TSTP Solution File: ALG397-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG397-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:54:42 EDT 2022
% Result : Unsatisfiable 1.70s 1.99s
% Output : Refutation 1.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : ALG397-1 : TPTP v8.1.0. Released v4.1.0.
% 0.02/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.29 % DateTime : Thu Jun 9 05:23:52 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.70/1.03 ============================== Prover9 ===============================
% 0.70/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.03 Process 2249 was started by sandbox2 on n032.cluster.edu,
% 0.70/1.03 Thu Jun 9 05:23:53 2022
% 0.70/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2088_n032.cluster.edu".
% 0.70/1.03 ============================== end of head ===========================
% 0.70/1.03
% 0.70/1.03 ============================== INPUT =================================
% 0.70/1.03
% 0.70/1.03 % Reading from file /tmp/Prover9_2088_n032.cluster.edu
% 0.70/1.03
% 0.70/1.03 set(prolog_style_variables).
% 0.70/1.03 set(auto2).
% 0.70/1.03 % set(auto2) -> set(auto).
% 0.70/1.03 % set(auto) -> set(auto_inference).
% 0.70/1.03 % set(auto) -> set(auto_setup).
% 0.70/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.70/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/1.03 % set(auto) -> set(auto_limits).
% 0.70/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/1.03 % set(auto) -> set(auto_denials).
% 0.70/1.03 % set(auto) -> set(auto_process).
% 0.70/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.70/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.70/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.70/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.70/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.70/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.70/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.70/1.03 % set(auto2) -> assign(stats, some).
% 0.70/1.03 % set(auto2) -> clear(echo_input).
% 0.70/1.03 % set(auto2) -> set(quiet).
% 0.70/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.70/1.03 % set(auto2) -> clear(print_given).
% 0.70/1.03 assign(lrs_ticks,-1).
% 0.70/1.03 assign(sos_limit,10000).
% 0.70/1.03 assign(order,kbo).
% 0.70/1.03 set(lex_order_vars).
% 0.70/1.03 clear(print_given).
% 0.70/1.03
% 0.70/1.03 % formulas(sos). % not echoed (713 formulas)
% 0.70/1.03
% 0.70/1.03 ============================== end of input ==========================
% 0.70/1.03
% 0.70/1.03 % From the command line: assign(max_seconds, 300).
% 0.70/1.03
% 0.70/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/1.03
% 0.70/1.03 % Formulas that are not ordinary clauses:
% 0.70/1.03
% 0.70/1.03 ============================== end of process non-clausal formulas ===
% 0.70/1.03
% 0.70/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.03
% 0.70/1.03 ============================== PREDICATE ELIMINATION =================
% 0.70/1.03 1 class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 0.70/1.03 2 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),A) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 0.70/1.03 3 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 0.70/1.03 4 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 0.70/1.03 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_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 0.70/1.03 6 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 0.70/1.03 7 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 0.70/1.03 8 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 0.70/1.03 9 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),A) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 0.70/1.03 10 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 0.70/1.03 11 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 0.70/1.03 12 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 0.70/1.03 13 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 0.70/1.03 14 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 0.70/1.03 15 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 0.70/1.03 16 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 0.70/1.03 17 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 0.70/1.03 18 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 0.70/1.03 19 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 0.70/1.03 20 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 0.70/1.03 21 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 0.70/1.03 22 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 0.70/1.03 23 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 0.70/1.03 24 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 0.70/1.03 25 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 0.70/1.03 26 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 0.70/1.03 27 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 0.70/1.03 28 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 0.70/1.03 29 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 0.70/1.03 30 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 0.70/1.03 31 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 0.70/1.03 32 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 0.70/1.03 33 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 0.70/1.03 34 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 0.70/1.03 35 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 0.70/1.03 36 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 0.70/1.03 37 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(D,B,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 0.70/1.03 38 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 0.70/1.03 39 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 0.70/1.03 40 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 0.70/1.03 41 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 0.70/1.03 42 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 0.70/1.03 43 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 0.70/1.03 44 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 0.70/1.03 45 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 0.70/1.03 46 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 0.70/1.03 47 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_0) # label(axiom). [assumption].
% 0.70/1.03 48 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_1) # label(axiom). [assumption].
% 0.70/1.03 49 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom). [assumption].
% 0.70/1.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal). [resolve(1,a,2,a)].
% 0.70/1.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(1,a,3,a)].
% 0.70/1.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,4,a)].
% 0.70/1.03 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal). [resolve(1,a,5,a)].
% 0.70/1.03 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),tc_RealDef_Oreal). [resolve(1,a,6,a)].
% 0.70/1.03 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal). [resolve(1,a,7,a)].
% 0.70/1.03 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),tc_RealDef_Oreal). [resolve(1,a,8,a)].
% 0.70/1.03 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),tc_RealDef_Oreal). [resolve(1,a,9,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal). [resolve(1,a,10,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal). [resolve(1,a,11,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal). [resolve(1,a,12,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal). [resolve(1,a,13,a)].
% 0.70/1.03 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,14,a)].
% 0.70/1.03 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(1,a,15,a)].
% 0.70/1.03 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,16,a)].
% 0.70/1.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,17,a)].
% 0.70/1.03 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,18,a)].
% 0.70/1.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,19,a)].
% 0.70/1.03 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,20,a)].
% 0.70/1.03 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,21,a)].
% 0.70/1.03 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,22,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,23,a)].
% 0.70/1.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),tc_RealDef_Oreal). [resolve(1,a,24,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal). [resolve(1,a,25,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal). [resolve(1,a,26,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal). [resolve(1,a,27,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal). [resolve(1,a,28,a)].
