TSTP Solution File: ALG427-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG427-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 17:54:49 EDT 2022
% Result : Unsatisfiable 5.37s 5.63s
% Output : Refutation 5.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG427-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 01:34:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.91/1.20 ============================== Prover9 ===============================
% 0.91/1.20 Prover9 (32) version 2009-11A, November 2009.
% 0.91/1.20 Process 9766 was started by sandbox on n018.cluster.edu,
% 0.91/1.20 Thu Jun 9 01:34:38 2022
% 0.91/1.20 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9611_n018.cluster.edu".
% 0.91/1.20 ============================== end of head ===========================
% 0.91/1.20
% 0.91/1.20 ============================== INPUT =================================
% 0.91/1.20
% 0.91/1.20 % Reading from file /tmp/Prover9_9611_n018.cluster.edu
% 0.91/1.20
% 0.91/1.20 set(prolog_style_variables).
% 0.91/1.20 set(auto2).
% 0.91/1.20 % set(auto2) -> set(auto).
% 0.91/1.20 % set(auto) -> set(auto_inference).
% 0.91/1.20 % set(auto) -> set(auto_setup).
% 0.91/1.20 % set(auto_setup) -> set(predicate_elim).
% 0.91/1.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.91/1.20 % set(auto) -> set(auto_limits).
% 0.91/1.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.91/1.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.91/1.20 % set(auto) -> set(auto_denials).
% 0.91/1.20 % set(auto) -> set(auto_process).
% 0.91/1.20 % set(auto2) -> assign(new_constants, 1).
% 0.91/1.20 % set(auto2) -> assign(fold_denial_max, 3).
% 0.91/1.20 % set(auto2) -> assign(max_weight, "200.000").
% 0.91/1.20 % set(auto2) -> assign(max_hours, 1).
% 0.91/1.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.91/1.20 % set(auto2) -> assign(max_seconds, 0).
% 0.91/1.20 % set(auto2) -> assign(max_minutes, 5).
% 0.91/1.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.91/1.20 % set(auto2) -> set(sort_initial_sos).
% 0.91/1.20 % set(auto2) -> assign(sos_limit, -1).
% 0.91/1.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.91/1.20 % set(auto2) -> assign(max_megs, 400).
% 0.91/1.20 % set(auto2) -> assign(stats, some).
% 0.91/1.20 % set(auto2) -> clear(echo_input).
% 0.91/1.20 % set(auto2) -> set(quiet).
% 0.91/1.20 % set(auto2) -> clear(print_initial_clauses).
% 0.91/1.20 % set(auto2) -> clear(print_given).
% 0.91/1.20 assign(lrs_ticks,-1).
% 0.91/1.20 assign(sos_limit,10000).
% 0.91/1.20 assign(order,kbo).
% 0.91/1.20 set(lex_order_vars).
% 0.91/1.20 clear(print_given).
% 0.91/1.20
% 0.91/1.20 % formulas(sos). % not echoed (838 formulas)
% 0.91/1.20
% 0.91/1.20 ============================== end of input ==========================
% 0.91/1.20
% 0.91/1.20 % From the command line: assign(max_seconds, 300).
% 0.91/1.20
% 0.91/1.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.91/1.20
% 0.91/1.20 % Formulas that are not ordinary clauses:
% 0.91/1.20
% 0.91/1.20 ============================== end of process non-clausal formulas ===
% 0.91/1.20
% 0.91/1.20 ============================== PROCESS INITIAL CLAUSES ===============
% 0.91/1.20
% 0.91/1.20 ============================== PREDICATE ELIMINATION =================
% 0.91/1.20 1 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) # label(axiom). [assumption].
% 0.91/1.20 2 -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].
% 0.91/1.20 3 -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].
% 0.91/1.20 4 -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].
% 0.91/1.20 5 -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].
% 0.91/1.20 6 -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].
% 0.91/1.20 7 -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].
% 0.91/1.20 8 -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].
% 0.91/1.20 9 -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].
% 0.91/1.20 10 -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].
% 0.91/1.20 11 -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].
% 0.91/1.20 12 -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].
% 0.91/1.20 13 -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].
% 0.91/1.20 14 -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].
% 0.91/1.20 15 -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].
% 0.91/1.20 16 -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].
% 0.91/1.20 17 -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].
% 0.91/1.20 18 -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].
% 0.91/1.20 19 -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].
% 0.91/1.20 20 -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].
% 0.91/1.20 21 -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].
% 0.91/1.20 22 -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].
% 0.91/1.20 23 -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].
% 0.91/1.20 24 -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].
% 0.91/1.20 25 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A),A),C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_gt__half__sum_0) # label(axiom). [assumption].
% 0.91/1.20 26 -class_Ring__and__Field_Oordered__field(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A),A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__half__sum_0) # label(axiom). [assumption].
% 0.91/1.20 27 -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].
% 0.91/1.20 28 -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].
% 0.91/1.21 29 -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].
% 0.91/1.21 30 -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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__1__iff_0) # label(axiom). [assumption].
% 0.91/1.21 31 -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(c_HOL_Oone__class_Oone(A),B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_divide__less__0__1__iff_1) # label(axiom). [assumption].
% 0.91/1.21 32 -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].
% 0.91/1.21 33 -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].
% 0.91/1.21 34 -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].
% 0.91/1.21 35 -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].
% 0.91/1.21 36 -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].
% 0.91/1.21 37 -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].
% 0.91/1.21 38 -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].
% 0.91/1.21 39 -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].
% 0.91/1.21 40 -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].
% 0.91/1.21 41 -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].
% 0.91/1.21 42 -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].
% 0.91/1.21 43 -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].
% 0.91/1.21 44 -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].
% 0.91/1.21 45 -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].
% 0.91/1.21 46 -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].
% 0.91/1.21 47 -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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),A) # label(cls_zero__less__divide__1__iff_0) # label(axiom). [assumption].
% 0.91/1.21 48 -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(c_HOL_Oone__class_Oone(A),B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__divide__1__iff_1) # label(axiom). [assumption].
% 0.91/1.21 49 -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].
% 0.91/1.21 50 -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].
% 0.91/1.21 51 -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].
% 0.91/1.21 52 -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].
% 0.91/1.21 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(1,a,2,a)].
% 0.91/1.21 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(1,a,3,a)].
% 0.91/1.21 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(1,a,4,a)].
% 0.91/1.21 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(1,a,5,a)].
% 0.91/1.21 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(1,a,6,a)].
% 0.91/1.21 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(1,a,7,a)].
% 0.91/1.21 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(1,a,8,a)].
% 0.91/1.21 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(1,a,9,a)].
% 0.91/1.21 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(1,a,10,a)].
% 0.91/1.21 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(1,a,11,a)].
% 0.91/1.21 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(1,a,12,a)].
% 0.91/1.21 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(1,a,13,a)].
% 0.91/1.21 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(1,a,14,a)].
% 0.91/1.21 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(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,15,a)].
% 0.91/1.21 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(A,c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,16,a)].
% 0.91/1.21 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(1,a,17,a)].
% 0.91/1.21 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(1,a,18,a)].
% 0.91/1.21 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_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(1,a,19,a)].
% 0.91/1.21 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_Otimes__class_Otimes(A,C,tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(1,a,20,a)].
% 0.91/1.21 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(1,a,21,a)].
% 0.91/1.21 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(1,a,22,a)].
% 0.91/1.21 Derived: c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(1,a,25,a)].
% 0.91/1.21 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(1,a,26,a)].
% 0.91/1.21 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(1,a,27,a)].
% 0.91/1.21 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(1,a,28,a)].
% 0.91/1.21 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(1,a,29,a)].
% 0.91/1.21 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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,30,a)].
% 0.91/1.21 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,31,a)].
% 0.91/1.21 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(1,a,32,a)].
% 0.91/1.21 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(1,a,33,a)].
% 0.91/1.21 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(1,a,34,a)].
% 0.91/1.21 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(1,a,35,a)].
% 0.91/1.21 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(1,a,36,a)].
% 0.91/1.21 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(1,a,37,a)].
% 0.91/1.21 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(1,a,38,a)].
% 0.91/1.21 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(1,a,39,a)].
% 0.91/1.21 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(1,a,40,a)].
% 0.91/1.21 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(1,a,41,a)].
% 0.91/1.21 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(1,a,42,a)].
% 0.91/1.22 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(1,a,43,a)].
% 0.91/1.22 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(1,a,44,a)].
% 0.91/1.22 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(1,a,45,a)].
% 0.91/1.22 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(1,a,46,a)].
% 0.91/1.22 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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,47,a)].
% 0.91/1.22 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(1,a,48,a)].
% 0.91/1.22 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(1,a,49,a)].
% 0.91/1.22 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(1,a,50,a)].
% 0.91/1.22 53 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 0.91/1.22 54 -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].
% 0.91/1.22 55 -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].
% 0.91/1.22 56 -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].
% 0.91/1.22 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(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].
% 0.91/1.22 58 -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].
% 0.91/1.22 59 -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].
% 0.91/1.22 60 -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].
% 0.91/1.22 61 -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].
% 0.91/1.22 62 -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].
% 0.91/1.22 63 -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].
% 0.91/1.22 64 -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].
% 0.91/1.22 65 -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].
% 0.91/1.22 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(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].
% 0.91/1.22 67 -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].
% 0.91/1.22 68 -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].
% 0.91/1.22 69 -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].
% 0.91/1.22 70 -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].
% 0.91/1.22 71 -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].
% 0.91/1.22 72 -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].
% 0.91/1.22 73 -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].
% 0.91/1.22 74 -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].
% 0.91/1.22 75 -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].
% 0.91/1.22 76 -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].
% 0.91/1.22 77 -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].
% 0.91/1.22 78 -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].
% 0.91/1.22 79 -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].
% 0.91/1.22 80 -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].
% 0.91/1.22 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(53,a,54,a)].
% 0.91/1.23 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(53,a,55,a)].
% 0.91/1.23 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(53,a,56,a)].
% 0.91/1.23 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(53,a,57,a)].
% 0.91/1.23 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(53,a,58,a)].
% 0.91/1.23 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(53,a,59,a)].
% 0.91/1.23 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(53,a,60,a)].
% 0.91/1.23 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(53,a,61,a)].
% 0.91/1.23 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(53,a,62,a)].
% 0.91/1.23 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(53,a,63,a)].
% 0.91/1.23 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(53,a,64,a)].
% 0.91/1.23 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(53,a,65,a)].
% 0.91/1.23 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(53,a,66,a)].
% 0.91/1.23 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(53,a,67,a)].
% 0.91/1.23 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(53,a,69,a)].
% 0.91/1.23 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(53,a,70,a)].
% 0.91/1.23 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(53,a,73,a)].
% 0.91/1.23 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(53,a,75,a)].
% 0.91/1.23 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(53,a,76,a)].
% 0.91/1.23 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(53,a,77,a)].
% 0.91/1.23 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(53,a,78,a)].
% 0.91/1.23 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(53,a,79,a)].
% 0.91/1.23 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(53,a,80,a)].
% 0.91/1.23 81 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].
% 0.91/1.23 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(81,a,54,a)].
% 0.91/1.23 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(81,a,55,a)].
% 0.91/1.23 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(81,a,56,a)].
% 0.91/1.23 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(81,a,57,a)].
% 0.91/1.23 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(81,a,58,a)].
% 0.91/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,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(81,a,59,a)].
% 0.91/1.23 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(81,a,60,a)].
% 0.91/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,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(81,a,61,a)].
% 0.91/1.23 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(81,a,62,a)].
% 0.91/1.23 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(81,a,63,a)].
% 0.91/1.23 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(81,a,64,a)].
% 0.91/1.23 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(81,a,65,a)].
% 0.91/1.23 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(81,a,66,a)].
% 0.91/1.23 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(81,a,67,a)].
% 0.91/1.25 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(81,a,69,a)].
% 0.91/1.25 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(81,a,70,a)].
% 0.91/1.25 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(81,a,73,a)].
% 0.91/1.25 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(81,a,75,a)].
% 0.91/1.25 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(81,a,76,a)].
% 0.91/1.25 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(81,a,77,a)].
% 0.91/1.25 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(81,a,78,a)].
% 0.91/1.25 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(81,a,79,a)].
% 0.91/1.25 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(81,a,80,a)].
