TSTP Solution File: SWV628-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV628-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:14:10 EDT 2022
% Result : Timeout 300.06s 300.30s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV628-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 23:23:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.42/1.67 ============================== Prover9 ===============================
% 1.42/1.67 Prover9 (32) version 2009-11A, November 2009.
% 1.42/1.67 Process 4001 was started by sandbox on n010.cluster.edu,
% 1.42/1.67 Wed Jun 15 23:23:40 2022
% 1.42/1.67 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3847_n010.cluster.edu".
% 1.42/1.67 ============================== end of head ===========================
% 1.42/1.67
% 1.42/1.67 ============================== INPUT =================================
% 1.42/1.67
% 1.42/1.67 % Reading from file /tmp/Prover9_3847_n010.cluster.edu
% 1.42/1.67
% 1.42/1.67 set(prolog_style_variables).
% 1.42/1.67 set(auto2).
% 1.42/1.67 % set(auto2) -> set(auto).
% 1.42/1.67 % set(auto) -> set(auto_inference).
% 1.42/1.67 % set(auto) -> set(auto_setup).
% 1.42/1.67 % set(auto_setup) -> set(predicate_elim).
% 1.42/1.67 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.42/1.67 % set(auto) -> set(auto_limits).
% 1.42/1.67 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.42/1.67 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.42/1.67 % set(auto) -> set(auto_denials).
% 1.42/1.67 % set(auto) -> set(auto_process).
% 1.42/1.67 % set(auto2) -> assign(new_constants, 1).
% 1.42/1.67 % set(auto2) -> assign(fold_denial_max, 3).
% 1.42/1.67 % set(auto2) -> assign(max_weight, "200.000").
% 1.42/1.67 % set(auto2) -> assign(max_hours, 1).
% 1.42/1.67 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.42/1.67 % set(auto2) -> assign(max_seconds, 0).
% 1.42/1.67 % set(auto2) -> assign(max_minutes, 5).
% 1.42/1.67 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.42/1.67 % set(auto2) -> set(sort_initial_sos).
% 1.42/1.67 % set(auto2) -> assign(sos_limit, -1).
% 1.42/1.67 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.42/1.67 % set(auto2) -> assign(max_megs, 400).
% 1.42/1.67 % set(auto2) -> assign(stats, some).
% 1.42/1.67 % set(auto2) -> clear(echo_input).
% 1.42/1.67 % set(auto2) -> set(quiet).
% 1.42/1.67 % set(auto2) -> clear(print_initial_clauses).
% 1.42/1.67 % set(auto2) -> clear(print_given).
% 1.42/1.67 assign(lrs_ticks,-1).
% 1.42/1.67 assign(sos_limit,10000).
% 1.42/1.67 assign(order,kbo).
% 1.42/1.67 set(lex_order_vars).
% 1.42/1.67 clear(print_given).
% 1.42/1.67
% 1.42/1.67 % formulas(sos). % not echoed (1573 formulas)
% 1.42/1.67
% 1.42/1.67 ============================== end of input ==========================
% 1.42/1.67
% 1.42/1.67 % From the command line: assign(max_seconds, 300).
% 1.42/1.67
% 1.42/1.67 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.42/1.67
% 1.42/1.67 % Formulas that are not ordinary clauses:
% 1.42/1.67
% 1.42/1.67 ============================== end of process non-clausal formulas ===
% 1.42/1.67
% 1.42/1.67 ============================== PROCESS INITIAL CLAUSES ===============
% 1.42/1.67
% 1.42/1.67 ============================== PREDICATE ELIMINATION =================
% 1.42/1.67 1 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 1.42/1.67 2 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 1.42/1.67 3 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 1.42/1.67 4 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 1.42/1.67 5 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 1.42/1.67 6 -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].
% 1.42/1.67 7 -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].
% 1.42/1.67 8 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 1.42/1.67 9 -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].
% 1.42/1.67 10 -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].
% 1.42/1.67 11 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,B,A),A) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 1.42/1.67 12 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 1.42/1.67 13 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 1.42/1.67 14 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 1.42/1.67 15 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 1.42/1.67 16 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 1.42/1.67 17 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 1.42/1.67 18 -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].
% 1.42/1.67 19 -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].
% 1.42/1.67 20 -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].
% 1.42/1.67 21 -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].
% 1.42/1.67 22 -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].
% 1.42/1.67 23 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 1.42/1.67 24 -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].
% 1.42/1.67 25 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 1.42/1.67 26 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 1.42/1.67 27 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 1.42/1.67 28 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 1.42/1.67 29 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 1.42/1.67 30 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 1.42/1.67 31 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Omonoid__mult(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__even__power_0) # label(axiom). [assumption].
% 1.42/1.67 32 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,C,A),c_HOL_Otimes__class_Otimes(B,B,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 1.42/1.67 33 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 1.42/1.67 34 -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].
% 1.42/1.67 35 -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].
% 1.42/1.67 36 -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].
% 1.42/1.67 37 -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].
% 1.42/1.67 38 -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].
% 1.42/1.67 39 -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].
% 1.42/1.67 40 -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].
% 1.42/1.67 41 -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].
% 1.42/1.67 42 -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].
% 1.42/1.67 43 -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].
% 1.42/1.67 44 -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].
% 1.42/1.67 45 -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].
% 1.42/1.67 46 -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].
% 1.42/1.67 47 -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].
% 1.42/1.67 48 -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].
% 1.42/1.67 49 -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].
% 1.42/1.67 50 -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].
% 1.42/1.67 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,2,a)].
% 1.42/1.67 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,3,a)].
% 1.42/1.67 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,4,a)].
% 1.42/1.67 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,5,a)].
% 1.42/1.67 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(1,a,6,a)].
% 1.42/1.67 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(1,a,7,a)].
% 1.42/1.67 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,8,a)].
% 1.42/1.67 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,9,a)].
% 1.42/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,10,a)].
% 1.42/1.67 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,11,a)].
% 1.42/1.67 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(1,a,12,a)].
% 1.42/1.67 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,13,a)].
% 1.42/1.67 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,14,a)].
% 1.42/1.67 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,15,a)].
% 1.42/1.67 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,16,a)].
% 1.42/1.67 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,17,a)].
% 1.42/1.67 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(1,a,18,a)].
% 1.42/1.67 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,19,a)].
% 1.42/1.67 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,20,a)].
% 1.42/1.67 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,21,a)].
% 1.42/1.67 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,22,a)].
% 1.42/1.67 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(1,a,23,a)].
% 1.42/1.67 Derived: -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,24,a)].
% 1.42/1.67 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(1,a,25,a)].
% 1.42/1.67 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,26,a)].
% 1.42/1.67 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(1,a,27,a)].
% 1.42/1.67 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(1,a,28,a)].
% 1.45/1.68 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,29,a)].
% 1.45/1.68 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,30,a)].
% 1.45/1.68 Derived: -class_OrderedGroup_Omonoid__mult(tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(1,a,31,a)].
% 1.45/1.68 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,32,a)].
% 1.45/1.68 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,33,a)].
% 1.45/1.68 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(1,a,34,a)].
% 1.45/1.68 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(1,a,35,a)].
% 1.45/1.68 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,36,a)].
% 1.45/1.68 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(1,a,37,a)].
% 1.45/1.68 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,39,a)].
% 1.45/1.68 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(1,a,40,a)].
% 1.45/1.68 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(1,a,43,a)].
% 1.45/1.68 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,45,a)].
% 1.45/1.68 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(1,a,46,a)].
% 1.45/1.68 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,47,a)].
% 1.54/1.79 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,48,a)].
% 1.54/1.79 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,49,a)].
% 1.54/1.79 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(1,a,50,a)].
% 1.54/1.79 51 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.54/1.79 52 -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].
% 1.54/1.79 53 -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].
% 1.54/1.79 54 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1__if_0) # label(axiom). [assumption].
% 1.54/1.79 55 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,E,A),A) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(E,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__mult__div__if__dvd_0) # label(axiom). [assumption].
% 1.54/1.79 56 -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].
% 1.54/1.79 57 -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].
% 1.54/1.79 58 -class_Divides_Osemiring__div(A) | B = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A) # label(cls_mod__div__decomp_0) # label(axiom). [assumption].
% 1.54/1.79 59 -class_Divides_Osemiring__div(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A) = B # label(cls_mod__div__equality_0) # label(axiom). [assumption].
% 1.54/1.79 60 -class_Divides_Osemiring__div(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A),c_Divides_Odiv__class_Omod(C,B,A),A) = C # label(cls_mod__div__equality2_0) # label(axiom). [assumption].
% 1.54/1.79 61 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2__is__id_0) # label(axiom). [assumption].
% 1.54/1.79 62 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),B,A) = C | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1__is__id_0) # label(axiom). [assumption].
% 1.54/1.79 63 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_Divides_Odiv__class_Odiv(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1_0) # label(axiom). [assumption].
% 1.54/1.79 64 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) = c_Divides_Odiv__class_Odiv(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult2_0) # label(axiom). [assumption].
% 1.54/1.79 65 -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].
% 1.54/1.79 66 -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].
% 1.54/1.79 67 -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].
% 1.54/1.79 68 -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].
% 1.54/1.79 69 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,D,A),c_Divides_Odiv__class_Odiv(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,A) # label(cls_div__add_0) # label(axiom). [assumption].
% 1.54/1.79 70 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,D,A),c_Divides_Odiv__class_Odiv(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,A) # label(cls_div__dvd__div_0) # label(axiom). [assumption].
% 1.54/1.79 71 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__dvd__div_1) # label(axiom). [assumption].
% 1.54/1.79 72 -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].
% 1.54/1.79 73 -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].
% 1.54/1.79 74 -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].
% 1.54/1.79 75 -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].
% 1.54/1.79 76 -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].
% 1.54/1.79 77 -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].
% 1.54/1.79 78 -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].
% 1.54/1.79 79 -class_Divides_Osemiring__div(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A),D,A) = c_HOL_Oplus__class_Oplus(B,D,A) # label(cls_div__mod__equality_0) # label(axiom). [assumption].
% 1.54/1.79 80 -class_Divides_Osemiring__div(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A),c_Divides_Odiv__class_Omod(C,B,A),A),D,A) = c_HOL_Oplus__class_Oplus(C,D,A) # label(cls_div__mod__equality2_0) # label(axiom). [assumption].
% 1.54/1.79 81 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__div__trivial_0) # label(axiom). [assumption].
% 1.54/1.79 82 -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].
% 1.54/1.79 83 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),D,A) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__mult_0) # label(axiom). [assumption].
% 1.54/1.79 84 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),D,A) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(B,D,A),A) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1_0) # label(axiom). [assumption].
% 1.54/1.79 85 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),C,A) = c_HOL_Oplus__class_Oplus(D,c_Divides_Odiv__class_Odiv(B,C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2_0) # label(axiom). [assumption].
% 1.54/1.79 86 -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].
% 1.54/1.79 87 -class_Divides_Osemiring__div(A) | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(B,C,A),D,A) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__power_0) # label(axiom). [assumption].
% 1.54/1.79 88 -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].
% 1.54/1.79 89 -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].
% 1.54/1.79 90 -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].
% 1.54/1.79 91 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A) = C | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mult__div__cancel_0) # label(axiom). [assumption].
% 1.54/1.79 92 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A) = B | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__mult__self_0) # label(axiom). [assumption].
% 1.54/1.79 93 -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].
% 1.54/1.79 94 -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].
% 1.54/1.79 95 -class_Int_Onumber(A) | -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_dvd__eq__mod__eq__0__number__of_0) # label(axiom). [assumption].
% 1.54/1.79 96 -class_Int_Onumber(A) | -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) != c_HOL_Ozero__class_Ozero(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_dvd__eq__mod__eq__0__number__of_1) # label(axiom). [assumption].
% 1.54/1.79 97 -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].
% 1.54/1.79 98 -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].
% 1.54/1.79 99 -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].
% 1.54/1.79 100 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__by__0_0) # label(axiom). [assumption].
% 1.54/1.79 101 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__0_0) # label(axiom). [assumption].
% 1.54/1.79 102 -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].
% 1.54/1.79 103 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,C,A),c_HOL_Oone__class_Oone(A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self2_0) # label(axiom). [assumption].
% 1.54/1.79 104 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,A),B,A) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(C,B,A),c_HOL_Oone__class_Oone(A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self1_0) # label(axiom). [assumption].
% 1.54/1.79 105 -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].
% 1.54/1.79 106 -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].
% 1.54/1.79 107 -class_Divides_Osemiring__div(A) | c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,A),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),A) = B # label(cls_semiring__div__class_Omod__div__equality_H_0) # label(axiom). [assumption].
% 1.54/1.79 108 -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].
% 1.54/1.79 109 -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].
% 1.54/1.79 110 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_div__by__1_0) # label(axiom). [assumption].
% 1.54/1.79 111 -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].
% 1.54/1.79 112 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__self_0) # label(axiom). [assumption].
% 1.54/1.79 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(51,a,52,a)].
% 1.54/1.79 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(51,a,53,a)].
% 1.54/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,54,a)].
% 1.54/1.79 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_Divides_Odiv__class_Odiv(C,D,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,D,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(51,a,55,a)].
% 1.54/1.79 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(51,a,56,a)].
% 1.54/1.79 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(51,a,57,a)].
% 1.54/1.79 Derived: A = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat),tc_nat). [resolve(51,a,58,a)].
% 1.54/1.79 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat),tc_nat) = A. [resolve(51,a,59,a)].
% 1.54/1.79 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(B,A,tc_nat),tc_nat) = B. [resolve(51,a,60,a)].
% 1.54/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat) = A | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,61,a)].
% 1.54/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat) = B | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,62,a)].
% 1.54/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(B,C,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,63,a)].
% 1.54/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(A,C,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,64,a)].
% 1.54/1.79 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(51,a,65,a)].
% 1.54/1.79 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(51,a,66,a)].
% 1.54/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,C,tc_nat),c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat). [resolve(51,a,69,a)].
% 1.54/1.79 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,C,tc_nat),c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat). [resolve(51,a,70,a)].
% 1.54/1.79 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_Divides_Odiv__class_Odiv(C,B,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(51,a,71,a)].
% 1.54/1.79 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(51,a,72,a)].
% 1.54/1.79 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(51,a,73,a)].
% 1.54/1.79 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(51,a,74,a)].
% 1.54/1.79 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(51,a,75,a)].
% 1.54/1.79 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(51,a,76,a)].
% 1.54/1.79 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(51,a,77,a)].
% 1.54/1.79 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(51,a,78,a)].
% 1.54/1.79 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat),tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(A,C,tc_nat). [resolve(51,a,79,a)].
% 1.54/1.79 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(B,A,tc_nat),tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(B,C,tc_nat). [resolve(51,a,80,a)].
% 1.54/1.79 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,81,a)].
% 1.54/1.79 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(51,a,82,a)].
% 1.54/1.79 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_nat),B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(51,a,83,a)].
% 1.54/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Odiv(A,C,tc_nat),tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,84,a)].
% 1.54/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),B,tc_nat) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(A,B,tc_nat),tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,85,a)].
% 1.54/1.79 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(51,a,86,a)].
% 1.54/1.79 Derived: c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(51,a,87,a)].
% 1.54/1.80 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(51,a,88,a)].
% 1.54/1.80 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(51,a,89,a)].
% 1.54/1.80 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(51,a,90,a)].
% 1.54/1.80 Derived: c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat) = B | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat). [resolve(51,a,91,a)].
% 1.54/1.80 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat) = A | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(51,a,92,a)].