% 0.70/1.03 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(1,a,29,a)].
% 0.70/1.03 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(1,a,30,a)].
% 0.70/1.03 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,31,a)].
% 0.70/1.03 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,32,a)].
% 0.70/1.03 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,33,a)].
% 0.70/1.03 Derived: A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,34,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1,a,35,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1,a,36,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,37,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(1,a,38,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,40,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(1,a,41,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(1,a,44,a)].
% 0.70/1.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(1,a,46,a)].
% 0.70/1.03 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1,a,47,a)].
% 0.70/1.03 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),B)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1,a,48,a)].
% 0.70/1.03 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(1,a,49,a)].
% 0.70/1.03 50 class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),tc_Polynomial_Opoly(A)). [resolve(50,a,2,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(50,a,3,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,4,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)). [resolve(50,a,5,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),tc_Polynomial_Opoly(A)). [resolve(50,a,6,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)). [resolve(50,a,7,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),tc_Polynomial_Opoly(A)). [resolve(50,a,8,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),tc_Polynomial_Opoly(A)). [resolve(50,a,9,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)). [resolve(50,a,10,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),tc_Polynomial_Opoly(A)). [resolve(50,a,11,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),tc_Polynomial_Opoly(A)). [resolve(50,a,12,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)). [resolve(50,a,13,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,14,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(50,a,15,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,16,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,17,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,18,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,19,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,20,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,21,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,22,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,23,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),tc_Polynomial_Opoly(A)). [resolve(50,a,24,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),tc_Polynomial_Opoly(A)). [resolve(50,a,25,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)). [resolve(50,a,26,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)). [resolve(50,a,27,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),tc_Polynomial_Opoly(A)). [resolve(50,a,28,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(50,a,29,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(50,a,30,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,31,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,32,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,33,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,34,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(50,a,35,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)),tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(50,a,36,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,37,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(50,a,38,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,40,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(50,a,41,a)].
% 0.70/1.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(50,a,44,a)].
% 0.70/1.06 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(50,a,46,a)].
% 0.70/1.06 Derived: -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(50,a,47,a)].
% 0.70/1.06 Derived: -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),C)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(50,a,48,a)].
% 0.70/1.06 Derived: -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(50,a,49,a)].
% 0.70/1.06 51 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 0.70/1.06 52 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 0.70/1.06 53 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 0.70/1.06 54 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 0.70/1.06 55 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 0.70/1.06 56 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,C,A) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 0.70/1.06 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,A,tc_RealDef_Oreal). [resolve(51,a,55,a)].
% 0.70/1.06 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(C,B,tc_RealDef_Oreal). [resolve(51,a,56,a)].
% 0.70/1.06 57 class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 0.70/1.07 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,B,tc_Polynomial_Opoly(A)). [resolve(57,a,55,a)].
% 0.70/1.07 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)). [resolve(57,a,56,a)].
% 0.70/1.07 58 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.70/1.07 59 -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].
% 0.70/1.07 60 -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].
% 0.70/1.07 61 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.70/1.07 62 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 0.70/1.07 63 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 0.70/1.07 64 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 0.80/1.07 65 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.80/1.07 66 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.80/1.07 67 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 0.80/1.07 68 -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].
% 0.80/1.07 69 -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].
% 0.80/1.07 70 -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].
% 0.80/1.07 71 -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].
% 0.80/1.07 72 -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].
% 0.80/1.07 73 -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].
% 0.80/1.07 74 -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].
% 0.80/1.07 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(58,a,59,a)].
% 0.80/1.07 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(58,a,61,a)].
% 0.80/1.07 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(58,a,65,a)].
% 0.80/1.07 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(58,a,66,a)].
% 0.80/1.07 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(58,a,67,a)].
% 0.80/1.09 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(58,a,68,a)].
% 0.80/1.09 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(58,a,71,a)].
% 0.80/1.09 75 class_Orderings_Olinorder(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Orderings_Olinorder) # label(axiom). [assumption].
% 0.80/1.09 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal). [resolve(75,a,59,a)].
% 0.80/1.09 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal). [resolve(75,a,61,a)].
% 0.80/1.09 Derived: -c_HOL_Oord__class_Oless(A,A,tc_RealDef_Oreal). [resolve(75,a,65,a)].
% 0.80/1.09 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal). [resolve(75,a,66,a)].
% 0.80/1.09 Derived: -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(75,a,67,a)].
% 0.80/1.09 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | c_lessequals(B,A,tc_RealDef_Oreal). [resolve(75,a,68,a)].
% 0.80/1.09 Derived: -c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(75,a,71,a)].
% 0.80/1.09 76 class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [assumption].
% 0.80/1.09 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = C | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(76,a,59,a)].
% 0.80/1.09 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = C | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(76,a,61,a)].
% 0.80/1.09 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,B,tc_Polynomial_Opoly(A)). [resolve(76,a,65,a)].
% 0.80/1.09 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(76,a,66,a)].
% 0.80/1.09 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)). [resolve(76,a,67,a)].
% 0.80/1.09 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(76,a,68,a)].
% 0.80/1.09 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(76,a,71,a)].
% 0.80/1.09 77 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 0.80/1.09 78 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 0.80/1.09 79 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1_0) # label(axiom). [assumption].
% 0.80/1.09 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C)). [resolve(77,a,78,a)].
% 0.80/1.09 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(77,a,79,a)].
% 0.80/1.09 80 class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 0.80/1.09 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C)). [resolve(80,a,78,a)].