% 0.91/1.25 82 class_Int_Onumber__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Int_Onumber__ring) # label(axiom). [assumption].
% 0.91/1.25 83 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A) != c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,E,A),A) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 0.91/1.25 84 -class_Int_Onumber__ring(A) | c_HOL_Ouminus__class_Ouminus(B,A) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A),B,A) # label(cls_class__ring_Oneg__mul_0) # label(axiom). [assumption].
% 0.91/1.25 85 -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].
% 0.91/1.25 86 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 0.91/1.25 87 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 0.91/1.25 88 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 0.91/1.25 89 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 0.91/1.25 90 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 0.91/1.25 91 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 0.91/1.25 92 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != c_HOL_Oplus__class_Oplus(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 0.91/1.25 93 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 0.91/1.25 94 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 0.91/1.25 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(82,a,83,b)].
% 0.91/1.25 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(82,a,84,a)].
% 0.91/1.25 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(82,a,85,a)].
% 0.91/1.25 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(82,a,86,b)].
% 0.91/1.25 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(82,a,88,b)].
% 0.91/1.25 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(82,a,89,b)].
% 0.91/1.25 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(82,a,91,b)].
% 0.91/1.25 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(82,a,92,b)].
% 0.91/1.25 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(82,a,93,b)].
% 0.91/1.25 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(82,a,94,b)].
% 0.91/1.25 95 class_Int_Onumber__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Onumber__ring) # label(axiom). [assumption].
% 0.91/1.25 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(95,a,83,b)].
% 0.91/1.25 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(95,a,84,a)].
% 0.91/1.25 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(95,a,85,a)].
% 0.91/1.25 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(95,a,86,b)].
% 0.91/1.25 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(95,a,88,b)].
% 0.91/1.25 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(95,a,89,b)].
% 0.91/1.25 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(95,a,91,b)].
% 0.91/1.25 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(95,a,92,b)].
% 0.91/1.25 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(95,a,93,b)].
% 0.91/1.25 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(95,a,94,b)].
% 0.91/1.25 96 class_Int_Onumber__ring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring__1(A) # label(clsarity_Polynomial__Opoly__Int_Onumber__ring) # label(axiom). [assumption].
% 0.91/1.27 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(96,a,83,b)].
% 0.91/1.27 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(96,a,84,a)].
% 0.91/1.27 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(96,a,85,a)].
% 0.91/1.27 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(96,a,86,b)].
% 0.91/1.27 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(96,a,88,b)].
% 0.91/1.27 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(96,a,89,b)].
% 0.91/1.27 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(96,a,91,b)].
% 0.91/1.27 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(96,a,92,b)].
% 0.91/1.27 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(96,a,93,b)].
% 0.91/1.27 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(96,a,94,b)].
% 0.91/1.27 97 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.91/1.27 98 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 0.91/1.27 99 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 0.91/1.27 100 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 0.91/1.27 101 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 0.91/1.27 102 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 0.91/1.27 103 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 0.91/1.27 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(97,a,98,a)].
% 0.91/1.27 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat). [resolve(97,a,99,a)].
% 0.91/1.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat). [resolve(97,a,100,a)].
% 0.91/1.27 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(97,a,101,a)].
% 0.91/1.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(97,a,102,a)].
% 0.91/1.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(97,a,103,a)].
% 0.91/1.27 104 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.91/1.27 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(104,a,98,a)].
% 0.91/1.27 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(104,a,99,a)].
% 0.91/1.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(104,a,100,a)].
% 0.91/1.27 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(104,a,101,a)].
% 0.91/1.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(104,a,102,a)].
% 0.91/1.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(104,a,103,a)].
% 0.91/1.27 105 class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.91/1.27 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(105,a,98,a)].
% 0.91/1.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(105,a,99,a)].
% 0.91/1.27 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(105,a,100,a)].
% 0.91/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(105,a,101,a)].
% 0.91/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(105,a,102,a)].
% 0.91/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(105,a,103,a)].
% 0.91/1.29 106 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 0.91/1.29 107 -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].
% 0.91/1.29 108 -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].
% 0.91/1.29 109 -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].
% 0.91/1.29 110 -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].
% 0.91/1.29 111 -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].
% 0.91/1.29 112 -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].
% 0.91/1.29 113 -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].
% 0.91/1.29 114 -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].
% 0.91/1.29 115 -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].
% 0.91/1.29 116 -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].
% 0.91/1.29 117 -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].
% 0.91/1.29 118 -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].
% 0.91/1.29 119 -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].
% 0.91/1.29 120 -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].
% 0.91/1.29 121 -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].
% 0.91/1.29 122 -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].
% 0.91/1.29 123 -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].
% 0.91/1.29 124 -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].
% 0.91/1.29 125 -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].
% 0.91/1.29 126 -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].
% 0.91/1.29 127 -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].
% 0.91/1.29 128 -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].
% 0.91/1.29 129 -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].
% 0.91/1.29 130 -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].
% 0.91/1.29 131 -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].
% 0.91/1.29 132 -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].
% 0.91/1.29 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(106,a,107,a)].
% 0.91/1.29 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal) | A = B. [resolve(106,a,108,a)].
% 0.91/1.29 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(106,a,109,a)].
% 0.91/1.29 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = A. [resolve(106,a,111,a)].
% 0.91/1.29 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(106,a,112,a)].
% 0.91/1.29 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(106,a,113,a)].
% 0.91/1.29 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(106,a,115,a)].
% 0.91/1.29 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(106,a,116,a)].
% 0.91/1.29 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(106,a,117,a)].
% 0.91/1.29 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),B,tc_RealDef_Oreal) = A. [resolve(106,a,118,a)].
% 0.91/1.29 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(106,a,119,a)].
% 0.91/1.29 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(106,a,120,a)].
% 0.91/1.29 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(106,a,123,a)].
% 0.91/1.29 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(106,a,124,a)].
% 0.91/1.29 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(106,a,125,a)].
% 0.91/1.29 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(106,a,126,a)].
% 0.91/1.29 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(106,a,127,a)].
% 0.91/1.29 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(106,a,128,a)].
% 0.91/1.29 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(106,a,129,a)].
% 0.91/1.29 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(106,a,131,a)].
% 0.91/1.29 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(106,a,132,a)].
% 0.91/1.29 133 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 0.91/1.29 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(133,a,107,a)].
% 0.91/1.29 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex) | A = B. [resolve(133,a,108,a)].
% 0.91/1.29 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(133,a,109,a)].
% 0.91/1.29 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A. [resolve(133,a,111,a)].
% 0.91/1.29 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(133,a,112,a)].
% 0.91/1.29 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(133,a,113,a)].
% 0.91/1.29 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(133,a,115,a)].
% 0.91/1.29 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(133,a,116,a)].
% 0.91/1.29 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(133,a,117,a)].
% 0.91/1.29 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A. [resolve(133,a,118,a)].
% 0.91/1.29 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(133,a,119,a)].
% 0.91/1.29 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(133,a,120,a)].
% 0.91/1.29 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(133,a,123,a)].
% 0.91/1.29 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(133,a,124,a)].
% 0.91/1.29 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(133,a,125,a)].
% 0.91/1.29 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(133,a,126,a)].
% 0.91/1.29 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(133,a,127,a)].
% 0.91/1.29 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(133,a,128,a)].
% 0.91/1.29 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(133,a,129,a)].
% 0.91/1.29 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(133,a,131,a)].
% 0.91/1.29 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(133,a,132,a)].
% 0.91/1.29 134 class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Oab__group__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 0.91/1.29 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(134,a,107,a)].
% 0.91/1.29 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(134,a,108,a)].
% 0.91/1.29 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(134,a,109,a)].
% 0.91/1.29 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(134,a,110,a)].
% 0.91/1.29 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(134,a,111,a)].
% 0.91/1.29 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(134,a,112,a)].
% 0.91/1.29 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(134,a,113,a)].
% 0.91/1.29 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(134,a,115,a)].
% 0.91/1.29 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(134,a,116,a)].
% 0.91/1.29 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(134,a,117,a)].
% 0.91/1.29 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(134,a,118,a)].
% 0.91/1.29 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(134,a,119,a)].
% 0.91/1.31 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(134,a,120,a)].
% 0.91/1.31 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(134,a,123,a)].
% 0.91/1.31 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(134,a,124,a)].
% 0.91/1.31 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(134,a,125,a)].
% 0.91/1.31 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(134,a,126,a)].
% 0.91/1.31 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(134,a,127,a)].
% 0.91/1.31 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(134,a,128,a)].
% 0.91/1.31 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(134,a,129,a)].
% 0.91/1.31 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(134,a,131,a)].
% 0.91/1.31 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(134,a,132,a)].
% 0.91/1.31 135 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 0.91/1.31 136 -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].
% 0.91/1.31 137 -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].
% 0.91/1.31 138 -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].
% 0.91/1.31 139 -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].
% 0.91/1.31 140 -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].
% 0.91/1.31 141 -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].
% 0.91/1.31 142 -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].
% 0.91/1.31 143 -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].
% 0.91/1.31 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(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(135,a,136,a)].
% 0.91/1.31 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(135,a,137,a)].
% 0.91/1.31 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(135,a,139,a)].
% 0.91/1.31 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(135,a,140,a)].
% 0.91/1.31 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(135,a,141,a)].
% 0.91/1.31 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(135,a,142,a)].
% 0.91/1.31 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(135,a,143,a)].
% 0.91/1.31 144 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 0.91/1.31 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(144,a,136,a)].
% 0.91/1.31 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(144,a,137,a)].
% 0.91/1.31 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(144,a,139,a)].
% 0.91/1.31 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(144,a,140,a)].
% 0.91/1.33 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(144,a,141,a)].
% 0.91/1.33 145 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].
% 0.91/1.33 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(145,a,136,a)].
% 0.91/1.33 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(145,a,137,a)].
% 0.91/1.33 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(145,a,139,a)].
% 0.91/1.33 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(145,a,140,a)].
% 0.91/1.33 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(145,a,141,a)].
% 0.91/1.33 146 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 0.91/1.33 147 -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].
% 0.91/1.33 148 -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].
% 0.91/1.33 149 -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].
% 0.91/1.33 150 -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].
% 0.91/1.33 151 -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].
% 0.91/1.33 152 -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].
% 0.91/1.33 153 -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].
% 0.91/1.33 154 -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].
% 0.91/1.33 155 -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].
% 0.91/1.33 156 -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].
% 0.91/1.33 157 -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].
% 0.91/1.33 158 -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].
% 0.91/1.33 159 -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].
% 0.91/1.33 160 -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].
% 0.91/1.33 161 -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].
% 0.91/1.33 162 -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].
% 0.91/1.33 163 -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].
% 0.91/1.33 164 -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].
% 0.91/1.33 165 -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].
% 0.91/1.33 166 -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].
% 0.91/1.33 167 -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].
% 0.91/1.33 168 -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].
% 0.91/1.33 169 -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].
% 0.91/1.33 170 -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].
% 0.91/1.33 171 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__by__1_0) # label(axiom). [assumption].
% 0.91/1.33 172 -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].
% 0.91/1.33 173 -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].
% 0.91/1.33 174 -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].
% 0.91/1.33 175 -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].
% 0.91/1.33 176 -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].
% 0.91/1.33 177 -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].
% 0.91/1.33 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(146,a,147,a)].
% 0.91/1.33 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(146,a,148,a)].
% 0.91/1.33 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(146,a,149,a)].
% 0.91/1.33 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(146,a,150,a)].
% 0.91/1.33 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(146,a,151,a)].
% 0.91/1.33 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(146,a,152,a)].
% 0.91/1.33 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(146,a,155,a)].
% 0.91/1.33 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(146,a,156,a)].
% 0.91/1.33 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(146,a,157,a)].
% 0.91/1.33 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(146,a,158,a)].
% 0.91/1.33 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(146,a,159,a)].
% 0.91/1.33 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(146,a,160,a)].
% 0.91/1.33 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(146,a,161,a)].
% 0.91/1.33 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(146,a,162,a)].
% 0.91/1.33 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(146,a,163,a)].
% 0.91/1.33 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(146,a,164,a)].
% 0.91/1.33 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(146,a,165,a)].
% 0.91/1.33 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(146,a,166,a)].
% 0.91/1.33 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(146,a,167,a)].
% 0.91/1.33 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(146,a,168,a)].
% 0.91/1.33 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(146,a,169,a)].