% 1.54/1.80 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(51,a,93,a)].
% 1.54/1.80 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(51,a,94,a)].
% 1.54/1.80 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(51,a,97,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,98,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(51,a,99,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,100,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,101,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,102,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,103,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,A,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,104,a)].
% 1.54/1.80 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(51,a,105,a)].
% 1.54/1.80 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(51,a,106,a)].
% 1.54/1.80 Derived: c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_nat),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat),tc_nat) = A. [resolve(51,a,107,a)].
% 1.54/1.80 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(51,a,108,a)].
% 1.54/1.80 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(51,a,109,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(51,a,110,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,111,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(51,a,112,a)].
% 1.54/1.80 113 class_Divides_Osemiring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(113,a,52,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),A,tc_Int_Oint) = c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint). [resolve(113,a,53,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,54,a)].
% 1.54/1.80 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),c_Divides_Odiv__class_Odiv(C,D,tc_Int_Oint),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(113,a,55,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint). [resolve(113,a,56,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),C,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(113,a,57,a)].
% 1.54/1.80 Derived: A = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(113,a,58,a)].
% 1.54/1.80 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),tc_Int_Oint) = A. [resolve(113,a,59,a)].
% 1.54/1.80 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint),tc_Int_Oint),c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint),tc_Int_Oint) = B. [resolve(113,a,60,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),B,tc_Int_Oint) = A | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,61,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),A,tc_Int_Oint) = B | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,62,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,63,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,64,a)].
% 1.54/1.80 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(113,a,65,a)].
% 1.54/1.80 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(113,a,66,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint),c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Int_Oint). [resolve(113,a,69,a)].
% 1.54/1.80 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint),c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Int_Oint). [resolve(113,a,70,a)].
% 1.54/1.80 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),c_Divides_Odiv__class_Odiv(C,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(113,a,71,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(113,a,72,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(113,a,73,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),C,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(113,a,74,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(113,a,75,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(113,a,76,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint). [resolve(113,a,77,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(113,a,78,a)].
% 1.54/1.80 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint). [resolve(113,a,79,a)].
% 1.54/1.80 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint),tc_Int_Oint),c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint). [resolve(113,a,80,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,81,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(113,a,82,a)].
% 1.54/1.80 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(113,a,83,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint),tc_Int_Oint) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,84,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,85,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(D,A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(113,a,86,a)].
% 1.54/1.80 Derived: c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(113,a,87,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(D,A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(113,a,88,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(113,a,89,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint). [resolve(113,a,90,a)].
% 1.54/1.80 Derived: c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint),tc_Int_Oint) = B | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(113,a,91,a)].
% 1.54/1.80 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint) = A | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(113,a,92,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(113,a,93,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint). [resolve(113,a,94,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint). [resolve(113,a,97,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,98,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(113,a,99,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,100,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,101,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,102,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,103,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,104,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,105,a)].
% 1.54/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,106,a)].
% 1.75/1.98 Derived: c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint),tc_Int_Oint) = A. [resolve(113,a,107,a)].
% 1.75/1.98 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(113,a,108,a)].
% 1.75/1.98 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(113,a,109,a)].
% 1.75/1.98 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(113,a,110,a)].
% 1.75/1.98 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,111,a)].
% 1.75/1.98 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(113,a,112,a)].
% 1.75/1.98 114 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.75/1.98 115 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | B = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(C,A),A) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of1_3) # label(axiom). [assumption].
% 1.75/1.98 116 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(C,A),A) = B | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_3) # label(axiom). [assumption].
% 1.75/1.98 117 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A) # label(cls_mult__frac__frac_0) # label(axiom). [assumption].
% 1.75/1.98 118 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(C,B,A) # label(cls_inverse__divide_0) # label(axiom). [assumption].
% 1.75/1.98 119 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__divide_0) # label(axiom). [assumption].
% 1.75/1.98 120 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(C,B,A),B,A) # label(cls_eq__divide__imp_0) # label(axiom). [assumption].
% 1.75/1.98 121 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(C,B,A),B,A) = C # label(cls_divide__eq__imp_0) # label(axiom). [assumption].
% 1.75/1.98 122 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom). [assumption].
% 1.75/1.98 123 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom). [assumption].
% 1.75/1.98 124 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) != c_Int_Onumber__class_Onumber__of(C,A) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_1) # label(axiom). [assumption].
% 1.75/1.98 125 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(C,c_HOL_Ozero__class_Ozero(A),A) = c_Int_Onumber__class_Onumber__of(B,A) # label(cls_divide__eq__eq__number__of_2) # label(axiom). [assumption].
% 1.75/1.98 126 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_eq__divide__eq__number__of1_4) # label(axiom). [assumption].
% 1.75/1.98 127 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Oinverse__class_Odivide(C,D,A) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A) = C | D = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_0) # label(axiom). [assumption].
% 1.75/1.98 128 -class_Ring__and__Field_Ofield(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A),c_HOL_Otimes__class_Otimes(C,E,A),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__frac__eq_0) # label(axiom). [assumption].
% 1.75/1.98 129 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),C,A) # label(cls_eq__divide__eq__number__of_4) # label(axiom). [assumption].
% 1.75/1.98 130 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_diff__divide__distrib_0) # label(axiom). [assumption].
% 1.75/1.98 131 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Oinverse__class_Odivide(C,c_HOL_Ozero__class_Ozero(A),A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_1) # label(axiom). [assumption].
% 1.75/1.98 132 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Oinverse__class_Odivide(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_eq__divide__eq__number__of_2) # label(axiom). [assumption].
% 1.75/1.98 133 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_eq__divide__eq__number__of1_2) # label(axiom). [assumption].
% 1.75/1.98 134 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Oinverse(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_inverse__eq__divide_0) # label(axiom). [assumption].
% 1.75/1.98 135 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_class__fieldgb_Oinverse__divide_0) # label(axiom). [assumption].
% 1.75/1.98 136 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oinverse__class_Oinverse(B,A),A),c_HOL_Oinverse__class_Oinverse(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__add_0) # label(axiom). [assumption].
% 1.75/1.98 137 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(D,C,A),A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom). [assumption].
% 1.75/1.98 138 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oinverse__class_Odivide(C,D,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(C,c_HOL_Otimes__class_Otimes(B,D,A),A),D,A) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom). [assumption].
% 1.75/1.98 139 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A) # label(cls_inverse__mult__distrib_0) # label(axiom). [assumption].
% 1.75/1.98 140 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),C,A) = c_Int_Onumber__class_Onumber__of(B,A) # label(cls_divide__eq__eq__number__of_4) # label(axiom). [assumption].
% 1.75/1.98 141 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),C,A) # label(cls_power__one__over_0) # label(axiom). [assumption].
% 1.75/1.98 142 -class_Ring__and__Field_Ofield(A) | c_Power_Opower__class_Opower(B,c_HOL_Ominus__class_Ominus(C,D,tc_nat),A) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(D,C,tc_nat) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__diff_0) # label(axiom). [assumption].
% 1.75/1.98 143 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_3) # label(axiom). [assumption].
% 1.75/1.98 144 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | B = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(C,A),A) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_0) # label(axiom). [assumption].
% 1.75/1.98 145 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(C,A),A) = B | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of1_0) # label(axiom). [assumption].
% 1.75/1.98 146 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),B,A) # label(cls_eq__divide__eq_4) # label(axiom). [assumption].
% 1.75/1.98 147 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),C,A) = c_Int_Onumber__class_Onumber__of(B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_3) # label(axiom). [assumption].
% 1.75/1.98 148 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A),c_HOL_Otimes__class_Otimes(C,E,A),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom). [assumption].
% 1.75/1.98 149 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom). [assumption].
% 1.75/1.98 150 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom). [assumption].
% 1.75/1.98 151 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) = c_HOL_Oinverse__class_Odivide(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom). [assumption].
% 1.75/1.98 152 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oinverse__class_Odivide(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom). [assumption].
% 1.75/1.98 153 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_mult__frac__num_0) # label(axiom). [assumption].
% 1.75/1.98 154 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(B,D,A),c_HOL_Oinverse__class_Odivide(C,D,A),A) # label(cls_add__divide__distrib_0) # label(axiom). [assumption].
% 1.75/1.98 155 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_4) # label(axiom). [assumption].
% 1.75/1.98 156 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_1) # label(axiom). [assumption].
% 1.75/1.98 157 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_Int_Onumber__class_Onumber__of(D,A) | B = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(D,A),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_0) # label(axiom). [assumption].
% 1.75/1.98 158 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(C,A),A) # label(cls_divide__inverse_0) # label(axiom). [assumption].
% 1.75/1.98 159 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(C,A),A) # label(cls_class__fieldgb_Odivide__inverse_0) # label(axiom). [assumption].
% 1.75/1.98 160 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(B,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_inverse__eq__divide__number__of_0) # label(axiom). [assumption].
% 1.75/1.98 161 -class_Ring__and__Field_Ofield(A) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__divide_0) # label(axiom). [assumption].
% 1.75/1.98 162 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_eq__divide__eq_2) # label(axiom). [assumption].
% 1.75/1.98 163 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom). [assumption].
% 1.75/1.98 164 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom). [assumption].
% 1.75/1.98 165 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom). [assumption].
% 1.75/1.98 166 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom). [assumption].
% 1.75/1.98 167 -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__inverse_0) # label(axiom). [assumption].
% 1.75/1.98 168 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Oinverse(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__divide_0) # label(axiom). [assumption].
% 1.75/1.98 169 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oinverse__class_Odivide(D,E,A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | c_HOL_Otimes__class_Otimes(B,E,A) = c_HOL_Otimes__class_Otimes(D,C,A) # label(cls_frac__eq__eq_0) # label(axiom). [assumption].
% 1.75/1.98 170 -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Otimes__class_Otimes(D,E,A) | C = c_HOL_Ozero__class_Ozero(A) | E = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,E,A) = c_HOL_Oinverse__class_Odivide(D,C,A) # label(cls_frac__eq__eq_1) # label(axiom). [assumption].
% 1.75/1.98 171 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom). [assumption].
% 1.75/1.98 172 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_1) # label(axiom). [assumption].
% 1.75/1.98 173 -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].
% 1.75/1.98 174 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oone__class_Oone(A) | B = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_0) # label(axiom). [assumption].
% 1.75/1.98 175 -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].
% 1.75/1.98 176 -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].
% 1.75/1.98 177 -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].
% 1.75/1.98 178 -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].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | A = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,115,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,116,a)].
% 1.75/1.98 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(114,a,117,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,A,tc_Complex_Ocomplex). [resolve(114,a,118,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(114,a,119,a)].
% 1.75/1.98 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(114,a,120,a)].
% 1.75/1.98 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(114,a,121,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,124,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex). [resolve(114,a,125,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(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),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(114,a,126,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = B | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,127,a)].
% 1.75/1.98 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(114,a,128,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(114,a,129,a)].
% 1.75/1.98 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(114,a,130,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,131,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(114,a,132,a)].
% 1.75/1.98 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(114,a,133,a)].
% 1.75/1.98 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(114,a,134,a)].
% 1.75/1.98 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,136,a)].
% 1.75/1.98 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(114,a,137,a)].
% 1.75/1.99 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(114,a,138,a)].
% 1.75/1.99 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(114,a,139,a)].
% 1.75/1.99 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex). [resolve(114,a,140,a)].
% 1.75/1.99 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(114,a,141,a)].
% 1.75/1.99 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_lessequals(C,B,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,142,a)].
% 1.75/1.99 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | A = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,144,a)].
% 1.75/1.99 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,145,a)].
% 1.75/1.99 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(114,a,146,a)].
% 1.75/1.99 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(114,a,148,a)].
% 1.75/1.99 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(114,a,149,a)].
% 1.75/1.99 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(114,a,150,a)].
% 1.75/1.99 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(114,a,151,a)].
% 1.75/1.99 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(114,a,152,a)].
% 1.75/1.99 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(114,a,153,a)].
% 1.75/1.99 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(114,a,154,a)].
% 1.75/1.99 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,155,a)].
% 1.75/1.99 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,156,a)].
% 1.75/1.99 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex) | A = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,157,a)].
% 1.75/1.99 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(114,a,158,a)].
% 1.75/1.99 Derived: c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,161,a)].
% 1.75/1.99 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(114,a,162,a)].
% 1.75/1.99 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(114,a,163,a)].
% 1.75/1.99 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(114,a,164,a)].
% 1.84/2.09 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(114,a,165,a)].
% 1.84/2.09 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(114,a,167,a)].
% 1.84/2.09 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(114,a,169,a)].
% 1.84/2.09 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(114,a,170,a)].
% 1.84/2.09 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(114,a,171,a)].
% 1.84/2.09 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(114,a,172,a)].
% 1.84/2.09 Derived: c_HOL_Oinverse__class_Odivide(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(114,a,173,a)].
% 1.84/2.09 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(114,a,174,a)].
% 1.84/2.09 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(114,a,175,a)].
% 1.84/2.09 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(114,a,176,a)].
% 1.84/2.09 179 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.84/2.09 180 -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].
% 1.84/2.09 181 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.84/2.09 182 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 1.84/2.09 183 -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_Power_Opower__class_Opower(B,C,A),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 1.84/2.09 184 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 1.84/2.09 185 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),A),A) # label(cls_of__nat__fact__gt__zero_0) # label(axiom). [assumption].
% 1.84/2.09 186 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 1.84/2.09 187 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 1.84/2.09 188 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 1.84/2.09 189 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) != c_Power_Opower__class_Opower(D,c_Suc(C),A) | B = D | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 1.84/2.09 190 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 1.84/2.09 191 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) | -c_lessequals(C,D,tc_nat) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 1.84/2.09 192 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_lessequals(B,C,tc_nat) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 1.84/2.09 193 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 1.84/2.09 194 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),A),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.84/2.09 195 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 1.84/2.09 196 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 1.84/2.09 197 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.84/2.09 198 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(D,C,tc_nat) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 1.84/2.09 199 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(B,D,A) # label(cls_power__mono_0) # label(axiom). [assumption].
% 1.84/2.09 200 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 1.84/2.09 201 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 1.84/2.09 202 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.84/2.09 203 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.84/2.09 204 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(D,C,A) | B = D | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 1.84/2.09 205 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.84/2.09 206 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.84/2.09 207 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),A),A) # label(cls_of__nat__fact__ge__zero_0) # label(axiom). [assumption].
% 1.84/2.09 208 -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].
% 1.84/2.09 209 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,c_Suc(C),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.84/2.09 210 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.84/2.09 211 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_nat) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.84/2.09 212 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_Power_Opower__class_Opower(B,c_Suc(D),A),c_Power_Opower__class_Opower(C,c_Suc(D),A),A) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 1.84/2.09 213 -class_Ring__and__Field_Oordered__semidom(A) | 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(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.84/2.09 214 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.84/2.09 215 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.84/2.09 216 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.84/2.09 217 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.84/2.09 218 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.84/2.09 219 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.84/2.09 220 -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].
% 1.84/2.09 221 -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].
% 1.84/2.09 222 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.84/2.09 223 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.84/2.09 224 -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].
% 1.84/2.09 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(179,a,180,a)].
% 1.84/2.09 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(179,a,181,a)].
% 1.84/2.09 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(179,a,182,a)].
% 1.84/2.09 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(179,a,183,a)].
% 1.84/2.09 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat). [resolve(179,a,184,a)].
% 1.84/2.09 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_nat),tc_nat). [resolve(179,a,185,a)].
% 1.84/2.09 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(C,A,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(179,a,186,a)].