% 0.80/1.09 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),A) = A. [resolve(80,a,79,a)].
% 0.80/1.11 81 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 0.80/1.11 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)). [resolve(81,a,78,a)].
% 0.80/1.11 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(81,a,79,a)].
% 0.80/1.11 82 class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 0.80/1.11 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D)). [resolve(82,a,78,a)].
% 0.80/1.11 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A))),B) = B. [resolve(82,a,79,a)].
% 0.80/1.11 83 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 0.80/1.11 84 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 0.80/1.11 85 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 0.80/1.11 86 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 0.80/1.11 87 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 0.80/1.11 88 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 0.80/1.11 89 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 0.80/1.11 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(83,a,84,a)].
% 0.80/1.11 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(83,a,85,a)].
% 0.80/1.13 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(83,a,86,a)].
% 0.80/1.13 90 class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 0.80/1.13 91 class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 0.80/1.13 92 class_Int_Onumber__ring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Int_Onumber__ring) # label(axiom). [assumption].
% 0.80/1.13 93 -class_Int_Onumber__ring(A) | c_HOL_Ouminus__class_Ouminus(B,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A)),B) # label(cls_class__ring_Oneg__mul_0) # label(axiom). [assumption].
% 0.80/1.13 94 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 0.80/1.13 95 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 0.80/1.13 96 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 0.80/1.13 97 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 0.80/1.13 98 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 0.80/1.13 99 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 0.80/1.13 100 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 0.80/1.13 101 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 0.80/1.13 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)),A). [resolve(92,a,93,a)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)) | B = D | A = C. [resolve(92,a,94,b)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)). [resolve(92,a,96,b)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)). [resolve(92,a,98,b)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(92,a,99,b)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(92,a,100,b)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B = C. [resolve(92,a,101,b)].
% 0.80/1.13 102 class_Int_Onumber__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Onumber__ring) # label(axiom). [assumption].
% 0.80/1.13 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)),A). [resolve(102,a,93,a)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) | B = D | A = C. [resolve(102,a,94,b)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)). [resolve(102,a,96,b)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(102,a,98,b)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(102,a,99,b)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(102,a,100,b)].
% 0.80/1.13 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(102,a,101,b)].
% 0.80/1.15 103 class_Int_Onumber__ring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring__1(A) # label(clsarity_Polynomial__Opoly__Int_Onumber__ring) # label(axiom). [assumption].
% 0.80/1.15 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A))),B). [resolve(103,a,93,a)].
% 0.80/1.15 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)) | C = E | B = D. [resolve(103,a,94,b)].
% 0.80/1.15 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)). [resolve(103,a,96,b)].
% 0.80/1.15 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))). [resolve(103,a,98,b)].
% 0.80/1.15 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | B != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(103,a,99,b)].
% 0.80/1.15 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),E)) | D = E | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(103,a,100,b)].
% 0.80/1.15 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D) | C = D. [resolve(103,a,101,b)].
% 0.80/1.15 104 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 0.80/1.15 105 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 0.80/1.15 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(104,a,105,a)].
% 0.80/1.15 106 class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 0.80/1.15 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(106,a,105,a)].
% 0.80/1.15 107 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 0.89/1.16 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(107,a,105,a)].
% 0.89/1.16 108 class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 0.89/1.16 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)). [resolve(108,a,105,a)].
% 0.89/1.16 109 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 0.89/1.16 110 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult__right_Oadd_0) # label(axiom). [assumption].
% 0.89/1.16 111 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult_Oadd__right_0) # label(axiom). [assumption].
% 0.89/1.16 112 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult__left_Oadd_0) # label(axiom). [assumption].
% 0.89/1.16 113 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult_Oadd__left_0) # label(axiom). [assumption].
% 0.89/1.16 114 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 0.89/1.16 115 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 0.89/1.16 116 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 0.89/1.16 117 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 0.89/1.16 118 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 0.89/1.16 119 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 0.89/1.16 120 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 0.89/1.18 121 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)). [resolve(109,a,110,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)). [resolve(109,a,112,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),B) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal). [resolve(109,a,114,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal). [resolve(109,a,116,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(109,a,118,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(109,a,120,a)].
% 0.89/1.18 122 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(122,a,110,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(122,a,112,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex). [resolve(122,a,114,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex). [resolve(122,a,116,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(122,a,118,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(122,a,120,a)].
% 0.89/1.18 123 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 0.89/1.18 124 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 0.93/1.20 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(123,a,124,a)].
% 0.93/1.20 125 class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 0.93/1.20 126 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 0.93/1.20 127 class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 0.93/1.20 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)). [resolve(127,a,124,a)].
% 0.93/1.20 128 class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 0.93/1.20 129 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 0.93/1.20 130 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__eq__neg__nonpos_0) # label(axiom). [assumption].
% 0.93/1.20 131 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__eq__neg__nonpos_1) # label(axiom). [assumption].
% 0.93/1.20 132 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) # label(cls_neg__less__eq__nonneg_0) # label(axiom). [assumption].
% 0.93/1.20 133 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__eq__nonneg_1) # label(axiom). [assumption].
% 0.93/1.20 134 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 0.93/1.20 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != A | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(128,a,129,a)].
% 0.93/1.20 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(128,a,130,a)].
% 0.93/1.20 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(128,a,131,a)].
% 0.93/1.20 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(128,a,132,a)].
% 0.93/1.20 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(128,a,133,a)].
% 0.93/1.20 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(128,a,134,a)].