% 0.91/1.33 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(146,a,170,a)].
% 0.91/1.33 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(146,a,171,a)].
% 0.91/1.33 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(146,a,172,a)].
% 0.91/1.33 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(146,a,173,a)].
% 0.91/1.33 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(146,a,174,a)].
% 0.91/1.33 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(146,a,175,a)].
% 0.91/1.33 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(146,a,176,a)].
% 0.91/1.34 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(146,a,177,a)].
% 0.91/1.34 178 class_Divides_Osemiring__div(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ofield(A) # label(clsarity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom). [assumption].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(178,a,147,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(A)). [resolve(178,a,148,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,149,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(178,a,150,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(178,a,151,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)). [resolve(178,a,152,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(178,a,155,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,156,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,157,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,158,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(178,a,159,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(178,a,160,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(178,a,161,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,162,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(D,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(E,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(F,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(F,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(178,a,163,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,164,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,165,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(178,a,166,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)). [resolve(178,a,167,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(178,a,168,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(178,a,169,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(D,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(E,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(F,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(F,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(178,a,170,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(178,a,171,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Polynomial_Opoly(A)). [resolve(178,a,172,a)].
% 0.91/1.34 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(178,a,173,a)].
% 0.91/1.38 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(178,a,174,a)].
% 0.91/1.38 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(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_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(178,a,175,a)].
% 0.91/1.38 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(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_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(178,a,176,a)].
% 0.91/1.38 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(178,a,177,a)].
% 0.91/1.38 179 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom). [assumption].
% 0.91/1.38 180 -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].
% 0.91/1.38 181 -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].
% 0.91/1.38 182 -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].
% 0.91/1.38 183 -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].
% 0.91/1.38 184 -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].
% 0.91/1.38 185 -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].
% 0.91/1.38 186 -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].
% 0.91/1.38 187 -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].
% 0.91/1.38 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(179,a,180,a)].
% 0.91/1.38 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(179,a,181,a)].
% 0.91/1.38 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(179,a,182,a)].
% 0.91/1.38 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(179,a,183,a)].
% 0.91/1.38 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(179,a,184,a)].
% 0.91/1.38 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(179,a,185,a)].
% 0.91/1.38 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(179,a,186,a)].
% 0.91/1.38 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(179,a,187,a)].
% 0.91/1.38 188 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 0.91/1.38 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(188,a,180,a)].
% 0.91/1.38 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(188,a,181,a)].
% 0.91/1.38 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(188,a,182,a)].
% 0.91/1.38 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(188,a,183,a)].
% 0.91/1.38 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(188,a,184,a)].
% 0.91/1.38 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(188,a,185,a)].
% 0.91/1.38 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(188,a,186,a)].
% 0.91/1.40 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(188,a,187,a)].
% 0.91/1.40 189 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].
% 0.91/1.40 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(189,a,180,a)].
% 0.91/1.40 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(189,a,181,a)].
% 0.91/1.40 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(189,a,182,a)].
% 0.91/1.40 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(189,a,183,a)].
% 0.91/1.40 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(189,a,184,a)].
% 0.91/1.40 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(189,a,185,a)].
% 0.91/1.40 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(189,a,186,a)].
% 0.91/1.40 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(189,a,187,a)].
% 0.91/1.40 190 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 0.91/1.40 191 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(B,A),A) # label(cls_sgn__minus_0) # label(axiom). [assumption].
% 0.91/1.40 192 -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].
% 0.91/1.40 193 -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].
% 0.91/1.40 194 -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].
% 0.91/1.40 195 -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].
% 0.91/1.40 196 -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].
% 0.91/1.40 197 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__zero_0) # label(axiom). [assumption].
% 0.91/1.40 198 -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].
% 0.91/1.40 199 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__zero__iff_0) # label(axiom). [assumption].
% 0.91/1.40 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(190,a,191,a)].
% 0.91/1.40 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(190,a,192,a)].
% 0.91/1.40 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(190,a,193,a)].
% 0.91/1.40 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(190,a,194,a)].
% 0.91/1.40 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(190,a,196,a)].
% 0.91/1.40 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(190,a,197,a)].
% 0.91/1.40 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(190,a,198,a)].
% 0.91/1.40 Derived: c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(190,a,199,a)].
% 0.91/1.40 200 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 0.91/1.40 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(200,a,191,a)].
% 0.91/1.43 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(200,a,192,a)].
% 0.91/1.43 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(200,a,193,a)].
% 0.91/1.43 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(200,a,194,a)].
% 0.91/1.43 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(200,a,196,a)].
% 0.91/1.43 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(200,a,197,a)].
% 0.91/1.43 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(200,a,198,a)].
% 0.91/1.43 Derived: c_HOL_Osgn__class_Osgn(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(200,a,199,a)].
% 0.91/1.43 201 class_Ring__and__Field_Ofield(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 0.91/1.43 202 -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].
% 0.91/1.43 203 -class_Ring__and__Field_Ofield(A) | B = C | -c_Polynomial_Opdivmod__rel(D,E,F,C,A) | -c_Polynomial_Opdivmod__rel(D,E,V6,B,A) # label(cls_pdivmod__rel__unique_1) # label(axiom). [assumption].
% 0.91/1.43 204 -class_Ring__and__Field_Ofield(A) | B = C | -c_Polynomial_Opdivmod__rel(D,E,C,F,A) | -c_Polynomial_Opdivmod__rel(D,E,B,V6,A) # label(cls_pdivmod__rel__unique_0) # label(axiom). [assumption].
% 0.91/1.43 205 -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].
% 0.91/1.43 206 -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].
% 0.91/1.43 207 -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].
% 0.91/1.43 208 -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].
% 0.91/1.43 209 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A) = c_Pair(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)) # label(cls_pdivmod__0_0) # label(axiom). [assumption].
% 0.91/1.43 210 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(B,C,A),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) # label(cls_smult__dvd__iff_4) # label(axiom). [assumption].
% 0.91/1.43 211 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oone__class_Oone(A) | C = c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__inverse__eq_0) # label(axiom). [assumption].
% 0.91/1.43 212 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(B,C,A),D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_smult__dvd__iff_2) # label(axiom). [assumption].
% 0.91/1.43 213 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(D,B,A),C,tc_Polynomial_Opoly(A)) # label(cls_smult__dvd__iff_1) # label(axiom). [assumption].
% 0.91/1.43 214 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Polynomial_Osmult(C,D,A),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_dvd__smult__iff_1) # label(axiom). [assumption].
% 0.91/1.43 215 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Polynomial_Osmult(D,C,A),tc_Polynomial_Opoly(A)) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_dvd__smult__iff_0) # label(axiom). [assumption].
% 0.91/1.43 216 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(B,C,A),D,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,tc_Polynomial_Opoly(A)) # label(cls_smult__dvd_0) # label(axiom). [assumption].
% 0.91/1.43 217 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Polynomial_Osmult(D,C,A),tc_Polynomial_Opoly(A)) # label(cls_dvd__smult__cancel_0) # label(axiom). [assumption].
% 0.91/1.43 218 -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].
% 0.91/1.43 219 -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].
% 0.91/1.43 220 -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].
% 0.91/1.43 221 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(B,C,A),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(B,C,A),A),A) = c_HOL_Oone__class_Oone(A) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_poly__gcd__monic_2) # label(axiom). [assumption].
% 0.91/1.43 222 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(B,C,A),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(B,C,A),A),A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_poly__gcd__monic_1) # label(axiom). [assumption].
% 0.91/1.43 223 -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].
% 0.91/1.43 224 -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].
% 0.91/1.43 225 -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].
% 0.91/1.43 226 -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].
% 0.91/1.43 227 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(B,C,A),D,c_Polynomial_Osmult(B,E,A),c_Polynomial_Osmult(B,F,A),A) | -c_Polynomial_Opdivmod__rel(C,D,E,F,A) # label(cls_pdivmod__rel__smult__left_0) # label(axiom). [assumption].
% 0.91/1.43 228 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)) | -c_Polynomial_Opdivmod__rel(B,D,C,E,A) # label(cls_pdivmod__rel__def_0) # label(axiom). [assumption].
% 0.91/1.43 229 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A),A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_poly__gcd__monic_0) # label(axiom). [assumption].
% 0.91/1.43 230 -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].
% 0.91/1.43 231 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opoly__gcd(B,c_Polynomial_Opoly__gcd(C,D,A),A) = c_Polynomial_Opoly__gcd(C,c_Polynomial_Opoly__gcd(B,D,A),A) # label(cls_poly__gcd__left__commute_0) # label(axiom). [assumption].
% 0.91/1.43 232 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(B,C,A),D,A) = c_Polynomial_Opoly__gcd(B,c_Polynomial_Opoly__gcd(C,D,A),A) # label(cls_poly__gcd__assoc_0) # label(axiom). [assumption].
% 0.91/1.43 233 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opoly__gcd(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),A) = c_Polynomial_Opoly__gcd(B,C,A) # label(cls_poly__gcd__minus__right_0) # label(axiom). [assumption].
% 0.91/1.43 234 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,A) = c_Polynomial_Opoly__gcd(B,C,A) # label(cls_poly__gcd__minus__left_0) # label(axiom). [assumption].
% 0.91/1.43 235 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) # label(cls_right__inverse__eq_1) # label(axiom). [assumption].
% 0.91/1.43 236 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self_0) # label(axiom). [assumption].
% 0.91/1.43 237 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_1) # label(axiom). [assumption].
% 0.91/1.43 238 -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].
% 0.91/1.43 239 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_divide__1_0) # label(axiom). [assumption].
% 0.91/1.43 240 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opoly__gcd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,A) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)) # label(cls_poly__gcd__1__left_0) # label(axiom). [assumption].
% 0.91/1.43 241 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opoly__gcd(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),A) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)) # label(cls_poly__gcd__1__right_0) # label(axiom). [assumption].
% 0.91/1.43 242 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(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)),tc_Polynomial_Opoly(A)),B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) # label(cls_pdivmod__rel__def_6) # label(axiom). [assumption].
% 0.91/1.43 243 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod__rel(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)),B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A) # label(cls_pdivmod__rel__def_5) # label(axiom). [assumption].
% 0.91/1.43 244 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Polynomial_Opoly__gcd(C,D,A),tc_Polynomial_Opoly(A)) # label(cls_dvd__poly__gcd__iff_0) # label(axiom). [assumption].
% 0.91/1.43 245 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Polynomial_Opoly__gcd(D,C,A),tc_Polynomial_Opoly(A)) # label(cls_dvd__poly__gcd__iff_1) # label(axiom). [assumption].
% 0.91/1.43 246 -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].
% 0.91/1.43 247 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Polynomial_Opdivmod__rel(C,B,D,E,A) | c_Polynomial_Opdivmod__rel(c_Polynomial_OpCons(F,C,A),B,c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_Polynomial_Ocoeff(c_Polynomial_OpCons(F,E,A),c_Polynomial_Odegree(B,A),A),c_Polynomial_Ocoeff(B,c_Polynomial_Odegree(B,A),A),A),D,A),c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(F,E,A),c_Polynomial_Osmult(c_HOL_Oinverse__class_Odivide(c_Polynomial_Ocoeff(c_Polynomial_OpCons(F,E,A),c_Polynomial_Odegree(B,A),A),c_Polynomial_Ocoeff(B,c_Polynomial_Odegree(B,A),A),A),B,A),tc_Polynomial_Opoly(A)),A) # label(cls_pdivmod__rel__pCons_0) # label(axiom). [assumption].
% 0.91/1.43 248 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod__rel(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),E,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,F,tc_Polynomial_Opoly(A)),V6,tc_Polynomial_Opoly(A)),A) | -c_Polynomial_Opdivmod__rel(V7,D,E,F,A) | -c_Polynomial_Opdivmod__rel(B,C,V7,V6,A) # label(cls_pdivmod__rel__mult_0) # label(axiom). [assumption].
% 0.91/1.43 249 -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].
% 0.91/1.43 250 -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].
% 0.91/1.43 251 -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].
% 0.91/1.43 252 -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].
% 0.91/1.43 253 -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].
% 0.91/1.43 254 -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].
% 0.91/1.43 255 -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].
% 0.91/1.43 256 -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].
% 0.91/1.43 257 -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].
% 0.91/1.43 258 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opoly__gcd(B,C,A) = c_Polynomial_Opoly__gcd(C,B,A) # label(cls_poly__gcd__commute_0) # label(axiom). [assumption].