% 1.84/2.09 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_lessequals(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(179,a,188,a)].
% 1.84/2.09 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_nat) | A = C | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(179,a,189,a)].
% 1.84/2.09 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(179,a,190,a)].
% 1.84/2.09 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(179,a,191,a)].
% 1.84/2.09 Derived: c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(179,a,192,a)].
% 1.84/2.09 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(179,a,193,a)].
% 1.84/2.09 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(179,a,194,a)].
% 1.84/2.09 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(179,a,195,a)].
% 1.84/2.09 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(179,a,196,a)].
% 1.84/2.09 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(179,a,197,a)].
% 1.84/2.09 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(179,a,198,a)].
% 1.84/2.09 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(179,a,199,a)].
% 1.84/2.09 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(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_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(179,a,200,a)].
% 1.84/2.09 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(179,a,201,a)].
% 1.84/2.09 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(179,a,202,a)].
% 1.84/2.09 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(179,a,203,a)].
% 1.84/2.10 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(C,B,tc_nat) | A = C | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(179,a,204,a)].
% 1.84/2.10 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(179,a,205,a)].
% 1.84/2.10 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(179,a,208,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(179,a,209,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(179,a,210,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(179,a,211,a)].
% 1.84/2.10 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_nat),c_Power_Opower__class_Opower(B,c_Suc(C),tc_nat),tc_nat). [resolve(179,a,212,a)].
% 1.84/2.10 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),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(179,a,213,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(179,a,214,a)].
% 1.84/2.10 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | B = C. [resolve(179,a,215,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(179,a,216,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(179,a,217,a)].
% 1.84/2.10 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(179,a,220,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(179,a,221,a)].
% 1.84/2.10 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(179,a,222,a)].
% 1.84/2.10 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(179,a,223,a)].
% 1.84/2.10 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(179,a,224,a)].
% 1.84/2.10 225 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(225,a,180,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(225,a,181,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,182,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,183,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(225,a,184,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_Int_Oint),tc_Int_Oint). [resolve(225,a,185,a)].
% 1.84/2.10 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(C,A,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),C,tc_Int_Oint). [resolve(225,a,186,a)].
% 1.84/2.10 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,188,a)].
% 1.84/2.10 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_Int_Oint) | A = C | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,189,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,190,a)].
% 1.84/2.10 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,C,tc_nat). [resolve(225,a,191,a)].
% 1.84/2.10 Derived: c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_nat). [resolve(225,a,192,a)].
% 1.84/2.10 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint). [resolve(225,a,193,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,194,a)].
% 1.84/2.10 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,195,a)].
% 1.84/2.10 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,196,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(225,a,197,a)].
% 1.84/2.10 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(C,B,tc_nat). [resolve(225,a,198,a)].
% 1.84/2.10 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(225,a,199,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,200,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(225,a,201,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,202,a)].
% 1.84/2.10 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(225,a,203,a)].
% 1.84/2.10 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_Power_Opower__class_Opower(C,B,tc_Int_Oint) | A = C | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,204,a)].
% 1.84/2.10 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint). [resolve(225,a,205,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,208,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(225,a,209,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint). [resolve(225,a,210,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(225,a,211,a)].
% 1.84/2.10 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_Int_Oint),c_Power_Opower__class_Opower(B,c_Suc(C),tc_Int_Oint),tc_Int_Oint). [resolve(225,a,212,a)].
% 1.84/2.10 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_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint). [resolve(225,a,213,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(225,a,214,a)].
% 1.84/2.10 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_Power_Opower__class_Opower(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | B = C. [resolve(225,a,215,a)].
% 1.84/2.10 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),C,tc_Int_Oint). [resolve(225,a,216,a)].
% 1.89/2.16 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(225,a,217,a)].
% 1.89/2.16 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(225,a,220,a)].
% 1.89/2.16 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(225,a,221,a)].
% 1.89/2.16 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(225,a,222,a)].
% 1.89/2.16 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(225,a,223,a)].
% 1.89/2.16 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(225,a,224,a)].
% 1.89/2.16 226 class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 1.89/2.16 227 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_3) # label(axiom). [assumption].
% 1.89/2.16 228 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_2) # label(axiom). [assumption].
% 1.89/2.16 229 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_1) # label(axiom). [assumption].
% 1.89/2.16 230 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_0) # label(axiom). [assumption].
% 1.89/2.16 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(226,a,227,a)].
% 1.89/2.16 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(226,a,228,a)].
% 1.89/2.16 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(226,a,229,a)].
% 1.89/2.16 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(226,a,230,a)].
% 1.94/2.21 231 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 1.94/2.21 232 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_abs__mult_0) # label(axiom). [assumption].
% 1.94/2.21 233 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__le__zero__eq_4) # label(axiom). [assumption].
% 1.94/2.21 234 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__less__zero__eq_2) # label(axiom). [assumption].
% 1.94/2.21 235 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_1) # label(axiom). [assumption].
% 1.94/2.21 236 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_lessequals(B,D,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__odd_0) # label(axiom). [assumption].
% 1.94/2.21 237 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A),A) # label(cls_zero__less__power__eq__number__of_3) # label(axiom). [assumption].
% 1.94/2.21 238 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(D,A),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__even_0) # label(axiom). [assumption].
% 1.94/2.21 239 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 1.94/2.21 240 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__less__0__iff_0) # label(axiom). [assumption].
% 1.94/2.21 241 -class_Ring__and__Field_Oordered__idom(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_even__less__0__iff_1) # label(axiom). [assumption].
% 1.94/2.21 242 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq__number__of_0) # label(axiom). [assumption].
% 1.94/2.21 243 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A),A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_zero__less__power__eq_1) # label(axiom). [assumption].
% 1.94/2.21 244 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_5) # label(axiom). [assumption].
% 1.94/2.21 245 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(B,A),A) = c_HOL_Osgn__class_Osgn(B,A) # label(cls_sgn__sgn_0) # label(axiom). [assumption].
% 1.94/2.21 246 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Osgn__class_Osgn(B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_Rational_Oordered__idom__class_Osgn__greater_1) # label(axiom). [assumption].
% 1.94/2.21 247 -class_Ring__and__Field_Oordered__idom(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_Osgn__class_Osgn(B,A),A) # label(cls_Rational_Oordered__idom__class_Osgn__greater_0) # label(axiom). [assumption].
% 1.94/2.21 248 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Oabs__class_Oabs(B,A),A) = B # label(cls_mult__sgn__abs_0) # label(axiom). [assumption].
% 1.94/2.21 249 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__le__power__eq__number__of_2) # label(axiom). [assumption].
% 1.94/2.21 250 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A) # label(cls_zero__le__power__eq__number__of_0) # label(axiom). [assumption].
% 1.94/2.21 251 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq_0) # label(axiom). [assumption].
% 1.94/2.21 252 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Osgn__class_Osgn(B,A),A) # label(cls_abs__sgn_0) # label(axiom). [assumption].
% 1.94/2.21 253 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_Rational_Oordered__idom__class_Osgn__less_0) # label(axiom). [assumption].
% 1.94/2.21 254 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_Rational_Oordered__idom__class_Osgn__less_1) # label(axiom). [assumption].
% 1.94/2.21 255 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(B,A),A) = c_Nat_Osemiring__1__class_Oof__nat(B,A) # label(cls_abs__of__nat_0) # label(axiom). [assumption].
% 1.94/2.21 256 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_3) # label(axiom). [assumption].
% 1.94/2.21 257 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_4) # label(axiom). [assumption].
% 1.94/2.21 258 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__le__power__eq__number__of_1) # label(axiom). [assumption].
% 1.94/2.21 259 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) # label(cls_zero__less__power__eq_0) # label(axiom). [assumption].
% 1.94/2.21 260 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_0) # label(axiom). [assumption].
% 1.94/2.21 261 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(C,A),E,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),D,A) # label(cls_abs__mult__less_0) # label(axiom). [assumption].
% 1.94/2.21 262 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_power__less__zero__eq__number__of_2) # label(axiom). [assumption].
% 1.94/2.21 263 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),C,A),A) # label(cls_zero__le__power__abs_0) # label(axiom). [assumption].
% 1.94/2.21 264 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_1) # label(axiom). [assumption].
% 1.94/2.21 265 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power__iff_1) # label(axiom). [assumption].
% 1.94/2.21 266 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_5) # label(axiom). [assumption].
% 1.94/2.21 267 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq_1) # label(axiom). [assumption].
% 1.94/2.21 268 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_3) # label(axiom). [assumption].
% 1.94/2.21 269 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_1) # label(axiom). [assumption].
% 1.94/2.21 270 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__iff_2) # label(axiom). [assumption].
% 1.94/2.21 271 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__le__zero__eq__number__of_4) # label(axiom). [assumption].
% 1.94/2.21 272 -class_Ring__and__Field_Oordered__idom(A) | c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),C,A) = c_Power_Opower__class_Opower(B,C,A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__even__abs_0) # label(axiom). [assumption].
% 1.94/2.21 273 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_2) # label(axiom). [assumption].
% 1.94/2.21 274 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq__number__of_1) # label(axiom). [assumption].
% 1.94/2.21 275 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_power__abs_0) # label(axiom). [assumption].
% 1.94/2.21 276 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__less__iff_0) # label(axiom). [assumption].
% 1.94/2.21 277 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Otimes__class_Otimes(B,B,A) # label(cls_abs__mult__self_0) # label(axiom). [assumption].
% 1.94/2.21 278 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__less__power__eq__number__of_2) # label(axiom). [assumption].
% 1.94/2.21 279 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),C,A) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_abs__mult__pos_0) # label(axiom). [assumption].
% 1.94/2.21 280 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__dvd__iff_0) # label(axiom). [assumption].
% 1.94/2.21 281 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_abs__dvd__iff_1) # label(axiom). [assumption].
% 1.94/2.21 282 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oabs__class_Oabs(C,A),A) # label(cls_dvd__abs__iff_0) # label(axiom). [assumption].
% 1.94/2.21 283 -class_Ring__and__Field_Oordered__idom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oabs__class_Oabs(C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__abs__iff_1) # label(axiom). [assumption].
% 1.94/2.21 284 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(D,B,A),A),C,A) # label(cls_abs__diff__less__iff_0) # label(axiom). [assumption].
% 1.94/2.21 285 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_5) # label(axiom). [assumption].
% 1.94/2.21 286 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),D,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(C,D,A),B,A) # label(cls_abs__diff__less__iff_2) # label(axiom). [assumption].
% 1.94/2.21 287 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(B,A),A) = c_Int_Onumber__class_Onumber__of(B,A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__number__of_1) # label(axiom). [assumption].
% 1.94/2.21 288 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_Power_Opower__class_Opower(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_2) # label(axiom). [assumption].
% 1.94/2.21 289 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A) # label(cls_zero__less__power__eq__number__of_0) # label(axiom). [assumption].
% 1.94/2.21 290 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_5) # label(axiom). [assumption].
% 1.94/2.21 291 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__0__0_1) # label(axiom). [assumption].
% 1.94/2.21 292 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__0__0_0) # label(axiom). [assumption].
% 1.94/2.21 293 -class_Ring__and__Field_Oordered__idom(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) # label(cls_sgn__1__pos_0) # label(axiom). [assumption].
% 1.94/2.21 294 -class_Ring__and__Field_Oordered__idom(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) # label(cls_sgn__pos_0) # label(axiom). [assumption].
% 1.94/2.21 295 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),B,A) | -c_lessequals(C,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__right__le__one__le_0) # label(axiom). [assumption].
% 1.94/2.21 296 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),C,A) | -c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__left__le__one__le_0) # label(axiom). [assumption].
% 1.94/2.21 297 -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_0) # label(axiom). [assumption].
% 1.94/2.21 298 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A),A) # label(cls_zero__less__power__eq_3) # label(axiom). [assumption].
% 1.94/2.21 299 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__less__power__eq_2) # label(axiom). [assumption].
% 1.94/2.21 300 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),D,A) # label(cls_abs__diff__less__iff_1) # label(axiom). [assumption].
% 1.94/2.21 301 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_4) # label(axiom). [assumption].
% 1.94/2.21 302 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A),A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_1) # label(axiom). [assumption].
% 1.94/2.21 303 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(C,B,A),A) # label(cls_zero__le__power__iff_0) # label(axiom). [assumption].
% 1.94/2.21 304 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_1) # label(axiom). [assumption].
% 1.94/2.21 305 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_0) # label(axiom). [assumption].
% 1.94/2.21 306 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_2) # label(axiom). [assumption].
% 1.94/2.21 307 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) # label(cls_zero__le__power__eq_0) # label(axiom). [assumption].
% 1.94/2.21 308 -class_Ring__and__Field_Oordered__idom(A) | c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat),A) = c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_power__even__abs__number__of_0) # label(axiom). [assumption].
% 1.94/2.21 309 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Osgn__class_Osgn(C,A),A) # label(cls_sgn__times_0) # label(axiom). [assumption].
% 1.94/2.21 310 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(B,A) != c_HOL_Oabs__class_Oabs(C,A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__if__abs__eq_0) # label(axiom). [assumption].
% 1.94/2.21 311 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_abs__one_0) # label(axiom). [assumption].
% 1.94/2.21 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint). [resolve(231,a,232,a)].
% 1.94/2.21 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(231,a,233,a)].
% 1.94/2.21 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(231,a,234,a)].
% 1.94/2.21 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,235,a)].
% 1.94/2.22 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(231,a,236,a)].
% 1.94/2.22 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint),tc_Int_Oint). [resolve(231,a,237,a)].
% 1.94/2.22 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(C,tc_Int_Oint),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(231,a,238,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | B = A. [resolve(231,a,239,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,240,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,241,a)].
% 1.94/2.22 Derived: -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,242,a)].
% 1.94/2.22 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(231,a,243,a)].
% 1.94/2.22 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(A,tc_Int_Oint),tc_Int_Oint) = c_HOL_Osgn__class_Osgn(A,tc_Int_Oint). [resolve(231,a,245,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Osgn__class_Osgn(A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(231,a,246,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Osgn__class_Osgn(A,tc_Int_Oint),tc_Int_Oint). [resolve(231,a,247,a)].
% 1.94/2.22 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint) = A. [resolve(231,a,248,a)].
% 1.94/2.22 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Int_Oint),tc_Int_Oint). [resolve(231,a,250,a)].
% 1.94/2.22 Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,251,a)].
% 1.94/2.22 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_HOL_Osgn__class_Osgn(A,tc_Int_Oint),tc_Int_Oint). [resolve(231,a,252,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,253,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,254,a)].
% 1.94/2.22 Derived: c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint). [resolve(231,a,255,a)].
% 1.94/2.22 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,256,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(231,a,257,a)].
% 1.94/2.22 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Int_Oint),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(231,a,258,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(231,a,259,a)].
% 1.94/2.22 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,260,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),C,tc_Int_Oint). [resolve(231,a,261,a)].
% 1.94/2.22 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint),tc_Int_Oint). [resolve(231,a,263,a)].
% 1.94/2.22 Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat) | c_lessequals(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,266,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,267,a)].
% 1.94/2.22 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,268,a)].
% 1.94/2.22 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(231,a,269,a)].
% 1.94/2.22 Derived: c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint) = c_Power_Opower__class_Opower(A,B,tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(231,a,272,a)].
% 1.94/2.22 Derived: c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,273,a)].
% 1.94/2.22 Derived: c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(231,a,275,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(231,a,276,a)].
% 1.94/2.22 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint). [resolve(231,a,277,a)].
% 1.94/2.22 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,278,a)].