% 0.93/1.20 135 class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 0.93/1.20 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) != B | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(135,a,129,a)].
% 0.93/1.22 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,130,a)].
% 0.93/1.22 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(135,a,131,a)].
% 0.93/1.22 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(135,a,132,a)].
% 0.93/1.22 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(135,a,133,a)].
% 0.93/1.22 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(135,a,134,a)].
% 0.93/1.22 136 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.93/1.22 137 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 0.93/1.22 138 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Suc(C)) | 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].
% 0.93/1.22 139 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),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].
% 0.93/1.22 140 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)),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].
% 0.93/1.22 141 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 0.93/1.22 142 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 0.93/1.22 143 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 0.93/1.22 144 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 0.93/1.22 145 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 0.93/1.22 146 -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(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D),A) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 0.93/1.22 147 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 0.93/1.22 148 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 0.93/1.22 149 -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].
% 0.93/1.22 150 -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].
% 0.93/1.22 151 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 0.93/1.22 152 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 0.93/1.22 153 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Suc(D)),A) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 0.93/1.22 154 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 0.93/1.22 155 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(B,D,A) # label(cls_power__mono_0) # label(axiom). [assumption].
% 0.93/1.22 156 -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].
% 0.93/1.22 157 -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].
% 0.93/1.22 158 -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].
% 0.93/1.22 159 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 0.93/1.22 160 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(136,a,137,a)].
% 0.93/1.22 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),c_Suc(B)) | 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(136,a,138,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),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(136,a,139,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)),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(136,a,140,a)].
% 0.93/1.22 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(136,a,141,a)].
% 0.93/1.22 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(136,a,142,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(136,a,143,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(136,a,144,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(136,a,145,a)].
% 0.93/1.22 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(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C),tc_nat). [resolve(136,a,146,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(136,a,147,a)].
% 0.93/1.22 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(136,a,148,a)].
% 0.93/1.22 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(136,a,149,a)].
% 0.93/1.22 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(136,a,150,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(136,a,151,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(136,a,152,a)].
% 0.93/1.22 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),c_Suc(C)),tc_nat). [resolve(136,a,153,a)].
% 0.93/1.22 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | B = C. [resolve(136,a,154,a)].
% 0.93/1.22 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(136,a,155,a)].
% 0.93/1.22 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(136,a,156,a)].
% 0.93/1.22 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(136,a,157,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),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(136,a,159,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),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(136,a,160,a)].
% 0.93/1.22 161 class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(161,a,137,a)].
% 0.93/1.22 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Suc(B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),c_Suc(B)) | A = C | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(161,a,138,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(161,a,139,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Suc(B)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(161,a,140,a)].
% 0.93/1.22 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(161,a,141,a)].
% 0.93/1.22 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(161,a,142,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(161,a,143,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal). [resolve(161,a,144,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(161,a,145,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal). [resolve(161,a,146,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(161,a,147,a)].
% 0.93/1.22 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(161,a,148,a)].
% 0.93/1.22 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(161,a,149,a)].
% 0.93/1.22 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(161,a,150,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Suc(B)),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(161,a,151,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(161,a,152,a)].
% 0.93/1.22 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Suc(C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),c_Suc(C)),tc_RealDef_Oreal). [resolve(161,a,153,a)].
% 0.93/1.22 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | B = C. [resolve(161,a,154,a)].
% 0.93/1.22 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(161,a,155,a)].
% 0.93/1.22 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(161,a,156,a)].
% 0.93/1.22 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(161,a,157,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(161,a,159,a)].
% 0.93/1.22 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(161,a,160,a)].
% 0.93/1.22 162 class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.93/1.22 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A))),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A))),tc_Polynomial_Opoly(A)). [resolve(162,a,137,a)].
% 0.93/1.22 Derived: -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Suc(C)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),c_Suc(C)) | B = D | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(162,a,138,a)].
% 0.93/1.22 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(162,a,139,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Suc(C)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(162,a,140,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(162,a,141,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(162,a,142,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(162,a,143,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A))),tc_Polynomial_Opoly(A)). [resolve(162,a,144,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(162,a,145,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)). [resolve(162,a,146,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(162,a,147,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(162,a,148,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(162,a,149,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(162,a,150,a)].
% 0.93/1.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Suc(C)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(162,a,151,a)].
% 0.97/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(162,a,152,a)].
% 0.97/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Suc(D)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),C),c_Suc(D)),tc_Polynomial_Opoly(A)). [resolve(162,a,153,a)].
% 0.97/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | C = D. [resolve(162,a,154,a)].
% 0.97/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(162,a,155,a)].
% 0.97/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(162,a,156,a)].
% 0.97/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(162,a,157,a)].
% 0.97/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(162,a,159,a)].
% 0.97/1.25 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(162,a,160,a)].
% 0.97/1.25 163 class_Ring__and__Field_Oring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring) # label(axiom). [assumption].
% 0.97/1.25 164 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),c_HOL_Ouminus__class_Ouminus(C,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 0.97/1.25 165 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 0.97/1.25 166 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 0.97/1.25 167 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 0.97/1.25 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B). [resolve(163,a,164,a)].
% 0.97/1.27 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)). [resolve(163,a,165,a)].
% 0.97/1.27 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),B). [resolve(163,a,166,a)].
% 0.97/1.27 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)). [resolve(163,a,167,a)].
% 0.97/1.27 168 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 0.97/1.27 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B). [resolve(168,a,164,a)].
% 0.97/1.27 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)). [resolve(168,a,165,a)].
% 0.97/1.27 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B). [resolve(168,a,166,a)].