% 0.91/1.43 259 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(B,C,A),C,tc_Polynomial_Opoly(A)) # label(cls_poly__gcd__dvd2_0) # label(axiom). [assumption].
% 0.91/1.43 260 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(B,C,A),B,tc_Polynomial_Opoly(A)) # label(cls_poly__gcd__dvd1_0) # label(axiom). [assumption].
% 0.91/1.43 261 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Polynomial_Opoly__gcd(C,D,A),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) # label(cls_dvd__poly__gcd__iff_2) # label(axiom). [assumption].
% 0.91/1.43 262 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Polynomial_Opoly__gcd(C,D,A),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) # label(cls_poly__gcd__greatest_0) # label(axiom). [assumption].
% 0.91/1.43 263 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),B,C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) # label(cls_pdivmod__rel__def_3) # label(axiom). [assumption].
% 0.91/1.43 264 -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].
% 0.91/1.43 265 -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].
% 0.91/1.43 266 -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].
% 0.91/1.43 267 -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].
% 0.91/1.43 268 -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].
% 0.91/1.43 269 -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].
% 0.91/1.43 270 -class_Ring__and__Field_Ofield(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(A),B,A),C,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_smult__dvd__iff_0) # label(axiom). [assumption].
% 0.91/1.43 271 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) # label(cls_smult__dvd__iff_3) # label(axiom). [assumption].
% 0.91/1.43 272 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod__rel(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A) # label(cls_pdivmod__rel__by__0_0) # label(axiom). [assumption].
% 0.91/1.43 273 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) # label(cls_pdivmod__rel__0_0) # label(axiom). [assumption].
% 0.91/1.43 274 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opoly__gcd(B,C,A) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_poly__gcd__zero__iff_1) # label(axiom). [assumption].
% 0.91/1.43 275 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opoly__gcd(B,C,A) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_poly__gcd__zero__iff_0) # label(axiom). [assumption].
% 0.91/1.43 276 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Polynomial_Opdivmod__rel(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,D,A) # label(cls_pdivmod__rel__by__0__iff_0) # label(axiom). [assumption].
% 0.91/1.43 277 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,D,B,A) # label(cls_pdivmod__rel__0__iff_1) # label(axiom). [assumption].
% 0.91/1.43 278 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,B,D,A) # label(cls_pdivmod__rel__0__iff_0) # label(axiom). [assumption].
% 0.91/1.43 279 -class_Ring__and__Field_Ofield(A) | -c_Polynomial_Opdivmod__rel(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,D,A) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_pdivmod__rel__def_1) # label(axiom). [assumption].
% 0.91/1.43 280 -class_Ring__and__Field_Ofield(A) | B = C | -c_Polynomial_Opdivmod__rel(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,B,A) # label(cls_pdivmod__rel__by__0__iff_1) # label(axiom). [assumption].
% 0.91/1.43 281 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_poly__gcd__0__0_0) # label(axiom). [assumption].
% 0.91/1.43 282 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod(c_Polynomial_OpCons(B,C,A),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(B,C,A),tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)) # label(cls_pdivmod__pCons_0) # label(axiom). [assumption].
% 0.91/1.43 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(201,a,202,a)].
% 0.91/1.43 Derived: A = B | -c_Polynomial_Opdivmod__rel(C,D,E,B,tc_RealDef_Oreal) | -c_Polynomial_Opdivmod__rel(C,D,F,A,tc_RealDef_Oreal). [resolve(201,a,203,a)].
% 0.91/1.43 Derived: A = B | -c_Polynomial_Opdivmod__rel(C,D,B,E,tc_RealDef_Oreal) | -c_Polynomial_Opdivmod__rel(C,D,A,F,tc_RealDef_Oreal). [resolve(201,a,204,a)].
% 0.91/1.43 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(201,a,205,a)].
% 0.91/1.43 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(201,a,206,a)].
% 0.91/1.43 Derived: c_Polynomial_Opdivmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,tc_RealDef_Oreal) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,209,a)].
% 0.91/1.43 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,210,a)].
% 0.91/1.43 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = B. [resolve(201,a,211,a)].
% 0.91/1.43 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(A,B,tc_RealDef_Oreal),C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(201,a,212,a)].
% 0.91/1.43 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(C,A,tc_RealDef_Oreal),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,213,a)].
% 0.91/1.43 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Polynomial_Osmult(B,C,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(201,a,214,a)].
% 0.91/1.43 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_Polynomial_Osmult(C,B,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) | C = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(201,a,215,a)].
% 0.91/1.43 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(201,a,218,a)].
% 0.91/1.43 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(201,a,219,a)].
% 0.91/1.43 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(201,a,220,a)].
% 0.91/1.43 Derived: c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,221,a)].
% 0.91/1.43 Derived: c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,222,a)].
% 0.91/1.43 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(201,a,223,a)].
% 0.91/1.43 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(201,a,224,a)].
% 0.91/1.43 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(201,a,225,a)].
% 0.91/1.43 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(201,a,226,a)].
% 0.91/1.43 Derived: c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(A,B,tc_RealDef_Oreal),C,c_Polynomial_Osmult(A,D,tc_RealDef_Oreal),c_Polynomial_Osmult(A,E,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_Polynomial_Opdivmod__rel(B,C,D,E,tc_RealDef_Oreal). [resolve(201,a,227,a)].
% 0.91/1.43 Derived: A = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),D,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Polynomial_Opdivmod__rel(A,C,B,D,tc_RealDef_Oreal). [resolve(201,a,228,a)].
% 0.91/1.43 Derived: c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(201,a,229,a)].
% 0.91/1.43 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(201,a,230,a)].
% 0.91/1.43 Derived: c_Polynomial_Opoly__gcd(A,c_Polynomial_Opoly__gcd(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(B,c_Polynomial_Opoly__gcd(A,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(201,a,231,a)].
% 0.91/1.43 Derived: c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal),C,tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(A,c_Polynomial_Opoly__gcd(B,C,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(201,a,232,a)].
% 0.91/1.43 Derived: c_Polynomial_Opoly__gcd(A,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal). [resolve(201,a,233,a)].
% 0.91/1.43 Derived: c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(A,tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal). [resolve(201,a,234,a)].
% 0.91/1.43 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Oinverse__class_Odivide(A,A,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(201,a,235,a)].
% 0.91/1.43 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(201,a,238,a)].
% 0.91/1.43 Derived: c_HOL_Oinverse__class_Odivide(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(201,a,239,a)].
% 0.91/1.43 Derived: c_Polynomial_Opoly__gcd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,240,a)].
% 0.91/1.43 Derived: c_Polynomial_Opoly__gcd(A,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,241,a)].
% 0.91/1.43 Derived: c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(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)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(201,a,242,a)].
% 0.91/1.43 Derived: c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,tc_RealDef_Oreal). [resolve(201,a,243,a)].
% 0.91/1.43 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_Polynomial_Opoly__gcd(B,C,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,244,a)].
% 0.91/1.43 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_Polynomial_Opoly__gcd(C,B,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,245,a)].
% 0.91/1.43 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(201,a,246,a)].
% 0.91/1.43 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Polynomial_Opdivmod__rel(B,A,C,D,tc_RealDef_Oreal) | c_Polynomial_Opdivmod__rel(c_Polynomial_OpCons(E,B,tc_RealDef_Oreal),A,c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_Polynomial_Ocoeff(c_Polynomial_OpCons(E,D,tc_RealDef_Oreal),c_Polynomial_Odegree(A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Polynomial_Ocoeff(A,c_Polynomial_Odegree(A,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),C,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(E,D,tc_RealDef_Oreal),c_Polynomial_Osmult(c_HOL_Oinverse__class_Odivide(c_Polynomial_Ocoeff(c_Polynomial_OpCons(E,D,tc_RealDef_Oreal),c_Polynomial_Odegree(A,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Polynomial_Ocoeff(A,c_Polynomial_Odegree(A,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),A,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(201,a,247,a)].
% 0.91/1.43 Derived: c_Polynomial_Opdivmod__rel(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_RealDef_Oreal)),D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,tc_Polynomial_Opoly(tc_RealDef_Oreal)),F,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) | -c_Polynomial_Opdivmod__rel(V6,C,D,E,tc_RealDef_Oreal) | -c_Polynomial_Opdivmod__rel(A,B,V6,F,tc_RealDef_Oreal). [resolve(201,a,248,a)].
% 0.91/1.43 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(201,a,249,a)].
% 0.91/1.43 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(201,a,250,a)].
% 0.91/1.43 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(201,a,251,a)].
% 0.91/1.43 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(201,a,252,a)].
% 0.91/1.43 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(201,a,253,a)].
% 0.91/1.43 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(201,a,254,a)].
% 0.91/1.43 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(201,a,255,a)].
% 0.91/1.43 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(201,a,256,a)].
% 0.91/1.43 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(201,a,257,a)].
% 0.91/1.43 Derived: c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(B,A,tc_RealDef_Oreal). [resolve(201,a,258,a)].
% 0.91/1.43 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,259,a)].
% 0.91/1.43 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal),A,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,260,a)].
% 0.91/1.43 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Polynomial_Opoly__gcd(B,C,tc_RealDef_Oreal),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,B,tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,261,a)].
% 0.91/1.43 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,A,tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(201,a,263,a)].
% 0.91/1.43 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(201,a,264,a)].
% 0.91/1.43 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(201,a,265,a)].
% 0.91/1.43 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(201,a,266,a)].
% 0.91/1.43 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(201,a,267,a)].
% 0.91/1.43 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(201,a,268,a)].
% 0.91/1.43 Derived: -c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal),B,tc_Polynomial_Opoly(tc_RealDef_Oreal)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,270,a)].
% 0.91/1.43 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,271,a)].
% 0.91/1.43 Derived: c_Polynomial_Opdivmod__rel(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,tc_RealDef_Oreal). [resolve(201,a,272,a)].
% 0.91/1.43 Derived: c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(201,a,273,a)].
% 0.91/1.43 Derived: c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,274,a)].
% 0.91/1.43 Derived: c_Polynomial_Opoly__gcd(A,B,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,275,a)].
% 0.91/1.43 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Polynomial_Opdivmod__rel(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),A,C,tc_RealDef_Oreal). [resolve(201,a,276,a)].
% 0.91/1.43 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,C,A,tc_RealDef_Oreal). [resolve(201,a,277,a)].
% 0.91/1.43 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) | -c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),B,A,C,tc_RealDef_Oreal). [resolve(201,a,278,a)].
% 0.91/1.43 Derived: A = B | -c_Polynomial_Opdivmod__rel(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),C,A,tc_RealDef_Oreal). [resolve(201,a,280,a)].
% 0.91/1.43 Derived: c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,281,a)].
% 0.91/1.44 Derived: c_Polynomial_Opdivmod(c_Polynomial_OpCons(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_Polynomial_OpCons(A,B,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(201,a,282,a)].
% 0.91/1.44 283 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 0.91/1.44 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(283,a,202,a)].
% 0.91/1.44 Derived: A = B | -c_Polynomial_Opdivmod__rel(C,D,E,B,tc_Complex_Ocomplex) | -c_Polynomial_Opdivmod__rel(C,D,F,A,tc_Complex_Ocomplex). [resolve(283,a,203,a)].
% 0.91/1.44 Derived: A = B | -c_Polynomial_Opdivmod__rel(C,D,B,E,tc_Complex_Ocomplex) | -c_Polynomial_Opdivmod__rel(C,D,A,F,tc_Complex_Ocomplex). [resolve(283,a,204,a)].
% 0.91/1.44 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(283,a,205,a)].
% 0.91/1.44 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(283,a,206,a)].
% 0.91/1.44 Derived: c_Polynomial_Opdivmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Complex_Ocomplex) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,209,a)].
% 0.91/1.44 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(A,B,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,210,a)].
% 0.91/1.44 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(283,a,211,a)].
% 0.91/1.44 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(A,B,tc_Complex_Ocomplex),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(283,a,212,a)].
% 0.91/1.44 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(C,A,tc_Complex_Ocomplex),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,213,a)].
% 0.91/1.44 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Polynomial_Osmult(B,C,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(283,a,214,a)].
% 0.91/1.44 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_Polynomial_Osmult(C,B,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(283,a,215,a)].