% 1.94/2.22 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(231,a,279,a)].
% 1.94/2.22 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(231,a,280,a)].
% 1.94/2.22 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(231,a,281,a)].
% 1.94/2.22 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint). [resolve(231,a,282,a)].
% 1.94/2.22 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(231,a,283,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,A,tc_Int_Oint),tc_Int_Oint),B,tc_Int_Oint). [resolve(231,a,284,a)].
% 1.94/2.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),A,tc_Int_Oint). [resolve(231,a,286,a)].
% 1.94/2.22 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,287,a)].
% 1.94/2.22 Derived: c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_Power_Opower__class_Opower(B,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,288,a)].
% 1.94/2.22 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(231,a,291,a)].
% 1.94/2.22 Derived: c_HOL_Osgn__class_Osgn(A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(231,a,292,a)].
% 1.94/2.22 Derived: c_HOL_Osgn__class_Osgn(A,tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(231,a,293,a)].
% 1.94/2.22 Derived: c_HOL_Osgn__class_Osgn(A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(231,a,294,a)].
% 1.94/2.22 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(231,a,295,a)].
% 1.94/2.22 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(231,a,296,a)].
% 1.94/2.22 Derived: -c_lessequals(c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,297,a)].
% 2.02/2.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint),tc_Int_Oint). [resolve(231,a,298,a)].
% 2.02/2.27 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(231,a,299,a)].
% 2.02/2.27 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(231,a,300,a)].
% 2.02/2.27 Derived: c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(231,a,303,a)].
% 2.02/2.27 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(A,tc_Int_Oint),c_HOL_Osgn__class_Osgn(B,tc_Int_Oint),tc_Int_Oint). [resolve(231,a,309,a)].
% 2.02/2.27 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) != c_HOL_Oabs__class_Oabs(B,tc_Int_Oint) | c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(231,a,310,a)].
% 2.02/2.27 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(231,a,311,a)].
% 2.02/2.27 312 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.02/2.27 313 -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].
% 2.02/2.27 314 -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].
% 2.02/2.27 315 -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].
% 2.02/2.27 316 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 2.02/2.27 317 -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].
% 2.02/2.27 318 -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].
% 2.02/2.27 319 -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].
% 2.02/2.27 320 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 2.02/2.27 321 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 2.02/2.27 322 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 2.02/2.27 323 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 2.02/2.27 324 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 2.02/2.27 325 -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].
% 2.02/2.27 326 -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].
% 2.02/2.27 327 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 2.02/2.27 328 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 2.02/2.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(312,a,313,a)].
% 2.02/2.27 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(312,a,314,a)].
% 2.02/2.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(312,a,316,a)].
% 2.02/2.27 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(312,a,317,a)].
% 2.02/2.28 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(312,a,318,a)].
% 2.02/2.28 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(312,a,319,a)].
% 2.02/2.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(312,a,320,a)].
% 2.02/2.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat). [resolve(312,a,321,a)].
% 2.02/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(312,a,322,a)].
% 2.02/2.28 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(312,a,323,a)].
% 2.02/2.28 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat). [resolve(312,a,324,a)].
% 2.02/2.28 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(312,a,325,a)].
% 2.02/2.28 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(312,a,326,a)].
% 2.02/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(312,a,327,a)].
% 2.02/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(312,a,328,a)].
% 2.02/2.28 329 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.02/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(329,a,313,a)].
% 2.02/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(329,a,314,a)].
% 2.02/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(329,a,316,a)].
% 2.07/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(329,a,317,a)].
% 2.07/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(329,a,318,a)].
% 2.07/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(329,a,319,a)].
% 2.07/2.33 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(329,a,320,a)].
% 2.07/2.33 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(329,a,321,a)].
% 2.07/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(329,a,322,a)].
% 2.07/2.33 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(329,a,323,a)].
% 2.07/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(329,a,327,a)].
% 2.07/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(329,a,328,a)].
% 2.07/2.33 330 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.07/2.33 331 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mult_0) # label(axiom). [assumption].
% 2.07/2.33 332 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mult2_0) # label(axiom). [assumption].
% 2.07/2.33 333 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_dvd__mult__left_0) # label(axiom). [assumption].
% 2.07/2.33 334 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(D,B,A),C,A) # label(cls_dvd__mult__right_0) # label(axiom). [assumption].
% 2.07/2.33 335 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_class__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 2.07/2.33 336 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__trans_0) # label(axiom). [assumption].
% 2.07/2.33 337 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,B,A) # label(cls_dvd__refl_0) # label(axiom). [assumption].
% 2.07/2.33 338 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Otimes__class_Otimes(D,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),E,A),A) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 2.07/2.33 339 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(D,E,A),A),A) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 2.07/2.33 340 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 2.07/2.33 341 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 2.07/2.33 342 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 2.07/2.33 343 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 2.07/2.33 344 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) = c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 2.07/2.33 345 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 2.07/2.33 346 -class_Ring__and__Field_Ocomm__semiring__1(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_class__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 2.07/2.33 347 -class_Ring__and__Field_Ocomm__semiring__1(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_class__semiring_Omul__d_0) # label(axiom). [assumption].
% 2.07/2.33 348 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 2.07/2.33 349 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) = c_Power_Opower__class_Opower(B,c_HOL_Oplus__class_Oplus(C,D,tc_nat),A) # label(cls_class__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 2.07/2.33 350 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A),A) # label(cls_dvd__power_1) # label(axiom). [assumption].
% 2.07/2.33 351 -class_Ring__and__Field_Ocomm__semiring__1(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,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__add_0) # label(axiom). [assumption].
% 2.07/2.33 352 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 2.07/2.33 353 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_dvd__triv__right_0) # label(axiom). [assumption].
% 2.07/2.33 354 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_dvd__triv__left_0) # label(axiom). [assumption].
% 2.07/2.33 355 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A) = c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),A) # label(cls_class__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 2.07/2.33 356 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A) # label(cls_class__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 2.07/2.33 357 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) = c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A) # label(cls_class__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 2.07/2.33 358 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,C,A) = c_HOL_Otimes__class_Otimes(C,B,A) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 2.07/2.33 359 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,C,A) = c_HOL_Otimes__class_Otimes(C,B,A) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 2.07/2.33 360 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 2.07/2.33 361 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 2.07/2.33 362 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 2.07/2.33 363 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 2.07/2.33 364 -class_Ring__and__Field_Ocomm__semiring__1(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_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 2.07/2.33 365 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(C,D,tc_nat) # label(cls_le__imp__power__dvd_0) # label(axiom). [assumption].
% 2.07/2.33 366 -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].
% 2.07/2.33 367 -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_Oadd__c_0) # label(axiom). [assumption].
% 2.07/2.33 368 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__power__same_0) # label(axiom). [assumption].
% 2.07/2.33 369 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,B,A) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A),B,A) # label(cls_class__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 2.07/2.33 370 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),C,A) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A),C,A) # label(cls_class__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 2.07/2.33 371 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,B,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(C,c_HOL_Oone__class_Oone(A),A),B,A) # label(cls_class__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 2.07/2.33 372 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(B,c_Suc(C),A) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 2.07/2.33 373 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A) = c_Power_Opower__class_Opower(B,c_Suc(C),A) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 2.07/2.33 374 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,E,A),A) | -c_lessequals(C,E,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__power__le_0) # label(axiom). [assumption].
% 2.07/2.33 375 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,E,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_mult__dvd__mono_0) # label(axiom). [assumption].
% 2.07/2.33 376 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 2.07/2.33 377 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 2.07/2.33 378 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 2.07/2.33 379 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_dvd__0__right_0) # label(axiom). [assumption].
% 2.07/2.33 380 -class_Ring__and__Field_Ocomm__semiring__1(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_dvd__0__left_0) # label(axiom). [assumption].
% 2.07/2.33 381 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 2.07/2.33 382 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 2.07/2.33 383 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 2.07/2.33 384 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) # label(cls_dvd__power_0) # label(axiom). [assumption].
% 2.07/2.33 385 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),D,A) | -c_lessequals(C,E,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,E,A),D,A) # label(cls_power__le__dvd_0) # label(axiom). [assumption].
% 2.07/2.33 386 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__dvd_0) # label(axiom). [assumption].
% 2.07/2.33 387 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_class__semiring_Omul__1_0) # label(axiom). [assumption].
% 2.07/2.33 388 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 2.07/2.33 389 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 2.07/2.33 390 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(330,a,331,a)].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat). [resolve(330,a,332,a)].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,C,tc_nat),B,tc_nat). [resolve(330,a,333,a)].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_nat),B,tc_nat). [resolve(330,a,334,a)].
% 2.07/2.33 Derived: c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat). [resolve(330,a,335,a)].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(330,a,336,a)].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_nat). [resolve(330,a,337,a)].
% 2.07/2.33 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),D,tc_nat),tc_nat). [resolve(330,a,338,a)].
% 2.07/2.33 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat),tc_nat). [resolve(330,a,339,a)].
% 2.07/2.33 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,D,tc_nat),tc_nat). [resolve(330,a,340,a)].
% 2.07/2.33 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,C,tc_nat),B,tc_nat). [resolve(330,a,341,a)].
% 2.07/2.33 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(330,a,342,a)].
% 2.07/2.33 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat). [resolve(330,a,343,a)].
% 2.07/2.33 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). [resolve(330,a,344,a)].
% 2.07/2.33 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(330,a,346,a)].
% 2.07/2.33 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). [resolve(330,a,347,a)].
% 2.07/2.33 Derived: c_HOL_Oplus__class_Oplus(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_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). [resolve(330,a,348,a)].
% 2.07/2.33 Derived: c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) = c_Power_Opower__class_Opower(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(330,a,349,a)].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),tc_nat). [resolve(330,a,350,a)].
% 2.07/2.33 Derived: 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,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat). [resolve(330,a,351,a)].
% 2.07/2.33 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,D,tc_nat),tc_nat). [resolve(330,a,352,a)].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat). [resolve(330,a,353,a)].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). [resolve(330,a,354,a)].
% 2.07/2.33 Derived: c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_nat),C,tc_nat) = c_Power_Opower__class_Opower(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(330,a,355,a)].
% 2.07/2.33 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat) = c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat). [resolve(330,a,356,a)].
% 2.07/2.33 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_nat) = c_HOL_Otimes__class_Otimes(B,A,tc_nat). [resolve(330,a,358,a)].
% 2.07/2.33 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat). [resolve(330,a,360,a)].
% 2.07/2.33 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). [resolve(330,a,362,a)].
% 2.07/2.33 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat). [resolve(330,a,363,a)].
% 2.07/2.33 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(330,a,364,a)].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(330,a,365,a)].
% 2.07/2.33 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) = c_HOL_Oplus__class_Oplus(B,A,tc_nat). [resolve(330,a,366,a)].
% 2.07/2.33 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(330,a,368,a)].
% 2.07/2.33 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),A,tc_nat). [resolve(330,a,369,a)].
% 2.07/2.34 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),B,tc_nat). [resolve(330,a,370,a)].
% 2.07/2.34 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_nat),tc_nat),A,tc_nat). [resolve(330,a,371,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat). [resolve(330,a,372,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_nat),A,tc_nat) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat). [resolve(330,a,373,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(330,a,374,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(330,a,375,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(330,a,376,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(330,a,377,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(330,a,379,a)].
% 2.07/2.34 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(330,a,380,a)].
% 2.07/2.34 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = A. [resolve(330,a,381,a)].
% 2.07/2.34 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(330,a,382,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(330,a,384,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,D,tc_nat),C,tc_nat). [resolve(330,a,385,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(330,a,386,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = A. [resolve(330,a,387,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(330,a,388,a)].
% 2.07/2.34 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(330,a,390,a)].
% 2.07/2.34 391 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(391,a,331,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(391,a,332,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(391,a,333,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),B,tc_Int_Oint). [resolve(391,a,334,a)].
% 2.07/2.34 Derived: c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,335,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(391,a,336,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_Int_Oint). [resolve(391,a,337,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),D,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,338,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(391,a,339,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,340,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(391,a,341,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,342,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint). [resolve(391,a,343,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,344,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,346,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,347,a)].
% 2.07/2.34 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(391,a,348,a)].
% 2.07/2.34 Derived: c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) = c_Power_Opower__class_Opower(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_Int_Oint). [resolve(391,a,349,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,350,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(391,a,351,a)].
% 2.07/2.34 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,352,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,353,a)].
% 2.07/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,354,a)].
% 2.07/2.34 Derived: c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Power_Opower__class_Opower(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_Int_Oint). [resolve(391,a,355,a)].
% 2.11/2.34 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,356,a)].
% 2.11/2.34 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint). [resolve(391,a,358,a)].
% 2.11/2.34 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint). [resolve(391,a,360,a)].
% 2.11/2.34 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(391,a,362,a)].
% 2.11/2.34 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,363,a)].
% 2.11/2.34 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,364,a)].
% 2.11/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_nat). [resolve(391,a,365,a)].
% 2.11/2.34 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,A,tc_Int_Oint). [resolve(391,a,366,a)].
% 2.11/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(391,a,368,a)].
% 2.11/2.34 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A,tc_Int_Oint). [resolve(391,a,369,a)].
% 2.11/2.34 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),B,tc_Int_Oint). [resolve(391,a,370,a)].
% 2.11/2.34 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A,tc_Int_Oint). [resolve(391,a,371,a)].
% 2.11/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint). [resolve(391,a,372,a)].
% 2.11/2.34 Derived: c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),A,tc_Int_Oint) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint). [resolve(391,a,373,a)].
% 2.11/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(391,a,374,a)].
% 2.11/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(391,a,375,a)].
% 2.11/2.34 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,376,a)].
% 2.11/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,377,a)].
% 2.11/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,379,a)].
% 2.11/2.34 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(391,a,380,a)].
% 2.11/2.34 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = A. [resolve(391,a,381,a)].
% 2.12/2.34 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(391,a,382,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(391,a,384,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,D,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,D,tc_Int_Oint),C,tc_Int_Oint). [resolve(391,a,385,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(391,a,386,a)].
% 2.12/2.34 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) = A. [resolve(391,a,387,a)].
% 2.12/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(391,a,388,a)].
% 2.12/2.34 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(391,a,390,a)].
% 2.12/2.34 392 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(392,a,331,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex). [resolve(392,a,332,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(392,a,333,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(392,a,334,a)].
% 2.12/2.34 Derived: c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,335,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(392,a,336,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_Complex_Ocomplex). [resolve(392,a,337,a)].
% 2.12/2.34 Derived: c_HOL_Otimes__class_Otimes(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_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,338,a)].
% 2.12/2.34 Derived: c_HOL_Otimes__class_Otimes(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_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,339,a)].
% 2.12/2.34 Derived: c_HOL_Otimes__class_Otimes(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_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,340,a)].
% 2.12/2.34 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(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(392,a,341,a)].
% 2.12/2.34 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(392,a,342,a)].
% 2.12/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex). [resolve(392,a,343,a)].
% 2.12/2.34 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,344,a)].
% 2.12/2.34 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(392,a,346,a)].
% 2.12/2.34 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(392,a,347,a)].
% 2.12/2.34 Derived: c_HOL_Oplus__class_Oplus(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_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(392,a,348,a)].
% 2.12/2.34 Derived: c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_Complex_Ocomplex). [resolve(392,a,349,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,350,a)].
% 2.12/2.34 Derived: 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,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex). [resolve(392,a,351,a)].
% 2.12/2.34 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,352,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(B,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,353,a)].
% 2.12/2.34 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,354,a)].