% 0.97/1.27 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)). [resolve(168,a,167,a)].
% 0.97/1.27 169 class_Ring__and__Field_Oring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring) # label(axiom). [assumption].
% 0.97/1.27 Derived: -class_Ring__and__Field_Ocomm__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A))),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C). [resolve(169,a,164,a)].
% 0.97/1.27 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A))). [resolve(169,a,165,a)].
% 0.97/1.27 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A))),C). [resolve(169,a,166,a)].
% 0.97/1.27 Derived: -class_Ring__and__Field_Ocomm__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A))),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A))). [resolve(169,a,167,a)].
% 0.97/1.27 170 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 0.97/1.27 171 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 0.97/1.27 172 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 0.97/1.29 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(170,a,171,a)].
% 0.97/1.29 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(170,a,172,a)].
% 0.97/1.29 173 class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 0.97/1.29 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(173,a,171,a)].
% 0.97/1.29 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(173,a,172,a)].
% 0.97/1.29 174 class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 0.97/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(174,a,171,a)].
% 0.97/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(174,a,172,a)].
% 0.97/1.29 175 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.97/1.29 176 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.29 177 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.29 178 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.29 179 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.29 180 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 0.97/1.29 181 -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) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 0.97/1.29 182 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != 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].
% 0.97/1.29 183 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != 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].
% 0.97/1.29 184 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.29 185 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 0.97/1.29 186 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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].
% 0.97/1.29 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(175,a,176,a)].
% 0.97/1.29 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(175,a,177,a)].
% 0.97/1.29 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(175,a,178,a)].
% 0.97/1.29 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(175,a,179,a)].
% 0.97/1.29 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(175,a,180,a)].
% 0.97/1.29 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(175,a,181,a)].
% 0.97/1.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != 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(175,a,182,a)].
% 0.97/1.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != 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(175,a,183,a)].
% 0.97/1.29 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(175,a,184,a)].
% 0.97/1.29 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),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(175,a,186,a)].
% 0.97/1.29 187 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.97/1.29 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(187,a,176,a)].
% 0.97/1.29 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(187,a,177,a)].
% 0.97/1.29 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(187,a,178,a)].
% 0.97/1.29 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(187,a,179,a)].
% 0.97/1.29 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(187,a,180,a)].
% 0.97/1.29 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(187,a,181,a)].
% 0.97/1.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(187,a,182,a)].
% 0.97/1.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(187,a,183,a)].
% 0.97/1.29 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(187,a,184,a)].
% 0.97/1.29 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(187,a,186,a)].
% 0.97/1.29 188 class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.97/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(188,a,176,a)].
% 0.97/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(188,a,177,a)].
% 0.97/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(188,a,178,a)].
% 0.97/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(188,a,179,a)].
% 0.97/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(188,a,180,a)].
% 0.97/1.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(188,a,181,a)].
% 1.03/1.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(188,a,182,a)].
% 1.03/1.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(188,a,183,a)].
% 1.03/1.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(188,a,184,a)].
% 1.03/1.31 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(188,a,186,a)].
% 1.03/1.31 189 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.03/1.31 190 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 1.03/1.31 191 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom). [assumption].
% 1.03/1.31 192 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 1.03/1.31 193 -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].
% 1.03/1.31 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)). [resolve(189,a,190,a)].
% 1.03/1.31 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(189,a,191,a)].
% 1.03/1.31 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(189,a,192,a)].
% 1.03/1.31 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(189,a,193,a)].
% 1.03/1.31 194 class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.03/1.31 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal)). [resolve(194,a,190,a)].
% 1.03/1.33 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(194,a,191,a)].
% 1.03/1.33 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_RealDef_Oreal)). [resolve(194,a,192,a)].
% 1.03/1.33 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(194,a,193,a)].
% 1.03/1.33 195 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.03/1.33 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)). [resolve(195,a,190,a)].
% 1.03/1.33 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(195,a,191,a)].
% 1.03/1.33 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)). [resolve(195,a,192,a)].
% 1.03/1.33 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(195,a,193,a)].
% 1.03/1.33 196 class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.03/1.33 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A))),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A))). [resolve(196,a,190,a)].
% 1.03/1.33 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(196,a,191,a)].
% 1.03/1.33 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A))),c_Nat_Osemiring__1__class_Oof__nat(C,tc_Polynomial_Opoly(A))). [resolve(196,a,192,a)].
% 1.03/1.33 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(196,a,193,a)].
% 1.03/1.33 197 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.03/1.33 198 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 1.03/1.33 199 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 1.03/1.33 200 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 1.03/1.33 201 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 1.03/1.33 202 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 1.03/1.33 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(197,a,198,a)].
% 1.03/1.33 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(197,a,199,a)].
% 1.03/1.33 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(197,a,200,a)].
% 1.03/1.33 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(197,a,201,a)].
% 1.03/1.33 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(197,a,202,a)].
% 1.03/1.33 203 class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.03/1.33 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(203,a,198,a)].
% 1.03/1.33 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) | -class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) | -class_Power_Opower(tc_RealDef_Oreal) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(203,a,199,a)].
% 1.03/1.33 Derived: c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(203,a,200,a)].
% 1.03/1.33 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) | -class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) | -class_Power_Opower(tc_RealDef_Oreal) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(203,a,201,a)].
% 1.03/1.33 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) | -class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) | -class_Power_Opower(tc_RealDef_Oreal) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(203,a,202,a)].
% 1.03/1.33 204 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.03/1.33 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(204,a,198,a)].