% 0.91/1.44 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(283,a,218,a)].
% 0.91/1.44 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(283,a,219,a)].
% 0.91/1.44 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(283,a,220,a)].
% 0.91/1.44 Derived: c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,221,a)].
% 0.91/1.44 Derived: c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,222,a)].
% 0.91/1.44 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(283,a,223,a)].
% 0.91/1.44 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(283,a,224,a)].
% 0.91/1.44 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(283,a,225,a)].
% 0.91/1.44 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(283,a,226,a)].
% 0.91/1.44 Derived: c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(A,B,tc_Complex_Ocomplex),C,c_Polynomial_Osmult(A,D,tc_Complex_Ocomplex),c_Polynomial_Osmult(A,E,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Polynomial_Opdivmod__rel(B,C,D,E,tc_Complex_Ocomplex). [resolve(283,a,227,a)].
% 0.91/1.44 Derived: A = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),D,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Polynomial_Opdivmod__rel(A,C,B,D,tc_Complex_Ocomplex). [resolve(283,a,228,a)].
% 0.91/1.44 Derived: c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(283,a,229,a)].
% 0.91/1.44 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(283,a,230,a)].
% 0.91/1.44 Derived: c_Polynomial_Opoly__gcd(A,c_Polynomial_Opoly__gcd(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(B,c_Polynomial_Opoly__gcd(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(283,a,231,a)].
% 0.91/1.44 Derived: c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(A,c_Polynomial_Opoly__gcd(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(283,a,232,a)].
% 0.91/1.44 Derived: c_Polynomial_Opoly__gcd(A,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex). [resolve(283,a,233,a)].
% 0.91/1.44 Derived: c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex). [resolve(283,a,234,a)].
% 0.91/1.44 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(283,a,235,a)].
% 0.91/1.44 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(283,a,238,a)].
% 0.91/1.44 Derived: c_HOL_Oinverse__class_Odivide(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(283,a,239,a)].
% 0.91/1.44 Derived: c_Polynomial_Opoly__gcd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,240,a)].
% 0.91/1.44 Derived: c_Polynomial_Opoly__gcd(A,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,241,a)].
% 0.91/1.44 Derived: c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(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)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex). [resolve(283,a,242,a)].
% 0.91/1.44 Derived: c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Complex_Ocomplex). [resolve(283,a,243,a)].
% 0.91/1.44 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_Polynomial_Opoly__gcd(B,C,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,244,a)].
% 0.91/1.44 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_Polynomial_Opoly__gcd(C,B,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,245,a)].
% 0.91/1.44 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(283,a,246,a)].
% 0.91/1.44 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Polynomial_Opdivmod__rel(B,A,C,D,tc_Complex_Ocomplex) | c_Polynomial_Opdivmod__rel(c_Polynomial_OpCons(E,B,tc_Complex_Ocomplex),A,c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_Polynomial_Ocoeff(c_Polynomial_OpCons(E,D,tc_Complex_Ocomplex),c_Polynomial_Odegree(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Ocoeff(A,c_Polynomial_Odegree(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),C,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(E,D,tc_Complex_Ocomplex),c_Polynomial_Osmult(c_HOL_Oinverse__class_Odivide(c_Polynomial_Ocoeff(c_Polynomial_OpCons(E,D,tc_Complex_Ocomplex),c_Polynomial_Odegree(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Ocoeff(A,c_Polynomial_Odegree(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex). [resolve(283,a,247,a)].
% 0.91/1.44 Derived: c_Polynomial_Opdivmod__rel(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),F,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) | -c_Polynomial_Opdivmod__rel(V6,C,D,E,tc_Complex_Ocomplex) | -c_Polynomial_Opdivmod__rel(A,B,V6,F,tc_Complex_Ocomplex). [resolve(283,a,248,a)].
% 0.91/1.44 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(283,a,249,a)].
% 0.91/1.44 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(283,a,250,a)].
% 0.91/1.44 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(283,a,251,a)].
% 0.91/1.44 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(283,a,252,a)].
% 0.91/1.44 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(283,a,253,a)].
% 0.91/1.44 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(283,a,254,a)].
% 0.91/1.44 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(283,a,255,a)].
% 0.91/1.44 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(283,a,256,a)].
% 0.91/1.44 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(283,a,257,a)].
% 0.91/1.44 Derived: c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(B,A,tc_Complex_Ocomplex). [resolve(283,a,258,a)].
% 0.91/1.44 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,259,a)].
% 0.91/1.44 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,260,a)].
% 0.91/1.44 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Polynomial_Opoly__gcd(B,C,tc_Complex_Ocomplex),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,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,261,a)].
% 0.91/1.44 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex). [resolve(283,a,263,a)].
% 0.91/1.44 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(283,a,264,a)].
% 0.91/1.44 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(283,a,265,a)].
% 0.91/1.44 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(283,a,266,a)].
% 0.91/1.44 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(283,a,267,a)].
% 0.91/1.44 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(283,a,268,a)].
% 0.91/1.44 Derived: -c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,270,a)].
% 0.91/1.44 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,271,a)].
% 0.91/1.44 Derived: c_Polynomial_Opdivmod__rel(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Complex_Ocomplex). [resolve(283,a,272,a)].
% 0.91/1.44 Derived: c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex). [resolve(283,a,273,a)].
% 0.91/1.44 Derived: c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,274,a)].
% 0.91/1.45 Derived: c_Polynomial_Opoly__gcd(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,275,a)].
% 0.91/1.45 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Polynomial_Opdivmod__rel(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,C,tc_Complex_Ocomplex). [resolve(283,a,276,a)].
% 0.91/1.45 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,C,A,tc_Complex_Ocomplex). [resolve(283,a,277,a)].
% 0.91/1.45 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,A,C,tc_Complex_Ocomplex). [resolve(283,a,278,a)].
% 0.91/1.45 Derived: A = B | -c_Polynomial_Opdivmod__rel(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,A,tc_Complex_Ocomplex). [resolve(283,a,280,a)].
% 0.91/1.45 Derived: c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,281,a)].
% 0.91/1.45 Derived: c_Polynomial_Opdivmod(c_Polynomial_OpCons(A,B,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(A,B,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(283,a,282,a)].
% 0.91/1.45 284 class_Divides_Oring__div(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ofield(A) # label(clsarity_Polynomial__Opoly__Divides_Oring__div) # label(axiom). [assumption].
% 0.91/1.45 Derived: class_Divides_Oring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(284,b,201,a)].
% 0.91/1.45 Derived: class_Divides_Oring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(284,b,283,a)].
% 0.91/1.45 285 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(178,a,147,a)].
% 0.91/1.45 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(285,a,201,a)].
% 0.91/1.45 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(285,a,283,a)].
% 0.91/1.45 286 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(A)). [resolve(178,a,148,a)].
% 0.91/1.45 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(286,a,201,a)].
% 0.91/1.45 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(286,a,283,a)].
% 0.91/1.45 287 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,149,a)].
% 0.91/1.45 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(287,a,201,a)].
% 0.91/1.45 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(287,a,283,a)].
% 0.91/1.45 288 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(178,a,150,a)].
% 0.91/1.45 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(288,a,201,a)].
% 0.91/1.45 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(288,a,283,a)].
% 0.91/1.45 289 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(178,a,151,a)].
% 0.91/1.45 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(289,a,201,a)].
% 0.91/1.45 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(289,a,283,a)].
% 0.91/1.45 290 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)). [resolve(178,a,152,a)].
% 0.91/1.45 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(290,a,201,a)].
% 0.91/1.45 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(290,a,283,a)].
% 0.91/1.45 291 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(178,a,155,a)].
% 0.91/1.45 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(291,a,201,a)].
% 0.91/1.45 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(291,a,283,a)].
% 0.91/1.45 292 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,156,a)].
% 0.91/1.45 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(292,a,201,a)].
% 0.91/1.45 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(292,a,283,a)].
% 0.91/1.45 293 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,157,a)].
% 0.91/1.45 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(293,a,201,a)].
% 0.91/1.45 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(293,a,283,a)].
% 0.91/1.45 294 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,158,a)].
% 0.91/1.45 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(294,a,201,a)].
% 0.91/1.45 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(294,a,283,a)].
% 0.91/1.45 295 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(178,a,159,a)].
% 0.91/1.45 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(295,a,201,a)].
% 0.91/1.45 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(295,a,283,a)].
% 0.91/1.45 296 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(178,a,160,a)].
% 0.91/1.45 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(296,a,201,a)].
% 0.91/1.45 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(296,a,283,a)].
% 0.91/1.45 297 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(178,a,161,a)].
% 0.91/1.45 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(297,a,201,a)].
% 0.91/1.45 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(297,a,283,a)].
% 0.91/1.45 298 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,162,a)].
% 0.91/1.45 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(298,a,201,a)].
% 0.91/1.45 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(298,a,283,a)].
% 0.91/1.45 299 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(D,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(E,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(F,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(F,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(178,a,163,a)].
% 0.91/1.45 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(299,a,201,a)].
% 0.91/1.45 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(299,a,283,a)].
% 0.91/1.45 300 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,164,a)].
% 0.91/1.45 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(300,a,201,a)].
% 0.91/1.45 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(300,a,283,a)].
% 0.91/1.45 301 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(178,a,165,a)].
% 0.91/1.45 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(301,a,201,a)].
% 0.91/1.45 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(301,a,283,a)].
% 0.91/1.45 302 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(178,a,166,a)].
% 0.91/1.45 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(302,a,201,a)].
% 0.91/1.45 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(302,a,283,a)].
% 0.91/1.45 303 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)). [resolve(178,a,167,a)].
% 0.91/1.45 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(303,a,201,a)].
% 0.91/1.45 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(303,a,283,a)].
% 0.91/1.45 304 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(178,a,168,a)].
% 0.91/1.45 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(304,a,201,a)].
% 0.91/1.45 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(304,a,283,a)].
% 0.91/1.45 305 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(178,a,169,a)].
% 0.91/1.45 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(305,a,201,a)].
% 0.91/1.45 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(305,a,283,a)].
% 0.91/1.45 306 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(D,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(E,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(F,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(F,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(178,a,170,a)].
% 0.91/1.45 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(306,a,201,a)].
% 0.91/1.45 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(306,a,283,a)].
% 0.91/1.45 307 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(178,a,171,a)].
% 0.91/1.46 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(307,a,201,a)].
% 0.91/1.46 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(307,a,283,a)].
% 0.91/1.46 308 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Polynomial_Opoly(A)). [resolve(178,a,172,a)].
% 0.91/1.46 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(308,a,201,a)].
% 0.91/1.46 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(308,a,283,a)].
% 0.91/1.46 309 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(178,a,173,a)].
% 0.91/1.46 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(309,a,201,a)].
% 0.91/1.46 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(309,a,283,a)].
% 0.91/1.46 310 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(178,a,174,a)].
% 0.91/1.46 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(310,a,201,a)].
% 0.91/1.46 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(310,a,283,a)].
% 0.91/1.46 311 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(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_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(178,a,175,a)].
% 0.91/1.46 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(311,a,201,a)].
% 0.91/1.46 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(311,a,283,a)].
% 0.91/1.47 312 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(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_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(178,a,176,a)].
% 0.91/1.47 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(312,a,201,a)].
% 0.91/1.47 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(312,a,283,a)].
% 0.91/1.47 313 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(178,a,177,a)].
% 0.91/1.47 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(313,a,201,a)].
% 0.91/1.47 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(313,a,283,a)].
% 0.91/1.47 314 class_RealVector_Oreal__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__vector) # label(axiom). [assumption].
% 0.91/1.47 315 -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].
% 0.91/1.47 316 -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].
% 0.91/1.47 317 -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].
% 0.91/1.47 318 -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].
% 0.91/1.47 319 -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].
% 0.91/1.47 320 -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].
% 0.91/1.47 321 -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].
% 0.91/1.47 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(314,a,319,a)].
% 0.91/1.47 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(314,a,320,a)].
% 0.91/1.50 322 class_RealVector_Oreal__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__vector) # label(axiom). [assumption].
% 0.91/1.50 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(322,a,319,a)].
% 0.91/1.50 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(322,a,320,a)].
% 0.91/1.50 323 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.91/1.50 324 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.91/1.50 325 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 0.91/1.50 326 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 0.91/1.50 327 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 0.91/1.50 328 -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].