% 2.12/2.34 Derived: c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_Complex_Ocomplex). [resolve(392,a,355,a)].
% 2.12/2.34 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,356,a)].
% 2.12/2.34 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(B,A,tc_Complex_Ocomplex). [resolve(392,a,358,a)].
% 2.12/2.34 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex). [resolve(392,a,360,a)].
% 2.12/2.34 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(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(392,a,362,a)].
% 2.12/2.34 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,363,a)].
% 2.12/2.35 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(392,a,364,a)].
% 2.12/2.35 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_lessequals(B,C,tc_nat). [resolve(392,a,365,a)].
% 2.12/2.35 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(B,A,tc_Complex_Ocomplex). [resolve(392,a,366,a)].
% 2.12/2.35 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(392,a,368,a)].
% 2.12/2.35 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(392,a,369,a)].
% 2.12/2.35 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(392,a,370,a)].
% 2.12/2.35 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(392,a,371,a)].
% 2.12/2.35 Derived: c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_Complex_Ocomplex). [resolve(392,a,372,a)].
% 2.12/2.35 Derived: c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(A,c_Suc(B),tc_Complex_Ocomplex). [resolve(392,a,373,a)].
% 2.12/2.35 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_lessequals(B,D,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(392,a,374,a)].
% 2.12/2.35 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(392,a,375,a)].
% 2.12/2.35 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(392,a,376,a)].
% 2.12/2.35 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(392,a,377,a)].
% 2.12/2.35 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(392,a,379,a)].
% 2.12/2.35 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(392,a,380,a)].
% 2.12/2.35 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A. [resolve(392,a,381,a)].
% 2.12/2.35 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(392,a,382,a)].
% 2.12/2.35 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(392,a,384,a)].
% 2.12/2.35 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_lessequals(B,D,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(A,D,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex). [resolve(392,a,385,a)].
% 2.23/2.51 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(392,a,386,a)].
% 2.23/2.51 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A. [resolve(392,a,387,a)].
% 2.23/2.51 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(392,a,388,a)].
% 2.23/2.51 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(392,a,390,a)].
% 2.23/2.51 393 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.23/2.51 394 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 2.23/2.51 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(393,a,394,a)].
% 2.23/2.51 395 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.23/2.51 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(395,a,394,a)].
% 2.23/2.51 396 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.23/2.51 397 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 2.23/2.51 398 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 2.23/2.51 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(396,a,398,a)].
% 2.23/2.51 399 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.23/2.51 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(399,a,398,a)].
% 2.23/2.51 400 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 2.23/2.51 401 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,C,A) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 2.23/2.51 402 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 2.23/2.51 403 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 2.23/2.51 404 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 2.23/2.52 405 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 2.23/2.52 406 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A) | -c_lessequals(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A),A) # label(cls_le__add__iff2_1) # label(axiom). [assumption].
% 2.23/2.52 407 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,A),E,A),F,A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,A),B,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,A),F,A),A) # label(cls_le__add__iff2_0) # label(axiom). [assumption].
% 2.23/2.52 408 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),F,A) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 2.23/2.52 409 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A),E,A),F,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),E,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,A),F,A),A) # label(cls_le__add__iff1_0) # label(axiom). [assumption].
% 2.23/2.52 410 -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].
% 2.23/2.52 411 -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].
% 2.23/2.52 412 -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].
% 2.23/2.52 413 -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].
% 2.23/2.52 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint). [resolve(400,a,401,a)].
% 2.23/2.52 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,A,tc_Int_Oint). [resolve(400,a,402,a)].
% 2.23/2.52 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(400,a,406,a)].
% 2.32/2.57 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),D,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(400,a,407,a)].
% 2.32/2.57 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint),E,tc_Int_Oint). [resolve(400,a,408,a)].
% 2.32/2.57 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint),D,tc_Int_Oint),E,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),D,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(400,a,409,a)].
% 2.32/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint),D,tc_Int_Oint),E,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),D,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(400,a,410,a)].
% 2.32/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint),E,tc_Int_Oint). [resolve(400,a,411,a)].
% 2.32/2.57 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),D,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(400,a,412,a)].
% 2.32/2.57 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),B,tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint). [resolve(400,a,413,a)].
% 2.32/2.57 414 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 2.32/2.57 415 -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].
% 2.32/2.57 416 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(C,c_HOL_Ozero__class_Ozero(A),A),A) # label(cls_dvd__mult__cancel__right_1) # label(axiom). [assumption].
% 2.32/2.57 417 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A) # label(cls_dvd__mult__cancel__left_1) # label(axiom). [assumption].
% 2.32/2.57 418 -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].
% 2.32/2.57 419 -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].
% 2.32/2.57 420 -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].
% 2.32/2.57 421 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,A) # label(cls_dvd__mult__cancel__left_2) # label(axiom). [assumption].
% 2.32/2.57 422 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mult__cancel__right_2) # label(axiom). [assumption].
% 2.32/2.57 423 -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].
% 2.32/2.57 424 -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].
% 2.32/2.57 425 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_dvd__mult__cancel__right_0) # label(axiom). [assumption].
% 2.32/2.57 426 -class_Ring__and__Field_Oidom(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | D = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_dvd__mult__cancel__left_0) # label(axiom). [assumption].
% 2.32/2.57 427 -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].
% 2.32/2.57 428 -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].
% 2.32/2.57 429 -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].
% 2.32/2.57 430 -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].
% 2.32/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),tc_Int_Oint) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(414,a,415,a)].
% 2.32/2.57 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(414,a,416,a)].
% 2.32/2.57 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint),tc_Int_Oint). [resolve(414,a,417,a)].
% 2.32/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C. [resolve(414,a,418,a)].
% 2.32/2.57 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Int_Oint). [resolve(414,a,421,a)].
% 2.32/2.57 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(414,a,422,a)].
% 2.32/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | B = D | A = C. [resolve(414,a,423,a)].
% 2.32/2.57 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(414,a,425,a)].
% 2.32/2.57 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(414,a,426,a)].
% 2.32/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(414,a,427,a)].
% 2.32/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(414,a,428,a)].
% 2.32/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(414,a,429,a)].
% 2.32/2.57 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(414,a,430,a)].
% 2.32/2.57 431 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 2.32/2.57 Derived: -class_Int_Onumber__ring(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(431,a,415,a)].
% 2.32/2.57 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(431,a,416,a)].
% 2.32/2.57 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(431,a,417,a)].
% 2.32/2.57 Derived: -class_Int_Onumber__ring(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(431,a,418,a)].
% 2.32/2.57 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Complex_Ocomplex). [resolve(431,a,421,a)].
% 2.32/2.57 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex). [resolve(431,a,422,a)].
% 2.37/2.63 Derived: -class_Int_Onumber__ring(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(431,a,423,a)].
% 2.37/2.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(431,a,425,a)].
% 2.37/2.63 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(431,a,426,a)].
% 2.37/2.63 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(431,a,427,a)].
% 2.37/2.63 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(431,a,428,a)].
% 2.37/2.63 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(431,a,429,a)].
% 2.37/2.63 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(431,a,430,a)].
% 2.37/2.63 432 class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) # label(axiom). [assumption].
% 2.37/2.63 433 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Oone__class_Oone(A) | c_HOL_Oinverse__class_Oinverse(B,A) = C # label(cls_inverse__unique_0) # label(axiom). [assumption].
% 2.37/2.63 434 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oinverse__class_Oinverse(C,A) | B = C # label(cls_inverse__eq__iff__eq_0) # label(axiom). [assumption].
% 2.37/2.63 435 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),C,A) # label(cls_power__inverse_0) # label(axiom). [assumption].
% 2.37/2.63 436 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oinverse__class_Oinverse(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_division__ring__inverse__add_0) # label(axiom). [assumption].
% 2.37/2.63 437 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(C,A),c_HOL_Oinverse__class_Oinverse(B,A),A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__mult__distrib_0) # label(axiom). [assumption].
% 2.37/2.63 438 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A) = B # label(cls_inverse__inverse__eq_0) # label(axiom). [assumption].
% 2.37/2.63 439 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(B,C,A),A) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),C,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__inverse_0) # label(axiom). [assumption].
% 2.37/2.63 440 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__zero__imp__zero_0) # label(axiom). [assumption].
% 2.37/2.63 441 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_0) # label(axiom). [assumption].
% 2.37/2.63 442 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A) = B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__inverse__eq_0) # label(axiom). [assumption].
% 2.37/2.63 443 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_1) # label(axiom). [assumption].
% 2.37/2.63 444 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oinverse__class_Oinverse(C,A) | B = C | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__imp__eq_0) # label(axiom). [assumption].
% 2.37/2.63 445 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(B,A),A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_right__inverse_0) # label(axiom). [assumption].
% 2.37/2.63 446 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_left__inverse_0) # label(axiom). [assumption].
% 2.37/2.63 447 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Ominus__class_Ominus(C,B,A),A),c_HOL_Oinverse__class_Oinverse(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_division__ring__inverse__diff_0) # label(axiom). [assumption].
% 2.37/2.63 448 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__1_0) # label(axiom). [assumption].
% 2.37/2.63 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) = B. [resolve(432,a,433,a)].
% 2.37/2.63 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex) | A = B. [resolve(432,a,434,a)].
% 2.37/2.63 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(432,a,435,a)].
% 2.37/2.63 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(432,a,436,a)].
% 2.37/2.63 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(432,a,437,a)].
% 2.42/2.69 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(432,a,438,a)].
% 2.42/2.69 Derived: c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(432,a,439,a)].
% 2.42/2.69 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(432,a,440,a)].
% 2.42/2.69 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(432,a,442,a)].
% 2.42/2.69 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(432,a,443,a)].
% 2.42/2.69 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex) | A = B | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(432,a,444,a)].
% 2.42/2.69 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(432,a,445,a)].
% 2.42/2.69 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(432,a,447,a)].
% 2.42/2.69 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(432,a,448,a)].
% 2.42/2.69 449 class_HOL_Oord(tc_nat) # label(clsarity_nat__HOL_Oord) # label(axiom). [assumption].
% 2.42/2.69 450 -class_Int_Onumber(A) | -class_HOL_Oord(A) | c_Orderings_Oord__class_Omax(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) = c_Int_Onumber__class_Onumber__of(B,A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) # label(cls_max__number__of_1) # label(axiom). [assumption].
% 2.42/2.69 451 -class_Int_Onumber(A) | -class_HOL_Oord(A) | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) = c_Int_Onumber__class_Onumber__of(C,A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) # label(cls_min__number__of_1) # label(axiom). [assumption].
% 2.42/2.69 452 -class_Int_Onumber(A) | -class_HOL_Oord(A) | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) = c_Int_Onumber__class_Onumber__of(B,A) | -c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) # label(cls_min__number__of_0) # label(axiom). [assumption].
% 2.42/2.69 453 -class_Int_Onumber(A) | -class_HOL_Oord(A) | c_Orderings_Oord__class_Omax(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) = c_Int_Onumber__class_Onumber__of(C,A) | -c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) # label(cls_max__number__of_0) # label(axiom). [assumption].
% 2.42/2.69 Derived: -class_Int_Onumber(tc_nat) | c_Orderings_Oord__class_Omax(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(A,tc_nat) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(449,a,450,b)].
% 2.49/2.74 Derived: -class_Int_Onumber(tc_nat) | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(B,tc_nat) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(449,a,451,b)].
% 2.49/2.74 Derived: -class_Int_Onumber(tc_nat) | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(A,tc_nat) | -c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(449,a,452,b)].
% 2.49/2.74 Derived: -class_Int_Onumber(tc_nat) | c_Orderings_Oord__class_Omax(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(B,tc_nat) | -c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(449,a,453,b)].
% 2.49/2.74 454 class_HOL_Oord(tc_Int_Oint) # label(clsarity_Int__Oint__HOL_Oord) # label(axiom). [assumption].
% 2.49/2.74 Derived: -class_Int_Onumber(tc_Int_Oint) | c_Orderings_Oord__class_Omax(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint). [resolve(454,a,450,b)].
% 2.49/2.74 Derived: -class_Int_Onumber(tc_Int_Oint) | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint). [resolve(454,a,451,b)].
% 2.49/2.74 Derived: -class_Int_Onumber(tc_Int_Oint) | c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) | -c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint). [resolve(454,a,452,b)].
% 2.49/2.74 Derived: -class_Int_Onumber(tc_Int_Oint) | c_Orderings_Oord__class_Omax(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | -c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint). [resolve(454,a,453,b)].
% 2.49/2.74 455 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.49/2.74 456 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(B,C,tc_nat),A) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 2.49/2.74 457 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 2.49/2.74 458 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(B,C,tc_nat),A) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__mult_0) # label(axiom). [assumption].
% 2.49/2.74 459 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 2.49/2.74 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(455,a,456,a)].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(455,a,457,a)].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(455,a,458,a)].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(455,a,459,a)].
% 2.55/2.80 460 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint). [resolve(460,a,456,a)].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint). [resolve(460,a,457,a)].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint). [resolve(460,a,458,a)].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(460,a,459,a)].
% 2.55/2.80 461 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(461,a,456,a)].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(461,a,457,a)].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(461,a,458,a)].
% 2.55/2.80 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(461,a,459,a)].
% 2.55/2.80 462 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 2.55/2.80 463 -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].
% 2.55/2.80 464 -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].
% 2.55/2.80 465 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(C,B,A) | -c_lessequals(E,D,A) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 2.55/2.80 466 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(E,D,A) | -c_lessequals(C,B,A) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 2.55/2.80 467 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,D,A),A) # label(cls_max__diff__distrib__left_0) # label(axiom). [assumption].
% 2.55/2.85 468 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,D,A),A) # label(cls_min__diff__distrib__left_0) # label(axiom). [assumption].
% 2.55/2.85 469 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,C,A) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 2.55/2.85 470 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 2.55/2.85 471 -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].
% 2.55/2.85 472 -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].
% 2.55/2.85 473 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(E,D,A) | -c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 2.55/2.85 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,D,tc_Int_Oint). [resolve(462,a,463,a)].
% 2.55/2.85 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_HOL_Oord__class_Oless(C,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(462,a,464,a)].
% 2.55/2.85 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint). [resolve(462,a,465,a)].
% 2.55/2.85 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(462,a,466,a)].
% 2.55/2.85 Derived: c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(A,C,tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(462,a,467,a)].
% 2.55/2.85 Derived: c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(A,C,tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(462,a,468,a)].
% 2.55/2.85 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(462,a,469,a)].
% 2.55/2.85 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(462,a,470,a)].
% 2.55/2.85 Derived: c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(462,a,471,a)].
% 2.55/2.85 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(462,a,472,a)].
% 2.55/2.85 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(A,c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint),tc_Int_Oint). [resolve(462,a,473,a)].
% 2.55/2.85 474 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.67/2.91 475 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 2.67/2.91 476 -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].
% 2.67/2.91 477 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.67/2.91 478 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 2.67/2.91 479 class_Ring__and__Field_Odvd(tc_nat) # label(clsarity_nat__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.67/2.91 480 -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].
% 2.67/2.91 481 -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].
% 2.67/2.91 482 -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].
% 2.67/2.91 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(479,a,480,a)].
% 2.67/2.91 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(479,a,481,a)].
% 2.67/2.91 483 class_Ring__and__Field_Odvd(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.67/2.91 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | 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_Int_Oint),tc_Int_Oint),E,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,E,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,D,tc_Int_Oint). [resolve(483,a,480,a)].
% 2.67/2.91 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -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_Int_Oint),tc_Int_Oint),C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,E,tc_Int_Oint). [resolve(483,a,481,a)].