% 1.03/1.33 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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(204,a,199,a)].
% 1.03/1.33 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(204,a,200,a)].
% 1.03/1.33 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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(204,a,201,a)].
% 1.03/1.36 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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(204,a,202,a)].
% 1.03/1.36 205 class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.03/1.36 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(205,a,198,a)].
% 1.03/1.36 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(205,a,199,a)].
% 1.03/1.36 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(205,a,200,a)].
% 1.03/1.36 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(205,a,201,a)].
% 1.03/1.36 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | -class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A)) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(205,a,202,a)].
% 1.03/1.36 206 class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.03/1.36 207 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__0__le__iff__le_0) # label(axiom). [assumption].
% 1.03/1.36 208 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__le__iff__le_1) # label(axiom). [assumption].
% 1.03/1.36 209 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__le__0__iff__le_1) # label(axiom). [assumption].
% 1.03/1.36 210 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__le__0__iff__le_0) # label(axiom). [assumption].
% 1.03/1.36 211 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_neg__less__iff__less_1) # label(axiom). [assumption].
% 1.03/1.36 212 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__less__iff__less_0) # label(axiom). [assumption].
% 1.03/1.36 213 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__le__iff__le_0) # label(axiom). [assumption].
% 1.03/1.36 214 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,B,A) # label(cls_le__imp__neg__le_0) # label(axiom). [assumption].
% 1.03/1.36 215 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(E,D,A) | -c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E),A) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 1.03/1.36 216 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_neg__0__less__iff__less_0) # label(axiom). [assumption].
% 1.03/1.36 217 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__less__iff__less_1) # label(axiom). [assumption].
% 1.03/1.36 218 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__0__iff__less_1) # label(axiom). [assumption].
% 1.03/1.36 219 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__less__0__iff__less_0) # label(axiom). [assumption].
% 1.03/1.36 220 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__less__iff_1) # label(axiom). [assumption].
% 1.03/1.36 221 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__less__iff_0) # label(axiom). [assumption].
% 1.03/1.36 222 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__minus__iff_1) # label(axiom). [assumption].
% 1.03/1.36 223 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__minus__iff_0) # label(axiom). [assumption].
% 1.03/1.36 224 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__le__iff_1) # label(axiom). [assumption].
% 1.03/1.36 225 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A) # label(cls_minus__le__iff_0) # label(axiom). [assumption].
% 1.03/1.36 226 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__iff_1) # label(axiom). [assumption].
% 1.03/1.36 227 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__iff_0) # label(axiom). [assumption].
% 1.03/1.36 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(206,a,207,a)].
% 1.03/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(206,a,208,a)].
% 1.09/1.36 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(206,a,209,a)].
% 1.09/1.36 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(206,a,210,a)].
% 1.09/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal). [resolve(206,a,211,a)].
% 1.09/1.36 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(206,a,212,a)].
% 1.09/1.36 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(206,a,213,a)].
% 1.09/1.36 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,A,tc_RealDef_Oreal). [resolve(206,a,214,a)].
% 1.09/1.36 Derived: c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_lessequals(D,C,tc_RealDef_Oreal) | -c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),D),tc_RealDef_Oreal). [resolve(206,a,215,a)].
% 1.09/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(206,a,216,a)].
% 1.09/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(206,a,217,a)].
% 1.09/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(206,a,218,a)].
% 1.09/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(206,a,219,a)].
% 1.09/1.36 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(206,a,220,a)].
% 1.09/1.36 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(206,a,222,a)].
% 1.09/1.36 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(206,a,224,a)].
% 1.09/1.36 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(206,a,226,a)].
% 1.09/1.36 228 class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(228,a,207,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(228,a,208,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(228,a,209,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(228,a,210,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)). [resolve(228,a,211,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(228,a,212,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(228,a,213,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(228,a,214,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)) | -c_lessequals(E,D,tc_Polynomial_Opoly(A)) | -c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E),tc_Polynomial_Opoly(A)). [resolve(228,a,215,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(228,a,216,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(228,a,217,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(228,a,218,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(228,a,219,a)].
% 1.09/1.36 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(228,a,220,a)].
% 1.09/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(228,a,222,a)].
% 1.09/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(228,a,224,a)].
% 1.09/1.38 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(228,a,226,a)].
% 1.09/1.38 229 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.09/1.38 230 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oone__class_Oone(A)),B) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 1.09/1.38 231 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_power__commutes_0) # label(axiom). [assumption].
% 1.09/1.38 232 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_power__one__right_0) # label(axiom). [assumption].
% 1.09/1.38 233 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_mult__1__right_0) # label(axiom). [assumption].
% 1.09/1.38 234 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1__left_0) # label(axiom). [assumption].
% 1.09/1.38 235 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(cls_power__Suc2_0) # label(axiom). [assumption].
% 1.09/1.38 236 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(cls_power__add_0) # label(axiom). [assumption].
% 1.09/1.38 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = c_HOL_Oone__class_Oone(tc_nat). [resolve(229,a,230,a)].
% 1.09/1.38 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(229,a,231,a)].
% 1.09/1.38 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(229,a,232,a)].
% 1.09/1.38 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(229,a,233,a)].
% 1.09/1.38 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A). [resolve(229,a,235,a)].
% 1.09/1.38 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)). [resolve(229,a,236,a)].
% 1.09/1.38 237 class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.09/1.38 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),A) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(237,a,230,a)].
% 1.09/1.38 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)). [resolve(237,a,231,a)].
% 1.09/1.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(237,a,232,a)].