% 0.91/1.50 329 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.91/1.50 330 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_1) # label(axiom). [assumption].
% 0.91/1.50 331 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 0.91/1.50 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(323,a,324,a)].
% 0.91/1.50 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(323,a,328,a)].
% 0.91/1.50 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(323,a,329,a)].
% 0.91/1.50 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(323,a,330,a)].
% 0.91/1.50 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(323,a,331,a)].
% 0.91/1.50 332 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 0.91/1.50 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(332,a,324,a)].
% 0.91/1.50 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) | 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(332,a,328,a)].
% 0.91/1.50 Derived: -c_HOL_Oord__class_Oless(A,A,tc_RealDef_Oreal). [resolve(332,a,329,a)].
% 0.91/1.50 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(332,a,330,a)].
% 0.91/1.55 Derived: -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(332,a,331,a)].
% 0.91/1.55 333 class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [assumption].
% 0.91/1.55 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(333,a,324,a)].
% 0.91/1.55 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)) = 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(333,a,328,a)].
% 0.91/1.55 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,B,tc_Polynomial_Opoly(A)). [resolve(333,a,329,a)].
% 0.91/1.55 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(333,a,330,a)].
% 0.91/1.55 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(333,a,331,a)].
% 0.91/1.55 334 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 0.91/1.55 335 -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].
% 0.91/1.55 336 -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].
% 0.91/1.55 337 -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].
% 0.91/1.55 338 -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].
% 0.91/1.55 339 -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].
% 0.91/1.55 340 -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].
% 0.91/1.55 341 -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].
% 0.91/1.55 342 -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].
% 0.91/1.55 343 -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].
% 0.91/1.55 344 -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].
% 0.91/1.55 345 -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].
% 0.91/1.55 346 -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].
% 0.91/1.55 347 -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].
% 0.91/1.55 348 -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].
% 0.91/1.55 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(334,a,335,a)].
% 0.91/1.55 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(334,a,336,a)].
% 0.91/1.55 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(334,a,337,a)].
% 0.91/1.55 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(334,a,338,a)].
% 0.91/1.55 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(334,a,339,a)].
% 0.91/1.55 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(334,a,340,a)].
% 0.91/1.55 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(334,a,341,a)].
% 0.91/1.55 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(334,a,343,a)].
% 0.91/1.55 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(334,a,345,a)].
% 0.91/1.55 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(334,a,346,a)].
% 0.91/1.55 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(334,a,347,a)].
% 0.91/1.55 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(334,a,348,a)].
% 0.91/1.55 349 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].
% 0.91/1.58 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(349,a,335,a)].
% 0.91/1.58 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(349,a,336,a)].
% 0.91/1.58 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(349,a,337,a)].
% 0.91/1.58 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(349,a,338,a)].
% 0.91/1.58 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(349,a,339,a)].
% 0.91/1.58 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(349,a,340,a)].
% 0.91/1.58 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(349,a,341,a)].
% 0.91/1.58 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(349,a,343,a)].
% 0.91/1.58 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(349,a,345,a)].
% 0.91/1.58 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(349,a,346,a)].
% 0.91/1.58 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(349,a,347,a)].
% 0.91/1.58 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(349,a,348,a)].
% 0.91/1.58 350 class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) # label(axiom). [assumption].
% 0.91/1.58 351 -class_Ring__and__Field_Osgn__if(A) | c_HOL_Osgn__class_Osgn(B,A) = c_HOL_Oone__class_Oone(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__if_1) # label(axiom). [assumption].
% 0.91/1.60 352 -class_Ring__and__Field_Osgn__if(A) | c_HOL_Osgn__class_Osgn(B,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__if_2) # label(axiom). [assumption].
% 0.91/1.60 353 -class_Ring__and__Field_Osgn__if(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn0_0) # label(axiom). [assumption].
% 0.91/1.60 Derived: c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(350,a,351,a)].
% 0.91/1.60 Derived: c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(350,a,352,a)].
% 0.91/1.60 354 class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if) # label(axiom). [assumption].
% 0.91/1.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(B,tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(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(354,a,351,a)].
% 0.91/1.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(B,tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(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)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(354,a,352,a)].
% 0.91/1.60 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(354,a,353,a)].
% 0.91/1.60 355 class_Ring__and__Field_Odvd(tc_nat) # label(clsarity_nat__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 0.91/1.60 356 -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].
% 0.91/1.60 357 -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].
% 0.91/1.60 358 -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].
% 0.91/1.60 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(355,a,356,a)].
% 0.91/1.60 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(355,a,357,a)].
% 1.36/1.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). [resolve(355,a,358,a)].
% 1.36/1.63 359 class_Ring__and__Field_Odvd(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 1.36/1.63 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(359,a,356,a)].
% 1.36/1.63 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(359,a,357,a)].
% 1.36/1.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(359,a,358,a)].
% 1.36/1.63 360 class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 1.36/1.63 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(360,a,356,a)].
% 1.36/1.63 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(360,a,357,a)].
% 1.36/1.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(360,a,358,a)].
% 1.36/1.63 361 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].
% 1.36/1.63 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(361,a,356,a)].
% 1.36/1.63 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(361,a,357,a)].
% 1.36/1.63 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(361,a,358,a)].
% 1.36/1.63 362 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.36/1.65 363 -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].
% 1.36/1.65 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(362,a,363,a)].
% 1.36/1.65 364 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.36/1.65 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(364,a,363,a)].
% 1.36/1.65 365 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.36/1.65 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(365,a,363,a)].
% 1.36/1.65 366 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].
% 1.36/1.65 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(366,a,363,a)].
% 1.36/1.65 367 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.36/1.65 368 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_Oadd_0) # label(axiom). [assumption].
% 1.36/1.65 369 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_Oadd__right_0) # label(axiom). [assumption].
% 1.36/1.65 370 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_Oadd_0) # label(axiom). [assumption].
% 1.36/1.65 371 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_Oadd__left_0) # label(axiom). [assumption].
% 1.36/1.65 372 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 1.36/1.65 373 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 1.36/1.65 374 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 1.36/1.65 375 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 1.36/1.66 376 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,E,A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,D,A),E,A),A),c_HOL_Otimes__class_Otimes(D,c_HOL_Ominus__class_Ominus(C,E,A),A),A) # label(cls_mult_Oprod__diff__prod_0) # label(axiom). [assumption].
% 1.36/1.66 377 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ominus__class_Ominus(C,D,A),A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_Odiff_0) # label(axiom). [assumption].
% 1.36/1.66 378 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ominus__class_Ominus(C,D,A),A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_Odiff__right_0) # label(axiom). [assumption].
% 1.36/1.66 379 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_Odiff__left_0) # label(axiom). [assumption].
% 1.36/1.66 380 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_Odiff_0) # label(axiom). [assumption].
% 1.36/1.66 381 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_OscaleR__left_0) # label(axiom). [assumption].
% 1.36/1.66 382 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_OscaleR_0) # label(axiom). [assumption].
% 1.36/1.66 383 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_OscaleR__right_0) # label(axiom). [assumption].
% 1.36/1.66 384 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_OscaleR_0) # label(axiom). [assumption].
% 1.36/1.66 385 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 1.36/1.66 386 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 1.36/1.66 387 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 1.36/1.66 388 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 1.36/1.66 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(367,a,368,a)].
% 1.36/1.66 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(367,a,370,a)].
% 1.36/1.66 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(367,a,372,a)].
% 1.36/1.66 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(367,a,374,a)].
% 1.36/1.66 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(367,a,376,a)].
% 1.36/1.66 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(367,a,377,a)].
% 1.36/1.66 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(367,a,379,a)].
% 1.36/1.66 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(367,a,381,a)].
% 1.36/1.66 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(367,a,383,a)].
% 1.36/1.66 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(367,a,385,a)].
% 1.36/1.66 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(367,a,387,a)].
% 1.36/1.66 389 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.36/1.66 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(389,a,368,a)].
% 1.36/1.66 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(389,a,370,a)].
% 1.36/1.66 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(389,a,372,a)].
% 1.36/1.66 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(389,a,374,a)].
% 1.36/1.66 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(389,a,376,a)].
% 1.43/1.71 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(389,a,377,a)].
% 1.43/1.71 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(389,a,379,a)].
% 1.43/1.71 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(389,a,381,a)].
% 1.43/1.71 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(389,a,383,a)].
% 1.43/1.71 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(389,a,385,a)].
% 1.43/1.71 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(389,a,387,a)].
% 1.43/1.71 390 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.43/1.71 391 -class_Ring__and__Field_Ocomm__semiring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 1.43/1.71 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(390,a,391,a)].
% 1.43/1.71 392 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.43/1.71 393 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.43/1.71 394 class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.43/1.71 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(394,a,391,a)].
% 1.43/1.71 395 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.43/1.71 396 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 1.43/1.71 397 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 1.43/1.71 398 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 1.43/1.74 399 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 1.43/1.74 400 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(B,B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom). [assumption].
% 1.43/1.74 401 -class_OrderedGroup_Olordered__ab__group__add(A) | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_pprt__0_0) # label(axiom). [assumption].
% 1.43/1.74 402 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom). [assumption].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(A,A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(395,a,396,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(395,a,398,a)].
% 1.43/1.74 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(395,a,399,a)].
% 1.43/1.74 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(395,a,400,a)].
% 1.43/1.74 Derived: c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(395,a,401,a)].
% 1.43/1.74 Derived: 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(395,a,402,a)].
% 1.43/1.74 403 class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 1.43/1.74 404 -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].
% 1.43/1.74 405 -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].
% 1.43/1.74 406 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__minus__cancel_0) # label(axiom). [assumption].
% 1.43/1.74 407 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__idempotent_0) # label(axiom). [assumption].
% 1.43/1.74 408 -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].
% 1.43/1.74 409 -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].
% 1.43/1.74 410 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_0) # label(axiom). [assumption].
% 1.43/1.74 411 -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].
% 1.43/1.74 412 -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].
% 1.43/1.74 413 -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].
% 1.43/1.74 414 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_1) # label(axiom). [assumption].
% 1.43/1.74 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(403,a,404,a)].
% 1.43/1.74 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(403,a,405,a)].
% 1.43/1.74 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(403,a,406,a)].
% 1.43/1.74 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(403,a,407,a)].
% 1.43/1.74 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(403,a,408,a)].
% 1.43/1.74 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(403,a,409,a)].
% 1.43/1.74 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(403,a,410,a)].
% 1.43/1.74 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(403,a,411,a)].
% 1.43/1.74 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(403,a,412,a)].
% 1.43/1.74 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(403,a,413,a)].
% 1.43/1.74 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(403,a,414,a)].
% 1.43/1.74 415 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].
% 1.43/1.74 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(415,a,404,a)].
% 1.43/1.74 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(415,a,405,a)].
% 1.43/1.77 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(415,a,406,a)].
% 1.43/1.77 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(415,a,407,a)].
% 1.43/1.77 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(415,a,408,a)].
% 1.43/1.77 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(415,a,409,a)].
% 1.43/1.77 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(415,a,410,a)].
% 1.43/1.77 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(415,a,411,a)].
% 1.43/1.77 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(415,a,412,a)].
% 1.43/1.77 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(415,a,413,a)].
% 1.43/1.77 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(415,a,414,a)].
% 1.43/1.77 416 class_Divides_Oring__div(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(284,b,201,a)].
% 1.43/1.77 417 -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].
% 1.43/1.77 418 -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].
% 1.43/1.77 419 -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].
% 1.43/1.77 420 -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].
% 1.43/1.77 421 -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].
% 1.43/1.77 422 -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].
% 1.43/1.78 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(416,a,417,a)].
% 1.43/1.78 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(416,a,418,a)].
% 1.43/1.78 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(416,a,419,a)].
% 1.43/1.78 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(416,a,420,a)].
% 1.43/1.78 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(416,a,421,a)].
% 1.43/1.78 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(416,a,422,a)].
% 1.43/1.78 423 class_Divides_Oring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(284,b,283,a)].
% 1.43/1.78 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(423,a,417,a)].
% 1.43/1.78 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(423,a,418,a)].
% 1.43/1.78 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(423,a,419,a)].
% 1.53/1.79 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(423,a,420,a)].
% 1.53/1.79 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(423,a,421,a)].
% 1.53/1.79 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(423,a,422,a)].
% 1.53/1.79 424 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.53/1.79 425 -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].