% 2.67/2.91 484 class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.67/2.91 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(484,a,480,a)].
% 2.70/2.96 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(484,a,481,a)].
% 2.70/2.96 485 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 2.70/2.96 486 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(C,D,A),A) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,A),c_Orderings_Oord__class_Omax(B,D,A),A) # label(cls_min__max_Osup__inf__distrib1_0) # label(axiom). [assumption].
% 2.70/2.96 487 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,D,A),c_Orderings_Oord__class_Omax(C,D,A),A) # label(cls_min__max_Osup__inf__distrib2_0) # label(axiom). [assumption].
% 2.70/2.96 488 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 2.70/2.96 489 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 2.70/2.96 490 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,B,A) = B # label(cls_min__max_Osup__idem_0) # label(axiom). [assumption].
% 2.70/2.96 491 -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].
% 2.70/2.96 492 -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].
% 2.70/2.96 493 -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].
% 2.70/2.96 494 -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].
% 2.70/2.96 495 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,B,A) = B # label(cls_min__max_Oinf__idem_0) # label(axiom). [assumption].
% 2.70/2.96 496 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(B,C,A),A) = c_Orderings_Oord__class_Omax(B,C,A) # label(cls_min__max_Osup__left__idem_0) # label(axiom). [assumption].
% 2.70/2.96 497 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(B,C,A),A) = B # label(cls_min__max_Osup__inf__absorb_0) # label(axiom). [assumption].
% 2.70/2.96 498 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,D,A),c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Oinf__sup__distrib2_0) # label(axiom). [assumption].
% 2.70/2.96 499 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(C,D,A),A) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,A),c_Orderings_Oord__class_Omin(B,D,A),A) # label(cls_min__max_Oinf__sup__distrib1_0) # label(axiom). [assumption].
% 2.70/2.96 500 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__sup__iff_2) # label(axiom). [assumption].
% 2.70/2.96 501 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Osup__least_0) # label(axiom). [assumption].
% 2.70/2.96 502 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__supI_0) # label(axiom). [assumption].
% 2.70/2.96 503 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(B,C,A),A) # label(cls_le__maxI1_0) # label(axiom). [assumption].
% 2.70/2.96 504 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,B,A),A) # label(cls_le__maxI2_0) # label(axiom). [assumption].
% 2.70/2.96 505 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(B,C,A),c_Orderings_Oord__class_Omin(B,D,A),A),c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(C,D,A),A),A) # label(cls_min__max_Odistrib__inf__le_0) # label(axiom). [assumption].
% 2.70/2.96 506 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = c_Orderings_Oord__class_Omax(C,B,A) # label(cls_min__max_Osup__commute_0) # label(axiom). [assumption].
% 2.70/2.96 507 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Oinf__assoc_0) # label(axiom). [assumption].
% 2.70/2.96 508 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(C,D,A),A) = c_Orderings_Oord__class_Omin(C,c_Orderings_Oord__class_Omin(B,D,A),A) # label(cls_min__max_Oinf__left__commute_0) # label(axiom). [assumption].
% 2.70/2.96 509 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_0) # label(axiom). [assumption].
% 2.70/2.96 510 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) != B | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__inf_1) # label(axiom). [assumption].
% 2.70/2.96 511 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_min__max_Oinf__absorb2_0) # label(axiom). [assumption].
% 2.70/2.96 512 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Oinf__greatest_0) # label(axiom). [assumption].
% 2.70/2.96 513 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__inf__iff_2) # label(axiom). [assumption].
% 2.70/2.96 514 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__infI_0) # label(axiom). [assumption].
% 2.70/2.96 515 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),C,A) # label(cls_min__max_Oinf__le2_0) # label(axiom). [assumption].
% 2.70/2.96 516 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),B,A) # label(cls_min__max_Oinf__le1_0) # label(axiom). [assumption].
% 2.70/2.96 517 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_max__less__iff__conj_2) # label(axiom). [assumption].
% 2.70/2.96 518 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__less__iff__conj_2) # label(axiom). [assumption].
% 2.70/2.96 519 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(B,C,A),A) = c_Orderings_Oord__class_Omin(B,C,A) # label(cls_min__max_Oinf__left__idem_0) # label(axiom). [assumption].
% 2.70/2.96 520 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 2.70/2.96 521 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 2.70/2.96 522 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 2.70/2.96 523 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 2.70/2.96 524 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 2.70/2.96 525 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 2.70/2.96 526 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 2.70/2.96 527 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__sup_0) # label(axiom). [assumption].
% 2.70/2.96 528 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) != C | c_lessequals(B,C,A) # label(cls_min__max_Ole__iff__sup_1) # label(axiom). [assumption].
% 2.70/2.96 529 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_min__max_Osup__absorb1_0) # label(axiom). [assumption].
% 2.70/2.96 530 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(B,D,A) | -c_lessequals(B,c_Orderings_Oord__class_Omax(D,C,A),A) # label(cls_le__max__iff__disj_0) # label(axiom). [assumption].
% 2.70/2.96 531 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Ole__infE_0) # label(axiom). [assumption].
% 2.70/2.96 532 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__max_Ole__infE_1) # label(axiom). [assumption].
% 2.70/2.96 533 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__infI1_0) # label(axiom). [assumption].
% 2.70/2.96 534 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_min__max_Ole__infI2_0) # label(axiom). [assumption].
% 2.70/2.96 535 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_min__le__iff__disj_1) # label(axiom). [assumption].
% 2.70/2.96 536 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_min__le__iff__disj_2) # label(axiom). [assumption].
% 2.70/2.96 537 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__max_Ole__inf__iff_0) # label(axiom). [assumption].
% 2.70/2.96 538 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omax(B,C,A),A) = B # label(cls_min__max_Oinf__sup__absorb_0) # label(axiom). [assumption].
% 2.70/2.96 539 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_max__less__iff__conj_1) # label(axiom). [assumption].
% 2.70/2.96 540 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_max__less__iff__conj_0) # label(axiom). [assumption].
% 2.70/2.96 541 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__max__iff__disj_2) # label(axiom). [assumption].
% 2.70/2.96 542 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__max__iff__disj_1) # label(axiom). [assumption].
% 2.70/2.96 543 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__supI2_0) # label(axiom). [assumption].
% 2.70/2.96 544 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_min__max_Oless__supI1_0) # label(axiom). [assumption].
% 2.70/2.96 545 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(B,C,A) = c_Orderings_Oord__class_Omin(C,B,A) # label(cls_min__max_Oinf__commute_0) # label(axiom). [assumption].
% 2.70/2.96 546 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__less__iff__disj_2) # label(axiom). [assumption].
% 2.70/2.96 547 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__less__iff__disj_1) # label(axiom). [assumption].
% 2.70/2.96 548 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__less__iff__conj_1) # label(axiom). [assumption].
% 2.70/2.96 549 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omin(C,D,A),A) # label(cls_min__less__iff__conj_0) # label(axiom). [assumption].
% 2.70/2.96 550 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_min__max_Oless__infI2_0) # label(axiom). [assumption].
% 2.70/2.96 551 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_min__max_Oless__infI1_0) # label(axiom). [assumption].
% 2.70/2.96 552 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Orderings_Oord__class_Omin(D,C,A),A) # label(cls_min__max_Ole__inf__iff_1) # label(axiom). [assumption].
% 2.70/2.96 553 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(D,C,A) | -c_lessequals(c_Orderings_Oord__class_Omin(D,B,A),C,A) # label(cls_min__le__iff__disj_0) # label(axiom). [assumption].
% 2.70/2.96 554 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_min__max_Ole__supE_0) # label(axiom). [assumption].
% 2.70/2.96 555 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_min__max_Ole__supE_1) # label(axiom). [assumption].
% 2.70/2.96 556 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_min__max_Ole__supI1_0) # label(axiom). [assumption].
% 2.70/2.96 557 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_min__max_Ole__supI2_0) # label(axiom). [assumption].
% 2.70/2.96 558 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__max__iff__disj_1) # label(axiom). [assumption].
% 2.70/2.96 559 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__max__iff__disj_2) # label(axiom). [assumption].
% 2.70/2.96 560 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(B,D,A),C,A) # label(cls_min__max_Ole__sup__iff_0) # label(axiom). [assumption].
% 2.70/2.96 561 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_Orderings_Oord__class_Omax(D,B,A),C,A) # label(cls_min__max_Ole__sup__iff_1) # label(axiom). [assumption].
% 2.70/2.96 562 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(D,C,A),A) # label(cls_less__max__iff__disj_0) # label(axiom). [assumption].
% 2.70/2.96 563 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(D,B,A),C,A) # label(cls_min__less__iff__disj_0) # label(axiom). [assumption].
% 2.70/2.96 564 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 2.70/2.96 565 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A) = c_Orderings_Oord__class_Omax(C,c_Orderings_Oord__class_Omax(B,D,A),A) # label(cls_min__max_Osup__left__commute_0) # label(axiom). [assumption].
% 2.70/2.96 566 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A) # label(cls_min__max_Osup__assoc_0) # label(axiom). [assumption].
% 2.70/2.96 567 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | -c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 2.70/2.96 568 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 2.70/2.96 569 -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].
% 2.70/2.96 570 -class_Orderings_Olinorder(A) | c_lessequals(c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omin(C,D,A),A),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(B,C,A),c_Orderings_Oord__class_Omax(B,D,A),A),A) # label(cls_min__max_Odistrib__sup__le_0) # label(axiom). [assumption].
% 2.70/2.96 571 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 2.70/2.96 572 -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].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_nat),c_Orderings_Oord__class_Omax(A,C,tc_nat),tc_nat). [resolve(485,a,486,a)].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,C,tc_nat),c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat). [resolve(485,a,487,a)].
% 2.70/2.96 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(485,a,488,a)].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omax(A,A,tc_nat) = A. [resolve(485,a,490,a)].
% 2.70/2.96 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(485,a,491,a)].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omin(A,A,tc_nat) = A. [resolve(485,a,495,a)].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(A,B,tc_nat),tc_nat) = c_Orderings_Oord__class_Omax(A,B,tc_nat). [resolve(485,a,496,a)].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(A,B,tc_nat),tc_nat) = A. [resolve(485,a,497,a)].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,C,tc_nat),c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(485,a,498,a)].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_nat),c_Orderings_Oord__class_Omin(A,C,tc_nat),tc_nat). [resolve(485,a,499,a)].
% 2.70/2.96 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(485,a,500,a)].
% 2.70/2.96 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(A,B,tc_nat),tc_nat). [resolve(485,a,503,a)].
% 2.70/2.96 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,A,tc_nat),tc_nat). [resolve(485,a,504,a)].
% 2.70/2.96 Derived: c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_nat),c_Orderings_Oord__class_Omin(A,C,tc_nat),tc_nat),c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat),tc_nat). [resolve(485,a,505,a)].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) = c_Orderings_Oord__class_Omax(B,A,tc_nat). [resolve(485,a,506,a)].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(485,a,507,a)].
% 2.70/2.96 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(A,C,tc_nat),tc_nat). [resolve(485,a,508,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(485,a,509,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(485,a,510,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(485,a,511,a)].
% 2.70/2.97 Derived: c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(485,a,512,a)].
% 2.70/2.97 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),B,tc_nat). [resolve(485,a,515,a)].
% 2.70/2.97 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),A,tc_nat). [resolve(485,a,516,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(485,a,517,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(485,a,518,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(A,B,tc_nat),tc_nat) = c_Orderings_Oord__class_Omin(A,B,tc_nat). [resolve(485,a,519,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(485,a,520,a)].
% 2.70/2.97 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(485,a,521,a)].
% 2.70/2.97 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(485,a,523,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(485,a,527,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(485,a,528,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omax(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(485,a,529,a)].
% 2.70/2.97 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(A,C,tc_nat) | -c_lessequals(A,c_Orderings_Oord__class_Omax(C,B,tc_nat),tc_nat). [resolve(485,a,530,a)].
% 2.70/2.97 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(485,a,531,a)].
% 2.70/2.97 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Orderings_Oord__class_Omin(C,B,tc_nat),tc_nat). [resolve(485,a,532,a)].
% 2.70/2.97 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(485,a,533,a)].
% 2.70/2.97 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(485,a,534,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(A,B,tc_nat),tc_nat) = A. [resolve(485,a,538,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(C,A,tc_nat),B,tc_nat). [resolve(485,a,539,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,C,tc_nat),B,tc_nat). [resolve(485,a,540,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(485,a,541,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(485,a,542,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omin(A,B,tc_nat) = c_Orderings_Oord__class_Omin(B,A,tc_nat). [resolve(485,a,545,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(485,a,546,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(485,a,547,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(C,B,tc_nat),tc_nat). [resolve(485,a,548,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat). [resolve(485,a,549,a)].
% 2.70/2.97 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(C,B,tc_nat) | -c_lessequals(c_Orderings_Oord__class_Omin(C,A,tc_nat),B,tc_nat). [resolve(485,a,553,a)].
% 2.70/2.97 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Orderings_Oord__class_Omax(A,C,tc_nat),B,tc_nat). [resolve(485,a,554,a)].
% 2.70/2.97 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Orderings_Oord__class_Omax(C,A,tc_nat),B,tc_nat). [resolve(485,a,555,a)].
% 2.70/2.97 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(485,a,556,a)].
% 2.70/2.97 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(485,a,557,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(C,B,tc_nat),tc_nat). [resolve(485,a,562,a)].
% 2.70/2.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(C,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(C,A,tc_nat),B,tc_nat). [resolve(485,a,563,a)].
% 2.70/2.97 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(485,a,564,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(A,C,tc_nat),tc_nat). [resolve(485,a,565,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_nat),tc_nat). [resolve(485,a,566,a)].
% 2.70/2.97 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(485,a,569,a)].
% 2.70/2.97 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(B,C,tc_nat),tc_nat),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_nat),c_Orderings_Oord__class_Omax(A,C,tc_nat),tc_nat),tc_nat). [resolve(485,a,570,a)].
% 2.70/2.97 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(485,a,571,a)].
% 2.70/2.97 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(485,a,572,a)].
% 2.70/2.97 573 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),c_Orderings_Oord__class_Omax(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,486,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,C,tc_Int_Oint),c_Orderings_Oord__class_Omax(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,487,a)].
% 2.70/2.97 Derived: A = B | -c_lessequals(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(573,a,488,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omax(A,A,tc_Int_Oint) = A. [resolve(573,a,490,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omin(A,A,tc_Int_Oint) = A. [resolve(573,a,495,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),tc_Int_Oint) = c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint). [resolve(573,a,496,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),tc_Int_Oint) = A. [resolve(573,a,497,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,C,tc_Int_Oint),c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,498,a)].
% 2.70/2.97 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(B,C,tc_Int_Oint),tc_Int_Oint) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),c_Orderings_Oord__class_Omin(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,499,a)].
% 2.70/2.97 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(573,a,500,a)].
% 2.70/2.97 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,503,a)].
% 2.70/2.98 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,504,a)].
% 2.70/2.98 Derived: c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),c_Orderings_Oord__class_Omin(A,C,tc_Int_Oint),tc_Int_Oint),c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(B,C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(573,a,505,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint) = c_Orderings_Oord__class_Omax(B,A,tc_Int_Oint). [resolve(573,a,506,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,507,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint) = c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,508,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint) = A | -c_lessequals(A,B,tc_Int_Oint). [resolve(573,a,509,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint) != A | c_lessequals(A,B,tc_Int_Oint). [resolve(573,a,510,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint) = B | -c_lessequals(B,A,tc_Int_Oint). [resolve(573,a,511,a)].