% 1.09/1.39 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = A. [resolve(237,a,233,a)].
% 1.09/1.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),A). [resolve(237,a,235,a)].
% 1.09/1.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),C)). [resolve(237,a,236,a)].
% 1.09/1.39 238 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.09/1.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(238,a,230,a)].
% 1.09/1.39 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(238,a,231,a)].
% 1.09/1.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(238,a,232,a)].
% 1.09/1.39 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(238,a,233,a)].
% 1.09/1.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A). [resolve(238,a,235,a)].
% 1.09/1.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)). [resolve(238,a,236,a)].
% 1.09/1.39 239 class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.09/1.39 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A))),B) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(239,a,230,a)].
% 1.09/1.39 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)). [resolve(239,a,231,a)].
% 1.09/1.39 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_HOL_Oone__class_Oone(tc_nat)) = B. [resolve(239,a,232,a)].
% 1.09/1.39 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A))) = B. [resolve(239,a,233,a)].
% 1.09/1.39 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),B). [resolve(239,a,235,a)].
% 1.09/1.39 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),D)). [resolve(239,a,236,a)].
% 1.09/1.43 240 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.09/1.43 241 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 1.09/1.43 242 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 1.09/1.43 243 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 1.09/1.43 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(240,a,241,a)].
% 1.09/1.43 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(240,a,242,a)].
% 1.09/1.43 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(240,a,243,a)].
% 1.09/1.43 244 class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.09/1.43 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(244,a,241,a)].
% 1.09/1.43 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(244,a,242,a)].
% 1.09/1.43 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(244,a,243,a)].
% 1.09/1.43 245 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.09/1.43 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),E),tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(245,a,241,a)].
% 1.09/1.43 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(245,a,242,a)].
% 1.09/1.43 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(245,a,243,a)].
% 1.09/1.43 246 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.09/1.43 247 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 1.09/1.44 248 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Suc(B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 1.09/1.44 249 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 1.09/1.44 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(246,a,247,a)].
% 1.09/1.44 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(246,a,248,a)].
% 1.09/1.44 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(246,a,249,a)].
% 1.09/1.44 250 class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.09/1.44 Derived: -class_Power_Opower(tc_RealDef_Oreal) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal). [resolve(250,a,247,a)].
% 1.09/1.44 Derived: -class_Power_Opower(tc_RealDef_Oreal) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(250,a,248,a)].
% 1.09/1.44 Derived: -class_Power_Opower(tc_RealDef_Oreal) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(250,a,249,a)].
% 1.09/1.44 251 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.09/1.44 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(251,a,247,a)].
% 1.09/1.44 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(251,a,248,a)].
% 1.09/1.44 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(251,a,249,a)].
% 1.09/1.44 252 class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.09/1.44 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(252,a,247,a)].
% 1.09/1.44 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_Suc(B)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(252,a,248,a)].
% 1.09/1.44 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(252,a,249,a)].
% 1.19/1.46 253 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.19/1.46 254 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),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].
% 1.19/1.46 255 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.19/1.46 256 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.19/1.46 257 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.19/1.46 258 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.19/1.46 259 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.19/1.46 260 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.19/1.46 261 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.19/1.46 262 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.19/1.46 263 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),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].
% 1.19/1.46 264 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.19/1.46 265 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.19/1.46 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(253,a,254,a)].
% 1.19/1.46 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(253,a,256,a)].
% 1.19/1.46 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(253,a,258,a)].
% 1.19/1.46 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(253,a,259,a)].
% 1.19/1.46 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(253,a,260,a)].
% 1.19/1.46 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(253,a,261,a)].
% 1.19/1.46 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(253,a,262,a)].
% 1.19/1.46 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(253,a,263,a)].
% 1.19/1.46 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(253,a,264,a)].
% 1.19/1.46 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(253,a,265,a)].
% 1.19/1.46 266 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.19/1.46 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(266,a,254,a)].
% 1.19/1.46 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal). [resolve(266,a,256,a)].
% 1.19/1.46 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal). [resolve(266,a,258,a)].
% 1.19/1.46 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal). [resolve(266,a,259,a)].
% 1.19/1.46 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,C,tc_RealDef_Oreal). [resolve(266,a,260,a)].
% 1.19/1.46 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal). [resolve(266,a,261,a)].
% 1.19/1.46 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(266,a,262,a)].
% 1.19/1.46 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(266,a,263,a)].
% 1.19/1.46 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(266,a,264,a)].
% 1.19/1.46 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal) | -c_lessequals(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal). [resolve(266,a,265,a)].
% 1.19/1.46 267 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.19/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(267,a,254,a)].
% 1.19/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)). [resolve(267,a,256,a)].
% 1.19/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)). [resolve(267,a,258,a)].
% 1.19/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)). [resolve(267,a,259,a)].
% 1.19/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)). [resolve(267,a,260,a)].
% 1.19/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)). [resolve(267,a,261,a)].
% 1.19/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(267,a,262,a)].
% 1.19/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(267,a,263,a)].
% 1.19/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(267,a,264,a)].
% 1.19/1.46 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(267,a,265,a)].
% 1.19/1.49 268 class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.19/1.49 269 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_le__minus__self__iff_0) # label(axiom). [assumption].
% 1.19/1.49 270 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__minus__self__iff_1) # label(axiom). [assumption].
% 1.19/1.49 271 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) # label(cls_minus__le__self__iff_0) # label(axiom). [assumption].
% 1.19/1.49 272 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_minus__le__self__iff_1) # label(axiom). [assumption].