% 1.53/1.79 426 -class_SEQ_Obanach(A) | -class_RealVector_Oreal__normed__field(A) | c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(B,A),c_Transcendental_Oexp(C,A),A) # label(cls_exp__diff_0) # label(axiom). [assumption].
% 1.53/1.79 427 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_divide_Ominus_0) # label(axiom). [assumption].
% 1.53/1.79 428 -class_SEQ_Obanach(A) | -class_RealVector_Oreal__normed__field(A) | c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(B,A),c_Transcendental_Oexp(C,A),A) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(B,C,A),A) # label(cls_mult__exp__exp_0) # label(axiom). [assumption].
% 1.53/1.79 429 -class_SEQ_Obanach(A) | -class_RealVector_Oreal__normed__field(A) | c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_exp__zero_0) # label(axiom). [assumption].
% 1.53/1.79 430 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_divide_OscaleR_0) # label(axiom). [assumption].
% 1.53/1.79 431 -class_SEQ_Obanach(A) | -class_RealVector_Oreal__normed__field(A) | c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(B,A),c_Transcendental_Oexp(C,A),A) # label(cls_exp__add_0) # label(axiom). [assumption].
% 1.53/1.79 432 -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].
% 1.53/1.79 433 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom). [assumption].
% 1.53/1.79 434 -class_SEQ_Obanach(A) | -class_RealVector_Oreal__normed__field(A) | c_Transcendental_Oexp(B,A) != c_HOL_Ozero__class_Ozero(A) # label(cls_exp__not__eq__zero_0) # label(axiom). [assumption].
% 1.56/1.82 Derived: -class_SEQ_Obanach(tc_RealDef_Oreal) | c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(A,tc_RealDef_Oreal),c_Transcendental_Oexp(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(424,a,426,b)].
% 1.56/1.82 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(424,a,427,a)].
% 1.56/1.82 Derived: -class_SEQ_Obanach(tc_RealDef_Oreal) | c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(A,tc_RealDef_Oreal),c_Transcendental_Oexp(B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(424,a,428,b)].
% 1.56/1.82 Derived: -class_SEQ_Obanach(tc_RealDef_Oreal) | c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(424,a,429,b)].
% 1.56/1.82 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(424,a,430,a)].
% 1.56/1.82 Derived: -class_SEQ_Obanach(tc_RealDef_Oreal) | c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(A,tc_RealDef_Oreal),c_Transcendental_Oexp(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(424,a,431,b)].
% 1.56/1.82 Derived: -class_SEQ_Obanach(tc_RealDef_Oreal) | c_Transcendental_Oexp(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(424,a,434,b)].
% 1.56/1.82 435 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.56/1.82 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(A,tc_Complex_Ocomplex),c_Transcendental_Oexp(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(435,a,426,b)].
% 1.56/1.82 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(435,a,427,a)].
% 1.56/1.82 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(A,tc_Complex_Ocomplex),c_Transcendental_Oexp(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(435,a,428,b)].
% 1.56/1.82 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(435,a,429,b)].
% 1.56/1.82 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(435,a,430,a)].
% 1.56/1.82 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(A,tc_Complex_Ocomplex),c_Transcendental_Oexp(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(435,a,431,b)].
% 1.56/1.82 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | c_Transcendental_Oexp(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(435,a,434,b)].
% 1.56/1.82 436 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 1.56/1.82 437 -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].
% 1.56/1.89 438 -class_Ring__and__Field_Oabs__if(A) | c_HOL_Oabs__class_Oabs(B,A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_1) # label(axiom). [assumption].
% 1.56/1.89 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(436,a,438,a)].
% 1.56/1.89 439 class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 1.56/1.89 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(439,a,438,a)].
% 1.56/1.89 440 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.56/1.89 441 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_mult__1__right_0) # label(axiom). [assumption].
% 1.56/1.89 442 -class_OrderedGroup_Omonoid__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_mult__1__left_0) # label(axiom). [assumption].
% 1.56/1.89 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(440,a,441,a)].
% 1.56/1.89 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = A. [resolve(440,a,442,a)].
% 1.56/1.89 443 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.56/1.89 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(443,a,441,a)].
% 1.56/1.89 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = A. [resolve(443,a,442,a)].
% 1.56/1.89 444 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.56/1.89 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(444,a,441,a)].
% 1.56/1.89 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A. [resolve(444,a,442,a)].
% 1.56/1.89 445 class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.56/1.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(445,a,441,a)].
% 1.56/1.89 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = B. [resolve(445,a,442,a)].
% 1.56/1.89 446 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.56/1.89 447 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_mult__1_0) # label(axiom). [assumption].
% 1.56/1.89 448 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.56/1.89 449 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.56/1.89 450 class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.56/1.89 451 class_Orderings_Oorder(tc_nat) # label(clsarity_nat__Orderings_Oorder) # label(axiom). [assumption].
% 1.56/1.89 452 -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].
% 1.64/1.95 453 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__le_1) # label(axiom). [assumption].
% 1.64/1.95 454 -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].
% 1.64/1.95 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(451,a,452,a)].
% 1.64/1.95 455 class_Orderings_Oorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Oorder) # label(axiom). [assumption].
% 1.64/1.95 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(455,a,452,a)].
% 1.64/1.95 456 class_Orderings_Oorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Oorder) # label(axiom). [assumption].
% 1.64/1.95 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(456,a,452,a)].
% 1.64/1.95 457 class_Orderings_Opreorder(tc_nat) # label(clsarity_nat__Orderings_Opreorder) # label(axiom). [assumption].
% 1.64/1.95 458 -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].
% 1.64/1.95 459 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__irrefl_0) # label(axiom). [assumption].
% 1.64/1.95 460 -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].
% 1.64/1.95 461 -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].
% 1.64/1.95 462 class_Orderings_Opreorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Opreorder) # label(axiom). [assumption].
% 1.64/1.95 463 class_Orderings_Opreorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Opreorder) # label(axiom). [assumption].
% 1.64/1.95 464 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.64/1.95 465 -class_OrderedGroup_Oab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 1.64/1.95 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(464,a,465,a)].
% 1.64/1.95 466 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.64/1.95 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(466,a,465,a)].
% 1.64/1.95 467 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.64/1.95 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(467,a,465,a)].
% 1.64/1.95 468 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].
% 1.64/1.95 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(468,a,465,a)].
% 1.73/2.00 469 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.73/2.00 470 -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].
% 1.73/2.00 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(469,a,470,a)].
% 1.73/2.00 471 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.73/2.00 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(471,a,470,a)].
% 1.73/2.00 472 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.73/2.00 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(472,a,470,a)].
% 1.73/2.00 473 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].
% 1.73/2.00 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(473,a,470,a)].
% 1.73/2.00 474 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.73/2.00 475 -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].
% 1.73/2.00 476 -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].
% 1.73/2.00 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(474,a,475,a)].
% 1.73/2.00 477 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.73/2.00 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(477,a,475,a)].
% 1.73/2.00 478 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].
% 1.73/2.07 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(478,a,475,a)].
% 1.73/2.07 479 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.73/2.07 480 -class_RealVector_Oreal__normed__algebra__1(A) | c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_sgn__one_0) # label(axiom). [assumption].
% 1.73/2.07 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(479,a,480,a)].
% 1.73/2.07 481 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.73/2.07 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(481,a,480,a)].
% 1.73/2.07 482 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.73/2.07 483 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 1.73/2.07 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(A,C,tc_nat) | B = C. [resolve(482,a,483,a)].
% 1.73/2.07 484 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.73/2.07 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(A,C,tc_RealDef_Oreal) | B = C. [resolve(484,a,483,a)].
% 1.73/2.07 485 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.73/2.07 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C. [resolve(485,a,483,a)].
% 1.73/2.07 486 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocancel__comm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.73/2.07 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(486,a,483,a)].
% 1.73/2.07 487 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.73/2.07 488 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 1.73/2.07 489 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(D,C,A) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 1.73/2.07 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C. [resolve(487,a,489,a)].
% 1.73/2.07 490 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.73/2.07 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(C,B,tc_RealDef_Oreal) | A = C. [resolve(490,a,489,a)].
% 1.73/2.07 491 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.87/2.14 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(C,B,tc_Complex_Ocomplex) | A = C. [resolve(491,a,489,a)].
% 1.87/2.14 492 class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocancel__comm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.87/2.14 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(492,a,489,a)].
% 1.87/2.14 493 class_RealVector_Oreal__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__algebra) # label(axiom). [assumption].
% 1.87/2.14 494 -class_RealVector_Oreal__algebra(A) | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A) = c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__scaleR__left_0) # label(axiom). [assumption].
% 1.87/2.14 495 -class_RealVector_Oreal__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A) = c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__scaleR__right_0) # label(axiom). [assumption].
% 1.87/2.14 496 class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) # label(axiom). [assumption].
% 1.87/2.14 497 class_RealVector_Oreal__field(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__field) # label(axiom). [assumption].
% 1.87/2.14 498 -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].
% 1.87/2.14 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(497,a,498,a)].
% 1.87/2.14 499 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 1.87/2.14 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(499,a,498,a)].
% 1.87/2.14 500 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 1.87/2.14 501 -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].
% 1.87/2.14 502 -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].
% 1.87/2.15 503 -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].
% 1.87/2.15 504 -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].
% 1.87/2.15 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(500,a,501,a)].
% 1.87/2.15 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(500,a,502,a)].
% 1.87/2.15 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(500,a,503,a)].
% 1.87/2.15 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(500,a,504,a)].
% 1.87/2.15 505 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].
% 1.87/2.15 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(505,a,501,a)].
% 1.87/2.15 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(505,a,502,a)].
% 1.96/2.22 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(505,a,503,a)].
% 1.96/2.22 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(505,a,504,a)].
% 1.96/2.22 506 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.96/2.22 507 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 1.96/2.22 508 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.96/2.22 509 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.96/2.22 510 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 1.96/2.22 511 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 1.96/2.22 512 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 1.96/2.22 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != A | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(510,a,512,a)].
% 1.96/2.22 513 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].
% 1.96/2.22 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(513,a,511,a)].
% 1.96/2.22 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(513,a,512,a)].
% 1.96/2.22 514 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.96/2.22 515 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 1.96/2.22 516 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 1.96/2.22 517 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 1.96/2.27 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(514,a,517,a)].
% 1.96/2.27 518 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.96/2.27 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(518,a,517,a)].
% 1.96/2.27 519 class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.96/2.27 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(519,a,515,a)].
% 1.96/2.27 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(519,a,516,a)].
% 1.96/2.27 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(519,a,517,a)].
% 1.96/2.27 520 class_Ring__and__Field_Omult__zero(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.96/2.27 521 -class_Ring__and__Field_Omult__zero(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__right_0) # label(axiom). [assumption].
% 1.96/2.27 522 -class_Ring__and__Field_Omult__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__zero__left_0) # label(axiom). [assumption].
% 1.96/2.27 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(520,a,521,a)].
% 1.96/2.27 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(520,a,522,a)].
% 1.96/2.27 523 class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.96/2.27 524 class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.96/2.27 525 class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.96/2.27 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(525,a,521,a)].
% 1.96/2.27 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(525,a,522,a)].
% 1.96/2.27 526 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.96/2.27 527 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 1.96/2.27 528 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 2.04/2.32 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(526,a,527,a)].
% 2.04/2.32 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(526,a,528,a)].
% 2.04/2.32 529 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.04/2.32 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(529,a,527,a)].
% 2.04/2.32 Derived: c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(529,a,528,a)].
% 2.04/2.32 530 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.04/2.32 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(530,a,527,a)].
% 2.04/2.32 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(530,a,528,a)].
% 2.04/2.32 531 class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.04/2.32 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(531,a,527,a)].
% 2.04/2.32 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(531,a,528,a)].
% 2.04/2.32 532 class_Ring__and__Field_Ono__zero__divisors(tc_nat) # label(clsarity_nat__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 2.04/2.32 533 -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].
% 2.04/2.32 534 -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].
% 2.04/2.32 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(532,a,533,a)].
% 2.04/2.32 535 class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 2.04/2.32 536 class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 2.04/2.32 537 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].
% 2.04/2.32 538 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.04/2.32 539 -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].
% 2.04/2.32 540 -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].
% 2.04/2.32 541 -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].
% 2.04/2.32 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(538,a,539,a)].
