_Complex_Ocnj=1. v_q=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Oplus__class_Oplus=1. c_Divides_Odiv__class_Omod=1. c_HOL_Oinverse__class_Odivide=1. c_HOL_Ominus__class_Ominus=1. c_Orderings_Oord__class_Omax=1. c_Orderings_Oord__class_Omin=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_RealVector_OscaleR__class_OscaleR=1. c_Polynomial_Opoly=1. c_Polynomial_OpCons=1. c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly=1. v_sko__local__Xthat__1=1. c_Polynomial_Opcompose=1.
% 5.07/5.33
% 5.07/5.33 ============================== end of process initial clauses ========
% 5.07/5.33
% 5.07/5.33 ============================== CLAUSES FOR SEARCH ====================
% 5.07/5.33
% 5.07/5.33 ============================== end of clauses for search =============
% 5.07/5.33
% 5.07/5.33 ============================== SEARCH ================================
% 5.07/5.33
% 5.07/5.33 % Starting search at 2.39 seconds.
% 5.07/5.33
% 5.07/5.33 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 40 (0.00 of 2.51 sec).
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=42.000, iters=3680
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=38.000, iters=3657
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=35.000, iters=3613
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=33.000, iters=3571
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=31.000, iters=3508
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=30.000, iters=3358
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=28.000, iters=3397
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=27.000, iters=3336
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=26.000, iters=3347
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=25.000, iters=3345
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=24.000, iters=3526
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=23.000, iters=3362
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=22.000, iters=3341
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=21.000, iters=3366
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=20.000, iters=3352
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=19.000, iters=3345
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=18.000, iters=3340
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=17.000, iters=3361
% 5.07/5.33
% 5.07/5.33 Low Water (keep): wt=16.000, iters=3349
% 5.07/5.33
% 5.47/5.82 Low Water (keep): wt=15.000, iters=3349
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=5540, wt=52.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=5710, wt=49.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=5658, wt=47.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=5508, wt=46.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=4887, wt=45.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=11396, wt=44.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=14175, wt=43.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=14605, wt=42.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=14557, wt=41.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=9646, wt=40.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=14609, wt=39.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=14877, wt=38.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=14794, wt=37.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=14563, wt=36.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=14881, wt=35.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=14961, wt=34.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=14567, wt=33.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=15146, wt=32.000
% 5.47/5.82
% 5.47/5.82 Low Water (displace): id=16402, wt=31.000
% 5.47/5.82
% 5.47/5.82 ============================== PROOF =================================
% 5.47/5.82 % SZS status Unsatisfiable
% 5.47/5.82 % SZS output start Refutation
% 5.47/5.82
% 5.47/5.82 % Proof 1 at 4.55 (+ 0.06) seconds.
% 5.47/5.82 % Length of proof is 12.
% 5.47/5.82 % Level of proof is 4.
% 5.47/5.82 % Maximum clause weight is 25.000.
% 5.47/5.82 % Given clauses 2687.
% 5.47/5.82
% 5.47/5.82 898 c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(A,B),C,tc_Complex_Ocomplex) = c_Polynomial_Opoly(B,c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) # label(cls_poly__offset_1) # label(axiom). [assumption].
% 5.47/5.82 899 c_Polynomial_Opoly(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(B,A),C,tc_Complex_Ocomplex). [copy(898),flip(a)].
% 5.47/5.82 922 -class_Ring__and__Field_Ocomm__semiring__0(A) | c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(B,C,A),D,A) = c_Polynomial_Opoly(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_poly__offset__poly_0) # label(axiom). [assumption].
% 5.47/5.82 923 -class_Ring__and__Field_Ocomm__semiring__0(A) | c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(B,C,A),A) = c_Polynomial_Odegree(B,A) # label(cls_degree__offset__poly_0) # label(axiom). [assumption].
% 5.47/5.82 937 c_Polynomial_Opoly(A,v_sko__local__Xthat__1(v_p,A,v_z),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,v_sko__local__Xthat__1(v_p,A,v_z),tc_Complex_Ocomplex),tc_Complex_Ocomplex) | c_Polynomial_Odegree(A,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) | v_thesis____ # label(cls_that_0) # label(axiom). [assumption].
% 5.47/5.82 938 c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(v_z,v_p),v_sko__local__Xthat__1(v_p,A,v_z),tc_Complex_Ocomplex) != c_Polynomial_Opoly(A,v_sko__local__Xthat__1(v_p,A,v_z),tc_Complex_Ocomplex) | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Polynomial_Odegree(A,tc_Complex_Ocomplex) | v_thesis____. [copy(937),rewrite([899(14)]),flip(a),flip(b)].
% 5.47/5.82 946 -v_thesis____ # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 5.47/5.82 971 class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) # label(axiom). [assumption].
% 5.47/5.82 2381 c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(v_z,v_p),v_sko__local__Xthat__1(v_p,A,v_z),tc_Complex_Ocomplex) != c_Polynomial_Opoly(A,v_sko__local__Xthat__1(v_p,A,v_z),tc_Complex_Ocomplex) | c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Polynomial_Odegree(A,tc_Complex_Ocomplex). [back_unit_del(938),unit_del(c,946)].
% 5.47/5.82 2774 c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Odegree(A,tc_Complex_Ocomplex). [resolve(971,a,923,a)].
% 5.47/5.82 2775 c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(B,A),C,tc_Complex_Ocomplex). [resolve(971,a,922,a),rewrite([899(8)])].
% 5.47/5.82 16536 $F. [resolve(2775,a,2381,a(flip)),rewrite([2774(9)]),xx(a)].
% 5.47/5.82
% 5.47/5.82 % SZS output end Refutation
% 5.47/5.82 ============================== end of proof ==========================
% 5.47/5.82
% 5.47/5.82 ============================== STATISTICS ============================
% 5.47/5.82
% 5.47/5.82 Given=2687. Generated=86501. Kept=15367. proofs=1.
% 5.47/5.82 Usable=2487. Sos=9999. Demods=1406. Limbo=0, Disabled=4963. Hints=0.
% 5.47/5.82 Megabytes=20.27.
% 5.47/5.82 User_CPU=4.55, System_CPU=0.06, Wall_clock=5.
% 5.47/5.82
% 5.47/5.82 ============================== end of statistics =====================
% 5.47/5.82
% 5.47/5.82 ============================== end of search =========================
% 5.47/5.82
% 5.47/5.82 THEOREM PROVED
% 5.47/5.82 % SZS status Unsatisfiable
% 5.47/5.82
% 5.47/5.82 Exiting with 1 proof.
% 5.47/5.82
% 5.47/5.82 Process 30049 exit (max_proofs) Wed Jun 8 13:36:40 2022
% 5.47/5.82 Prover9 interrupted
%------------------------------------------------------------------------------