% 2.70/2.98 Derived: c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(573,a,512,a)].
% 2.70/2.98 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),B,tc_Int_Oint). [resolve(573,a,515,a)].
% 2.70/2.98 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),A,tc_Int_Oint). [resolve(573,a,516,a)].
% 2.70/2.98 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(573,a,517,a)].
% 2.70/2.98 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(573,a,518,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),tc_Int_Oint) = c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint). [resolve(573,a,519,a)].
% 2.70/2.98 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(573,a,520,a)].
% 2.70/2.98 Derived: -c_lessequals(A,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(573,a,521,a)].
% 2.70/2.98 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(573,a,523,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint) = B | -c_lessequals(A,B,tc_Int_Oint). [resolve(573,a,527,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint) != B | c_lessequals(A,B,tc_Int_Oint). [resolve(573,a,528,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint) = A | -c_lessequals(B,A,tc_Int_Oint). [resolve(573,a,529,a)].
% 2.70/2.98 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(A,c_Orderings_Oord__class_Omax(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,530,a)].
% 2.70/2.98 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,531,a)].
% 2.70/2.98 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(A,c_Orderings_Oord__class_Omin(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,532,a)].
% 2.70/2.98 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(573,a,533,a)].
% 2.70/2.98 Derived: c_lessequals(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(573,a,534,a)].
% 2.70/2.98 Derived: c_Orderings_Oord__class_Omin(A,c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),tc_Int_Oint) = A. [resolve(573,a,538,a)].
% 2.70/2.98 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(C,A,tc_Int_Oint),B,tc_Int_Oint). [resolve(573,a,539,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(573,a,540,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(573,a,541,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(573,a,542,a)].
% 2.79/3.04 Derived: c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint) = c_Orderings_Oord__class_Omin(B,A,tc_Int_Oint). [resolve(573,a,545,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(573,a,546,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(573,a,547,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,548,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,549,a)].
% 2.79/3.04 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(C,B,tc_Int_Oint) | -c_lessequals(c_Orderings_Oord__class_Omin(C,A,tc_Int_Oint),B,tc_Int_Oint). [resolve(573,a,553,a)].
% 2.79/3.04 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_Orderings_Oord__class_Omax(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(573,a,554,a)].
% 2.79/3.04 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_Orderings_Oord__class_Omax(C,A,tc_Int_Oint),B,tc_Int_Oint). [resolve(573,a,555,a)].
% 2.79/3.04 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(573,a,556,a)].
% 2.79/3.04 Derived: c_lessequals(A,c_Orderings_Oord__class_Omax(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(573,a,557,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_Orderings_Oord__class_Omax(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,562,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(C,A,tc_Int_Oint),B,tc_Int_Oint). [resolve(573,a,563,a)].
% 2.79/3.04 Derived: -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(573,a,564,a)].
% 2.79/3.04 Derived: c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_Int_Oint),tc_Int_Oint) = c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,565,a)].
% 2.79/3.04 Derived: c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omax(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(573,a,566,a)].
% 2.79/3.04 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) | c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(573,a,569,a)].
% 2.79/3.04 Derived: c_lessequals(c_Orderings_Oord__class_Omax(A,c_Orderings_Oord__class_Omin(B,C,tc_Int_Oint),tc_Int_Oint),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),c_Orderings_Oord__class_Omax(A,C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(573,a,570,a)].
% 2.79/3.04 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(573,a,571,a)].
% 2.79/3.04 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(573,a,572,a)].
% 2.79/3.04 574 class_Orderings_Oorder(tc_nat) # label(clsarity_nat__Orderings_Oorder) # label(axiom). [assumption].
% 2.79/3.04 575 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | B = C | -c_lessequals(B,C,A) # label(cls_order__less__le_2) # label(axiom). [assumption].
% 2.79/3.04 576 -class_Orderings_Oorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_order__le__less_0) # label(axiom). [assumption].
% 2.79/3.04 577 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | B = C | -c_lessequals(B,C,A) # label(cls_order__le__neq__trans_0) # label(axiom). [assumption].
% 2.79/3.04 578 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) | B = C # label(cls_order__neq__le__trans_0) # label(axiom). [assumption].
% 2.79/3.04 579 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) | C = B # label(cls_xt1_I12_J_0) # label(axiom). [assumption].
% 2.79/3.04 580 -class_Orderings_Oorder(A) | B = C | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) # label(cls_order__antisym__conv_0) # label(axiom). [assumption].
% 2.79/3.04 581 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__eq__iff_2) # label(axiom). [assumption].
% 2.79/3.04 582 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__antisym_0) # label(axiom). [assumption].
% 2.79/3.04 583 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | -c_lessequals(B,C,A) # label(cls_xt1_I11_J_0) # label(axiom). [assumption].
% 2.79/3.04 584 -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].
% 2.79/3.04 585 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__le_1) # label(axiom). [assumption].
% 2.79/3.04 586 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_order__le__less_1) # label(axiom). [assumption].
% 2.79/3.04 587 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__iff_0) # label(axiom). [assumption].
% 2.79/3.04 588 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I8_J_0) # label(axiom). [assumption].
% 2.79/3.04 589 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_xt1_I7_J_0) # label(axiom). [assumption].
% 2.79/3.04 590 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I6_J_0) # label(axiom). [assumption].
% 2.79/3.04 591 -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].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,B,tc_nat) | B = A. [resolve(574,a,579,a)].
% 2.79/3.04 Derived: A = B | -c_lessequals(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(574,a,580,a)].
% 2.79/3.04 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(574,a,584,a)].
% 2.79/3.04 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(574,a,586,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(574,a,588,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(574,a,589,a)].
% 2.79/3.04 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(574,a,590,a)].
% 2.79/3.04 592 class_Orderings_Oorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Oorder) # label(axiom). [assumption].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint) | B = A. [resolve(592,a,579,a)].
% 2.79/3.04 Derived: A = B | -c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(592,a,580,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint). [resolve(592,a,584,a)].
% 2.79/3.04 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(592,a,586,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint). [resolve(592,a,588,a)].
% 2.79/3.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint). [resolve(592,a,589,a)].
% 2.79/3.04 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint). [resolve(592,a,590,a)].
% 2.86/3.10 593 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.86/3.10 594 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 2.86/3.10 595 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 2.86/3.10 596 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 2.86/3.10 597 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 2.86/3.10 598 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(B,C,A),D,A) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_max__add__distrib__left_0) # label(axiom). [assumption].
% 2.86/3.10 599 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 2.86/3.10 600 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 2.86/3.10 601 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(B,C,A),D,A) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_min__add__distrib__left_0) # label(axiom). [assumption].
% 2.86/3.10 602 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 2.86/3.10 603 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 2.86/3.10 604 -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].
% 2.86/3.10 605 -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].
% 2.86/3.10 606 -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].
% 2.86/3.10 607 -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].
% 2.86/3.10 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(593,a,594,a)].
% 2.86/3.10 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(593,a,595,a)].
% 2.86/3.10 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(593,a,596,a)].
% 2.86/3.10 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat). [resolve(593,a,597,a)].
% 2.86/3.10 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(593,a,598,a)].
% 2.86/3.10 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(593,a,599,a)].
% 2.86/3.10 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(593,a,600,a)].
% 2.86/3.10 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(A,B,tc_nat),C,tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(593,a,601,a)].
% 2.86/3.10 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(593,a,602,a)].
% 2.86/3.10 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(593,a,603,a)].
% 2.86/3.10 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(593,a,604,a)].
% 2.86/3.10 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(593,a,605,a)].
% 2.86/3.10 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(593,a,606,a)].
% 2.86/3.10 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(593,a,607,a)].
% 2.86/3.10 608 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.86/3.10 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(608,a,594,a)].
% 2.86/3.10 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(608,a,595,a)].
% 2.86/3.10 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(608,a,596,a)].
% 2.86/3.10 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(608,a,597,a)].
% 2.86/3.10 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(608,a,598,a)].
% 2.86/3.10 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(608,a,599,a)].
% 2.98/3.21 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(608,a,600,a)].
% 2.98/3.21 Derived: c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(608,a,601,a)].
% 2.98/3.21 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(608,a,602,a)].
% 2.98/3.21 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(608,a,603,a)].
% 2.98/3.21 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(608,a,604,a)].
% 2.98/3.21 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(608,a,605,a)].
% 2.98/3.21 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(608,a,606,a)].
% 2.98/3.21 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(608,a,607,a)].
% 2.98/3.21 609 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.98/3.21 610 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 2.98/3.21 611 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 2.98/3.21 612 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 2.98/3.21 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(609,a,612,a)].
% 2.98/3.21 613 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.98/3.21 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(613,a,612,a)].
% 2.98/3.21 614 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 2.98/3.21 615 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__nonneg_0) # label(axiom). [assumption].
% 2.98/3.21 616 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_0) # label(axiom). [assumption].
% 2.98/3.21 617 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),A) # label(cls_abs__triangle__ineq2_0) # label(axiom). [assumption].
% 2.98/3.21 618 -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].
% 2.98/3.21 619 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D1_0) # label(axiom). [assumption].
% 2.98/3.21 620 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_1) # label(axiom). [assumption].
% 2.98/3.21 621 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),A) # label(cls_abs__triangle__ineq3_0) # label(axiom). [assumption].
% 2.98/3.21 622 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__triangle__ineq_0) # label(axiom). [assumption].
% 2.98/3.21 623 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,A),A),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(C,E,A),A),A),A) # label(cls_abs__diff__triangle__ineq_0) # label(axiom). [assumption].
% 2.98/3.21 624 -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].
% 2.98/3.21 625 -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].
% 2.98/3.21 626 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__self_0) # label(axiom). [assumption].
% 2.98/3.21 627 -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].
% 2.98/3.21 628 -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].
% 2.98/3.21 629 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__triangle__ineq4_0) # label(axiom). [assumption].
% 2.98/3.21 630 -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].
% 2.98/3.21 631 -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].
% 2.98/3.21 632 -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].
% 2.98/3.21 633 -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].
% 2.98/3.21 634 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__zero_0) # label(axiom). [assumption].
% 2.98/3.21 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(614,a,615,a)].
% 2.98/3.21 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(614,a,616,a)].
% 2.98/3.21 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(614,a,617,a)].
% 2.98/3.21 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(614,a,618,a)].
% 2.98/3.21 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(614,a,619,a)].
% 2.98/3.21 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(614,a,620,a)].
% 2.98/3.21 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(614,a,621,a)].
% 2.98/3.21 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(614,a,622,a)].
% 2.98/3.21 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,C,tc_Int_Oint),tc_Int_Oint),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(B,D,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(614,a,623,a)].
% 2.98/3.21 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oabs__class_Oabs(A,tc_Int_Oint). [resolve(614,a,624,a)].
% 2.98/3.21 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(614,a,625,a)].
% 2.98/3.21 Derived: c_lessequals(A,c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint). [resolve(614,a,626,a)].
% 2.98/3.21 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(614,a,627,a)].
% 2.98/3.21 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(614,a,628,a)].
% 2.98/3.21 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(614,a,629,a)].
% 2.98/3.21 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint). [resolve(614,a,630,a)].
% 2.98/3.21 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(614,a,631,a)].
% 2.98/3.21 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(614,a,632,a)].
% 2.98/3.21 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(614,a,633,a)].
% 3.02/3.27 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint). [resolve(614,a,634,a)].
% 3.02/3.27 635 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 3.02/3.27 636 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 3.02/3.27 637 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 3.02/3.27 638 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 3.02/3.27 639 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 3.02/3.27 640 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 3.02/3.27 641 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 3.02/3.27 642 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 3.02/3.27 643 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 3.02/3.27 644 -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].
% 3.02/3.27 645 -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].
% 3.02/3.27 646 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 3.02/3.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(635,a,636,a)].
% 3.02/3.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(635,a,637,a)].
% 3.02/3.27 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(635,a,638,a)].
% 3.02/3.27 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(635,a,639,a)].
% 3.02/3.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(635,a,640,a)].
% 3.02/3.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(635,a,641,a)].
% 3.02/3.27 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(635,a,643,a)].
% 3.02/3.27 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(635,a,644,a)].
% 3.02/3.27 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(635,a,646,a)].
% 3.02/3.27 647 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 3.02/3.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(647,a,636,a)].
% 3.02/3.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(647,a,637,a)].
% 3.02/3.27 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(647,a,638,a)].
% 3.02/3.27 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(647,a,639,a)].
% 3.02/3.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(647,a,640,a)].
% 3.02/3.27 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(647,a,641,a)].
% 3.10/3.32 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(647,a,643,a)].
% 3.10/3.32 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(647,a,644,a)].
% 3.10/3.32 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(647,a,646,a)].
% 3.10/3.32 648 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 3.10/3.32 649 -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].
% 3.10/3.32 650 -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].
% 3.10/3.32 651 -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].
% 3.10/3.32 652 -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].
% 3.10/3.32 653 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 3.10/3.32 654 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 3.10/3.32 655 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 3.10/3.32 656 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 3.10/3.32 657 -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].
% 3.10/3.32 658 -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].
% 3.10/3.32 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(648,a,651,a)].
% 3.10/3.32 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(648,a,653,a)].
% 3.17/3.43 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(648,a,655,a)].
% 3.17/3.43 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(648,a,657,a)].
% 3.17/3.43 659 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 3.17/3.43 660 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 3.17/3.43 661 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 3.17/3.43 662 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 3.17/3.43 663 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 3.17/3.43 664 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 3.17/3.43 665 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 3.17/3.43 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(659,a,660,a)].
% 3.17/3.43 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(659,a,661,a)].
% 3.17/3.43 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(659,a,662,a)].
% 3.17/3.43 666 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 3.17/3.43 667 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.17/3.43 668 -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].
% 3.17/3.43 669 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.17/3.43 670 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.26/3.48 671 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.26/3.48 672 -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].
% 3.26/3.48 673 -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].
% 3.26/3.48 674 -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].
% 3.26/3.48 675 -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].
% 3.26/3.48 676 -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].
% 3.26/3.48 677 -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].
% 3.26/3.48 678 -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].
% 3.26/3.48 679 -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].
% 3.26/3.48 680 -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].
% 3.26/3.48 681 -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].
% 3.26/3.48 682 -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].
% 3.26/3.48 683 -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].
% 3.26/3.48 684 -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].
% 3.26/3.48 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(671,a,676,a)].
% 3.40/3.64 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(671,a,677,a)].
% 3.40/3.64 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(671,a,679,a)].
% 3.40/3.64 685 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.40/3.64 686 -class_Ring__and__Field_Ocomm__semiring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 3.40/3.64 687 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.40/3.64 688 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.40/3.64 689 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 3.40/3.64 690 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 3.40/3.64 691 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 3.40/3.64 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(689,a,690,a)].
% 3.40/3.64 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(689,a,691,a)].
% 3.40/3.64 692 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 3.40/3.64 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(692,a,690,a)].
% 3.40/3.64 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(692,a,691,a)].
% 3.40/3.64 693 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 3.40/3.64 694 -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].
% 3.47/3.69 695 -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].
% 3.47/3.69 696 -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].
% 3.47/3.69 697 -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].
% 3.47/3.69 698 -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].
% 3.47/3.69 699 -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].
% 3.47/3.69 700 -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].
% 3.47/3.69 701 -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].
% 3.47/3.69 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(693,a,695,b)].
% 3.47/3.69 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(693,a,696,b)].
% 3.47/3.69 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(693,a,697,b)].