% 2.04/2.34 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(538,a,540,a)].
% 2.04/2.34 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(538,a,541,a)].
% 2.04/2.34 542 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 2.04/2.34 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(542,a,539,a)].
% 2.04/2.34 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(542,a,540,a)].
% 2.04/2.34 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(542,a,541,a)].
% 2.04/2.34 543 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].
% 2.04/2.34 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(543,a,539,a)].
% 2.04/2.34 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(543,a,540,a)].
% 2.04/2.34 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(543,a,541,a)].
% 2.04/2.34 544 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.04/2.34 545 -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].
% 2.04/2.34 546 -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].
% 2.04/2.34 547 -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].
% 2.04/2.34 548 -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].
% 2.04/2.34 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(544,a,545,a)].
% 2.04/2.34 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(544,a,547,a)].
% 2.13/2.39 549 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].
% 2.13/2.39 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(549,a,545,a)].
% 2.13/2.39 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(549,a,547,a)].
% 2.13/2.39 550 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].
% 2.13/2.39 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_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(550,a,545,a)].
% 2.13/2.39 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_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(550,a,547,a)].
% 2.13/2.39 551 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 2.13/2.39 552 -class_RealVector_Oreal__normed__div__algebra(A) | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Osgn__class_Osgn(C,A),A) # label(cls_sgn__mult_0) # label(axiom). [assumption].
% 2.13/2.39 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(A,tc_RealDef_Oreal),c_HOL_Osgn__class_Osgn(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(551,a,552,a)].
% 2.13/2.39 553 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 2.13/2.39 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(A,tc_Complex_Ocomplex),c_HOL_Osgn__class_Osgn(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(553,a,552,a)].
% 2.13/2.39 554 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.13/2.39 555 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 2.13/2.39 556 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 2.13/2.39 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(554,a,555,a)].
% 2.13/2.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = A. [resolve(554,a,556,a)].
% 2.13/2.39 557 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.13/2.39 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(557,a,555,a)].
% 2.13/2.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) = A. [resolve(557,a,556,a)].
% 2.13/2.39 558 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.13/2.39 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(558,a,555,a)].
% 2.13/2.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A. [resolve(558,a,556,a)].
% 5.37/5.63 559 class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 5.37/5.63 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(559,a,555,a)].
% 5.37/5.63 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(559,a,556,a)].
% 5.37/5.63
% 5.37/5.63 ============================== end predicate elimination =============
% 5.37/5.63
% 5.37/5.63 Auto_denials: (non-Horn, no changes).
% 5.37/5.63
% 5.37/5.63 Term ordering decisions:
% 5.37/5.63 Function symbol KB weights: tc_RealDef_Oreal=1. tc_Complex_Ocomplex=1. tc_nat=1. v_p=1. v_q=1. c_Complex_Oii=1. c_HOL_Ouminus__class_Ouminus=1. c_HOL_Oabs__class_Oabs=1. c_HOL_Osgn__class_Osgn=1. c_Polynomial_Odegree=1. c_Transcendental_Oexp=1. c_OrderedGroup_Olordered__ab__group__add__class_Opprt=1. tc_prod=1. tc_Polynomial_Opoly=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Oone__class_Oone=1. c_Suc=1. c_Complex_Ocnj=1. v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1=1. v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2=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_Polynomial_OpCons=1. c_Polynomial_Osmult=1. c_Polynomial_Opoly__gcd=1. c_RealVector_OscaleR__class_OscaleR=1. c_Polynomial_Ocoeff=1. c_Polynomial_Opoly=1. c_Polynomial_Omonom=1. c_Polynomial_Osynthetic__div=1. c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly=1. c_Polynomial_Opcompose=1. c_Polynomial_Opdivmod=1. c_Polynomial_Osynthetic__divmod=1. c_Pair=1.
% 5.37/5.63
% 5.37/5.63 ============================== end of process initial clauses ========
% 5.37/5.63
% 5.37/5.63 ============================== CLAUSES FOR SEARCH ====================
% 5.37/5.63
% 5.37/5.63 ============================== end of clauses for search =============
% 5.37/5.63
% 5.37/5.63 ============================== SEARCH ================================
% 5.37/5.63
% 5.37/5.63 % Starting search at 1.32 seconds.
% 5.37/5.63
% 5.37/5.63 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 106 (0.00 of 1.41 sec).
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=35.000, iters=3378
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=31.000, iters=3370
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=30.000, iters=3348
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=29.000, iters=3344
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=27.000, iters=3334
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=26.000, iters=3391
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=25.000, iters=3367
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=24.000, iters=3340
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=23.000, iters=3349
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=22.000, iters=3339
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=21.000, iters=3341
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=20.000, iters=3335
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=19.000, iters=3335
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=18.000, iters=3348
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=17.000, iters=3334
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=4991, wt=69.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=4981, wt=65.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=11815, wt=45.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=12285, wt=44.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=13144, wt=43.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=13249, wt=42.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=12809, wt=41.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=12628, wt=40.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=13253, wt=39.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=12353, wt=38.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=11862, wt=37.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=13399, wt=36.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=12622, wt=35.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=13440, wt=34.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=13401, wt=33.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=13145, wt=32.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=13142, wt=31.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=13444, wt=30.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=14055, wt=29.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=14527, wt=28.000
% 5.37/5.63
% 5.37/5.63 Low Water (keep): wt=16.000, iters=3333
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=14238, wt=27.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=15025, wt=26.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=15102, wt=25.000
% 5.37/5.63
% 5.37/5.63 Low Water (displace): id=15914, wt=24.000
% 5.37/5.63
% 5.37/5.63 ============================== PROOF =================================
% 5.37/5.63 % SZS status Unsatisfiable
% 5.37/5.63 % SZS output start Refutation
% 5.37/5.63
% 5.37/5.63 % Proof 1 at 4.41 (+ 0.07) seconds.
% 5.37/5.63 % Length of proof is 39.
% 5.37/5.63 % Level of proof is 5.
% 5.37/5.63 % Maximum clause weight is 24.000.
% 5.37/5.63 % Given clauses 3240.
% 5.37/5.63
% 5.37/5.63 487 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 5.37/5.63 489 -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].
% 5.37/5.63 554 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 5.37/5.63 555 -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].
% 5.37/5.63 700 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,C,A) = c_HOL_Oplus__class_Oplus(C,B,A) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 5.37/5.63 732 -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Oplus__class_Oplus(B,c_Polynomial_Osmult(C,c_Polynomial_Osynthetic__div(B,C,A),A),tc_Polynomial_Opoly(A)) = c_Polynomial_OpCons(c_Polynomial_Opoly(B,C,A),c_Polynomial_Osynthetic__div(B,C,A),A) # label(cls_synthetic__div__correct_0) # label(axiom). [assumption].
% 5.37/5.63 761 -class_Ring__and__Field_Ocomm__semiring__0(A) | c_Polynomial_Odegree(B,A) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Polynomial_Osynthetic__div(B,C,A) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_synthetic__div__eq__0__iff_1) # label(axiom). [assumption].
% 5.37/5.63 804 -class_Ring__and__Field_Ocomm__semiring__0(A) | c_Polynomial_Osmult(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_smult__0__right_0) # label(axiom). [assumption].
% 5.37/5.63 818 -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 # label(cls_add__poly__code_I2_J_0) # label(axiom). [assumption].
% 5.37/5.63 820 -class_HOL_Ozero(A) | c_Polynomial_Omonom(B,c_HOL_Ozero__class_Ozero(tc_nat),A) = c_Polynomial_OpCons(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) # label(cls_monom__0_0) # label(axiom). [assumption].
% 5.37/5.63 821 -class_HOL_Ozero(A) | c_Polynomial_OpCons(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) = c_Polynomial_Omonom(B,c_HOL_Ozero__class_Ozero(tc_nat),A). [copy(820),flip(b)].
% 5.37/5.63 852 -class_HOL_Ozero(A) | c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_monom__eq__0_0) # label(axiom). [assumption].
% 5.37/5.63 868 v_p != c_Polynomial_OpCons(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) | v_thesis____ | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) # label(cls_that_0) # label(axiom). [assumption].
% 5.37/5.63 869 c_Polynomial_OpCons(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != v_p | v_thesis____ | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [copy(868),flip(a),flip(c)].
% 5.37/5.63 870 v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) # label(cls_pe_0) # label(axiom). [assumption].
% 5.37/5.63 871 c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p. [copy(870),flip(a)].
% 5.37/5.63 873 c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_CHAINED_0_01) # label(axiom). [assumption].
% 5.37/5.63 874 -v_thesis____ # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 5.37/5.63 880 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 5.37/5.63 900 class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) # label(axiom). [assumption].
% 5.37/5.63 901 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 5.37/5.63 907 class_HOL_Ozero(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__HOL_Ozero) # label(axiom). [assumption].
% 5.37/5.63 1794 c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C. [resolve(487,a,489,a)].
% 5.37/5.63 1854 c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(554,a,555,a)].
% 5.37/5.63 1866 c_Polynomial_OpCons(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != v_p | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [back_unit_del(869),unit_del(b,874)].
% 5.37/5.63 1984 c_HOL_Oplus__class_Oplus(A,B,tc_nat) = c_HOL_Oplus__class_Oplus(B,A,tc_nat). [resolve(880,a,700,a)].
% 5.37/5.63 2004 c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,A,tc_nat) | C = B. [back_rewrite(1794),rewrite([1984(4)]),flip(a)].
% 5.37/5.63 2332 c_Polynomial_Osmult(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(900,a,804,a)].
% 5.37/5.63 2336 c_Polynomial_Odegree(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Polynomial_Osynthetic__div(A,B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(900,a,761,a)].
% 5.37/5.63 2341 c_HOL_Oplus__class_Oplus(A,c_Polynomial_Osmult(B,c_Polynomial_Osynthetic__div(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(c_Polynomial_Opoly(A,B,tc_Complex_Ocomplex),c_Polynomial_Osynthetic__div(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(900,a,732,a)].
% 5.37/5.63 2365 c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A. [resolve(901,a,818,a)].
% 5.37/5.63 2406 c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(907,a,852,a)].
% 5.37/5.63 2409 c_Polynomial_OpCons(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Omonom(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex). [resolve(907,a,821,a)].
% 5.37/5.63 2423 c_Polynomial_Omonom(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) != v_p | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [back_rewrite(1866),rewrite([2409(5)])].
% 5.37/5.63 7181 A != B | B = A. [para(1854(a,1),2004(a,2)),rewrite([1984(4),1854(4)])].
% 5.37/5.63 17527 c_Polynomial_Osynthetic__div(v_p,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(2336,a,873,a)].
% 5.37/5.63 17576 c_Polynomial_Omonom(c_Polynomial_Opoly(v_p,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = v_p. [para(17527(a,1),2341(a,1,2,2)),rewrite([2332(6),2365(7),17527(7),2409(9)]),flip(a)].
% 5.37/5.63 17586 c_Polynomial_Opoly(v_p,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(17576,a,2423,a),flip(a)].
% 5.37/5.63 17593 $F. [resolve(17576,a,7181,a(flip)),rewrite([17586(3),2406(6)]),unit_del(a,871)].
% 5.37/5.63
% 5.37/5.63 % SZS output end Refutation
% 5.37/5.63 ============================== end of proof ==========================
% 5.37/5.63
% 5.37/5.63 ============================== STATISTICS ============================
% 5.37/5.63
% 5.37/5.63 Given=3240. Generated=97991. Kept=16662. proofs=1.
% 5.37/5.63 Usable=2981. Sos=9999. Demods=1869. Limbo=7, Disabled=5269. Hints=0.
% 5.37/5.63 Megabytes=24.06.
% 5.37/5.63 User_CPU=4.41, System_CPU=0.07, Wall_clock=5.
% 5.37/5.63
% 5.37/5.63 ============================== end of statistics =====================
% 5.37/5.63
% 5.37/5.63 ============================== end of search =========================
% 5.37/5.63
% 5.37/5.63 THEOREM PROVED
% 5.37/5.63 % SZS status Unsatisfiable
% 5.37/5.63
% 5.37/5.63 Exiting with 1 proof.
% 5.37/5.63
% 5.37/5.63 Process 9766 exit (max_proofs) Thu Jun 9 01:34:43 2022
% 5.37/5.63 Prover9 interrupted
%------------------------------------------------------------------------------