% 3.47/3.69 Derived: -class_SEQ_Obanach(tc_Complex_Ocomplex) | c_Transcendental_Oexp(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(693,a,700,b)].
% 3.47/3.69 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(693,a,701,b)].
% 3.47/3.69 702 class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 3.47/3.69 703 -class_Ring__and__Field_Ocomm__ring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ominus__class_Ominus(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__diff_0) # label(axiom). [assumption].
% 3.47/3.69 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(702,a,703,a)].
% 3.47/3.69 704 class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 3.60/3.84 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Complex_Ocomplex) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Complex_Ocomplex). [resolve(704,a,703,a)].
% 3.60/3.84 705 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 3.60/3.84 706 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 3.60/3.84 707 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 3.60/3.84 708 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 3.60/3.84 709 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 3.60/3.84 710 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 3.60/3.84 711 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__fact__not__zero_0) # label(axiom). [assumption].
% 3.60/3.84 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(709,a,710,a)].
% 3.60/3.84 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(709,a,711,a)].
% 3.60/3.84 712 class_Nat_Osemiring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 3.60/3.84 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint) | A = B. [resolve(712,a,710,a)].
% 3.60/3.84 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(712,a,711,a)].
% 3.60/3.84 713 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 3.60/3.84 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex) | A = B. [resolve(713,a,710,a)].
% 3.60/3.84 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(A,tc_nat),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(713,a,711,a)].
% 3.60/3.84 714 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 3.60/3.84 715 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ominus__class_Ominus(C,D,A),A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A) # label(cls_right__diff__distrib__number__of_0) # label(axiom). [assumption].
% 3.60/3.84 716 -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].
% 3.60/3.84 717 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,A),A),A) # label(cls_left__diff__distrib__number__of_0) # label(axiom). [assumption].
% 3.60/3.84 718 -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].
% 3.60/3.84 719 -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].
% 3.60/3.84 720 -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].
% 3.60/3.84 Derived: -class_Int_Onumber(tc_Int_Oint) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),C,tc_Int_Oint),tc_Int_Oint). [resolve(714,a,715,a)].
% 3.60/3.84 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,A,tc_Int_Oint),B,tc_Int_Oint),D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),D,tc_Int_Oint). [resolve(714,a,716,a)].
% 3.60/3.84 Derived: -class_Int_Onumber(tc_Int_Oint) | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(714,a,717,a)].
% 3.60/3.84 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint),tc_Int_Oint). [resolve(714,a,718,a)].
% 3.60/3.84 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint) = E. [resolve(714,a,719,a)].
% 3.60/3.84 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,B,tc_Int_Oint),E,tc_Int_Oint) | C = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),B,tc_Int_Oint),E,tc_Int_Oint). [resolve(714,a,720,a)].
% 3.60/3.84 721 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 3.60/3.84 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(721,a,716,a)].
% 3.60/3.84 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(721,a,718,a)].
% 3.77/3.99 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(721,a,719,a)].
% 3.77/3.99 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(721,a,720,a)].
% 3.77/3.99 722 class_Orderings_Obot(tc_nat) # label(clsarity_nat__Orderings_Obot) # label(axiom). [assumption].
% 3.77/3.99 723 -class_Orderings_Obot(A) | c_lessequals(c_Orderings_Obot__class_Obot(A),B,A) # label(cls_bot__least_0) # label(axiom). [assumption].
% 3.77/3.99 Derived: c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),A,tc_nat). [resolve(722,a,723,a)].
% 3.77/3.99 724 class_Ring__and__Field_Olordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Olordered__ring) # label(axiom). [assumption].
% 3.77/3.99 725 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A),A) # label(cls_abs__le__mult_0) # label(axiom). [assumption].
% 3.77/3.99 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(724,a,725,a)].
% 3.77/3.99 726 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 3.77/3.99 727 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 3.77/3.99 728 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left__number__of_1) # label(axiom). [assumption].
% 3.77/3.99 729 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left__number__of_0) # label(axiom). [assumption].
% 3.77/3.99 730 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 3.77/3.99 731 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 3.77/3.99 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(726,a,727,a)].
% 3.77/3.99 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(726,a,728,a)].
% 3.77/3.99 Derived: -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(726,a,729,a)].
% 3.77/4.04 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(726,a,730,a)].
% 3.77/4.04 732 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 3.77/4.04 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Suc(A),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(732,a,727,a)].
% 3.77/4.04 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(732,a,728,a)].
% 3.77/4.04 Derived: -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(732,a,729,a)].
% 3.77/4.04 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(732,a,730,a)].
% 3.77/4.04 733 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 3.77/4.04 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Suc(A),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(733,a,727,a)].
% 3.77/4.04 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(733,a,728,a)].
% 3.77/4.04 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(733,a,729,a)].
% 3.77/4.04 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(733,a,730,a)].
% 3.77/4.04 734 class_Divides_Oring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 3.77/4.04 735 -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].
% 3.77/4.04 736 -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].
% 3.77/4.04 737 -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].
% 3.77/4.04 738 -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].
% 3.93/4.19 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(734,a,735,a)].
% 3.93/4.19 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint). [resolve(734,a,736,a)].
% 3.93/4.19 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(734,a,737,a)].
% 3.93/4.19 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(E,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(734,a,738,a)].
% 3.93/4.19 739 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.93/4.19 740 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 3.93/4.19 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(A,C,tc_nat) | B = C. [resolve(739,a,740,a)].
% 3.93/4.19 741 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.93/4.19 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C. [resolve(741,a,740,a)].
% 3.93/4.19 742 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.93/4.19 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C. [resolve(742,a,740,a)].
% 3.93/4.19 743 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.93/4.19 744 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 3.93/4.19 745 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(D,C,A) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 3.93/4.19 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C. [resolve(743,a,745,a)].
% 3.93/4.19 746 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.93/4.19 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint) | A = C. [resolve(746,a,745,a)].
% 3.93/4.19 747 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.93/4.19 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(C,B,tc_Complex_Ocomplex) | A = C. [resolve(747,a,745,a)].
% 3.93/4.19 748 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 3.93/4.19 749 -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].
% 3.93/4.19 750 -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].
% 4.02/4.24 751 -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].
% 4.02/4.24 752 -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].
% 4.02/4.24 753 -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].
% 4.02/4.24 754 -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].
% 4.02/4.24 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),B,tc_Int_Oint) = A. [resolve(748,a,749,a)].
% 4.02/4.24 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),B,tc_Int_Oint) = A. [resolve(748,a,750,a)].
% 4.02/4.24 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(748,a,751,a)].
% 4.02/4.24 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(748,a,752,a)].
% 4.02/4.24 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(748,a,754,a)].
% 4.02/4.24 755 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 4.02/4.24 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A. [resolve(755,a,749,a)].
% 4.02/4.24 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = A. [resolve(755,a,750,a)].
% 4.02/4.24 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(755,a,751,a)].
% 4.02/4.24 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(755,a,752,a)].
% 4.02/4.24 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(755,a,754,a)].
% 4.02/4.24 756 class_Orderings_Opreorder(tc_nat) # label(clsarity_nat__Orderings_Opreorder) # label(axiom). [assumption].
% 4.02/4.24 757 -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].
% 4.02/4.24 758 -class_Orderings_Opreorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_less__le__not__le_1) # label(axiom). [assumption].
% 4.02/4.24 759 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__irrefl_0) # label(axiom). [assumption].
% 4.02/4.24 760 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_less__le__not__le_2) # label(axiom). [assumption].
% 4.02/4.24 761 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_order__less__imp__le_0) # label(axiom). [assumption].
% 4.02/4.24 762 -class_Orderings_Opreorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__refl_0) # label(axiom). [assumption].
% 4.02/4.24 763 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__le__less__trans_0) # label(axiom). [assumption].
% 4.02/4.24 764 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_order__less__le__trans_0) # label(axiom). [assumption].
% 4.02/4.24 765 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_lessequals(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__trans_0) # label(axiom). [assumption].
% 4.02/4.24 766 -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].
% 4.02/4.24 767 -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].
% 4.07/4.34 768 class_Orderings_Opreorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Opreorder) # label(axiom). [assumption].
% 4.07/4.34 769 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 4.07/4.34 770 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A) # label(cls_add__cancel__21_1) # label(axiom). [assumption].
% 4.07/4.34 771 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) != c_HOL_Oplus__class_Oplus(C,E,A) | c_HOL_Oplus__class_Oplus(B,D,A) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 4.07/4.34 772 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) != c_HOL_Ominus__class_Ominus(C,D,A) | C = D # label(cls_eq__eqI_0) # label(axiom). [assumption].
% 4.07/4.34 773 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,D,A) | B = C # label(cls_eq__eqI_1) # label(axiom). [assumption].
% 4.07/4.34 774 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,D,A),c_HOL_Ominus__class_Ominus(C,E,A),A) # label(cls_Deriv_Oadd__diff__add_0) # label(axiom). [assumption].
% 4.07/4.34 775 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__iff__diff__eq__0_0) # label(axiom). [assumption].
% 4.07/4.34 776 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_eq__iff__diff__eq__0_1) # label(axiom). [assumption].
% 4.07/4.34 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) = D. [resolve(769,a,771,a)].
% 4.07/4.34 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint) | B = C. [resolve(769,a,772,a)].
% 4.07/4.34 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,C,tc_Int_Oint) | A = B. [resolve(769,a,773,a)].
% 4.07/4.34 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,C,tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,D,tc_Int_Oint),tc_Int_Oint). [resolve(769,a,774,a)].
% 4.07/4.34 777 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 4.07/4.34 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(B,D,tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) = D. [resolve(777,a,771,a)].
% 4.07/4.34 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(B,C,tc_Complex_Ocomplex) | B = C. [resolve(777,a,772,a)].
% 4.07/4.34 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(C,C,tc_Complex_Ocomplex) | A = B. [resolve(777,a,773,a)].
% 4.07/4.34 Derived: c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(A,C,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(777,a,774,a)].
% 4.07/4.34 778 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 4.07/4.34 779 -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].
% 4.07/4.34 780 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 4.24/4.48 781 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 4.24/4.48 782 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 4.24/4.48 783 -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].
% 4.24/4.48 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(782,a,783,a)].
% 4.24/4.48 784 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 4.24/4.48 785 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A) # label(cls_right__distrib__number__of_0) # label(axiom). [assumption].
% 4.24/4.48 786 -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].
% 4.24/4.48 787 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,A),A),A) # label(cls_left__distrib__number__of_0) # label(axiom). [assumption].
% 4.24/4.48 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(784,a,786,a)].
% 4.24/4.48 788 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 4.24/4.48 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint),D,tc_Int_Oint). [resolve(788,a,786,a)].
% 4.24/4.48 789 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 4.24/4.48 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(789,a,786,a)].
% 4.24/4.48 790 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 4.36/4.58 791 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom). [assumption].
% 4.36/4.58 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(790,a,791,a)].
% 4.36/4.58 792 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption].
% 4.36/4.58 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) | A = B. [resolve(792,a,791,a)].
% 4.36/4.58 793 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 4.36/4.58 794 -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].
% 4.36/4.58 795 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 4.36/4.58 796 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 4.36/4.58 797 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_0) # label(axiom). [assumption].
% 4.36/4.58 798 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 4.36/4.58 799 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff__number__of_2) # label(axiom). [assumption].
% 4.36/4.58 800 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_1) # label(axiom). [assumption].
% 4.36/4.58 801 -class_Ring__and__Field_Ozero__neq__one(A) | c_Ring__and__Field_Ozero__neq__one(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__neq__one__class_Oaxioms_0) # label(axiom). [assumption].
% 4.36/4.58 802 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 4.36/4.58 803 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 4.36/4.58 804 -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].
% 4.36/4.58 805 -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].
% 4.36/4.58 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(796,a,797,a)].
% 4.36/4.58 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(796,a,798,a)].
% 4.36/4.58 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(796,a,800,a)].
% 4.36/4.58 Derived: c_Ring__and__Field_Ozero__neq__one(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(796,a,801,a)].
% 4.36/4.58 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(796,a,803,a)].
% 4.36/4.58 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(796,a,804,a)].
% 4.36/4.58 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(796,a,805,a)].
% 4.36/4.58 806 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 4.36/4.58 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(806,a,797,a)].
% 4.36/4.58 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(806,a,798,a)].
% 4.36/4.58 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(806,a,800,a)].
% 4.36/4.58 Derived: c_Ring__and__Field_Ozero__neq__one(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(806,a,801,a)].
% 4.36/4.58 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(806,a,803,a)].
% 4.36/4.58 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(806,a,804,a)].
% 4.36/4.58 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(806,a,805,a)].
% 4.36/4.58 807 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 4.36/4.58 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(807,a,797,a)].
% 4.42/4.63 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(807,a,798,a)].
% 4.42/4.63 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(807,a,800,a)].
% 4.42/4.63 Derived: c_Ring__and__Field_Ozero__neq__one(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(807,a,801,a)].
% 4.42/4.63 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(807,a,803,a)].
% 4.42/4.63 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(807,a,804,a)].
% 4.42/4.63 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(807,a,805,a)].
% 4.42/4.63 808 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.42/4.63 809 -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].
% 4.42/4.63 810 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 4.42/4.63 811 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 4.42/4.63 812 -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].
% 4.42/4.63 813 -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].
% 4.42/4.63 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(808,a,809,a)].
% 4.42/4.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(808,a,810,a)].
% 4.42/4.63 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(808,a,811,a)].
% 4.42/4.63 814 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.66/4.87 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(814,a,809,a)].
% 4.66/4.87 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(814,a,810,a)].
% 4.66/4.87 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(814,a,811,a)].
% 4.66/4.87 815 class_Ring__and__Field_Oabs__if(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 4.66/4.87 816 -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].
% 4.66/4.87 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(815,a,816,a)].
% 4.66/4.87 817 class_Ring__and__Field_Oring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 4.66/4.87 818 -class_Ring__and__Field_Oring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(B,C,tc_nat),A) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_lessequals(C,B,tc_nat) # label(cls_of__nat__diff_0) # label(axiom). [assumption].
% 4.66/4.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_Int_Oint) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,A,tc_nat). [resolve(817,a,818,a)].
% 4.66/4.87 819 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 4.66/4.87 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_lessequals(B,A,tc_nat). [resolve(819,a,818,a)].
% 4.66/4.87 820 class_Ring__and__Field_Osgn__if(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osgn__if) # label(axiom). [assumption].
% 4.66/4.87 821 -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].
% 4.66/4.87 822 -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].
% 4.66/4.87 823 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 4.66/4.87 824 -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].
% 4.66/4.87 825 -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].
% 4.66/4.87 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(823,a,824,a)].
% 4.66/4.87 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(823,a,825,a)].
% 4.66/4.87 826 class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 4.84/5.06 827 -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].
% 4.84/5.06 828 -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].
% 4.84/5.06 829 -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].
% 4.84/5.06 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(826,a,829,a)].
% 4.84/5.06 830 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].
% 4.84/5.06 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(830,a,829,a)].
% 4.84/5.06 831 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 4.84/5.06 832 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 4.84/5.06 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(831,a,832,a)].
% 4.84/5.06 833 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 4.84/5.06 Derived: c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(833,a,832,a)].
% 4.84/5.06 834 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 4.84/5.06 835 -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].
% 4.84/5.06 836 -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].
% 4.84/5.06 837 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 4.84/5.06 838 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 4.84/5.06 839 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 4.84/5.06 840 -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].
% 4.84/5.06 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(839,a,840,a)].
% 4.84/5.06 841 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 4.84/5.06 842 -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(axCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------