% 1.19/1.49 273 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__eq__neg_1) # label(axiom). [assumption].
% 1.19/1.49 274 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_le__eq__neg_0) # label(axiom). [assumption].
% 1.19/1.49 275 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom). [assumption].
% 1.19/1.49 276 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom). [assumption].
% 1.19/1.49 277 -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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 1.19/1.49 278 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 1.19/1.49 279 -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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 1.19/1.49 280 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 1.19/1.49 281 -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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 1.19/1.49 282 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),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].
% 1.27/1.54 283 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 1.27/1.54 284 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),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].
% 1.27/1.54 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(268,a,273,a)].
% 1.27/1.54 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(268,a,274,a)].
% 1.27/1.54 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(268,a,275,a)].
% 1.27/1.54 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(268,a,276,a)].
% 1.27/1.54 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(268,a,277,a)].
% 1.27/1.54 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal). [resolve(268,a,279,a)].
% 1.27/1.54 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),tc_RealDef_Oreal). [resolve(268,a,281,a)].
% 1.27/1.54 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(268,a,283,a)].
% 1.27/1.54 285 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 1.27/1.54 286 -class_RealVector_Oreal__normed__vector(A) | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_RealVector_Onorm__class_Onorm(B,A) # label(cls_norm__minus__cancel_0) # label(axiom). [assumption].
% 1.27/1.54 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(A,tc_RealDef_Oreal). [resolve(285,a,286,a)].
% 1.27/1.54 287 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 1.27/1.54 Derived: c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex). [resolve(287,a,286,a)].
% 1.27/1.54 288 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 1.27/1.54 289 -class_OrderedGroup_Osemigroup__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A)) # label(cls_foldl__assoc_0) # label(axiom). [assumption].
% 1.27/1.54 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)). [resolve(288,a,289,a)].
% 1.27/1.58 290 class_OrderedGroup_Osemigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 1.27/1.58 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),C,tc_RealDef_Oreal,tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B,C,tc_RealDef_Oreal,tc_RealDef_Oreal)). [resolve(290,a,289,a)].
% 1.27/1.58 291 class_OrderedGroup_Osemigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 1.27/1.58 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex)). [resolve(291,a,289,a)].
% 1.27/1.58 292 class_OrderedGroup_Osemigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 1.27/1.58 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),D,tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C,D,tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))). [resolve(292,a,289,a)].
% 1.27/1.58 293 class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 1.27/1.58 294 -class_Ring__and__Field_Oring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A)),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_power__minus_0) # label(axiom). [assumption].
% 1.27/1.58 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B)). [resolve(293,a,294,a)].
% 1.27/1.58 295 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 1.27/1.58 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(295,a,294,a)].
% 1.27/1.58 296 class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 1.27/1.58 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A))),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A))),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)). [resolve(296,a,294,a)].
% 1.27/1.58 297 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.27/1.58 298 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 1.27/1.58 299 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 1.27/1.58 300 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 1.27/1.58 301 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 1.27/1.58 302 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 1.27/1.58 303 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 1.27/1.58 304 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 1.27/1.58 305 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 1.27/1.58 306 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 1.27/1.58 307 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 1.27/1.58 308 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 1.27/1.58 309 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 1.27/1.58 310 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 1.27/1.58 311 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 1.27/1.58 312 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 1.27/1.58 313 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(297,a,298,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),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) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(297,a,299,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(297,a,300,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat). [resolve(297,a,302,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A),tc_nat). [resolve(297,a,303,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(297,a,304,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat). [resolve(297,a,305,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat). [resolve(297,a,306,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(297,a,307,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(297,a,308,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(297,a,309,a)].
% 1.27/1.58 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat). [resolve(297,a,310,a)].
% 1.27/1.58 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat). [resolve(297,a,311,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(297,a,312,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(297,a,313,a)].
% 1.27/1.58 314 class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(314,a,298,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(314,a,299,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(314,a,300,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal). [resolve(314,a,302,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),tc_RealDef_Oreal). [resolve(314,a,303,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal). [resolve(314,a,304,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal). [resolve(314,a,305,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal). [resolve(314,a,306,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(314,a,307,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(314,a,308,a)].
% 1.27/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(314,a,309,a)].
% 1.27/1.58 Derived: c_lessequals(A,B,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),C,tc_RealDef_Oreal) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),tc_RealDef_Oreal). [resolve(314,a,310,a)].
% 1.27/1.58 315 class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(315,a,298,a)].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(315,a,299,a)].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(315,a,300,a)].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)). [resolve(315,a,302,a)].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),B),tc_Polynomial_Opoly(A)). [resolve(315,a,303,a)].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(315,a,304,a)].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)). [resolve(315,a,305,a)].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)). [resolve(315,a,306,a)].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(315,a,307,a)].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(315,a,308,a)].
% 1.27/1.58 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),E),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(315,a,309,a)].
% 1.34/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D),tc_Polynomial_Opoly(A)). [resolve(315,a,310,a)].
% 1.34/1.64 316 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.34/1.64 317 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 1.34/1.64 318 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 1.34/1.64 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(316,a,317,a)].
% 1.34/1.64 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(316,a,318,a)].
% 1.34/1.64 319 class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.34/1.64 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(319,a,317,a)].
% 1.34/1.64 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),C),tc_RealDef_Oreal) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal) | -c_lessequals(B,C,tc_RealDef_Oreal). [resolve(319,a,318,a)].
% 1.34/1.64 320 class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.34/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(320,a,317,a)].
% 1.34/1.64 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(320,a,318,a)].
% 1.34/1.64 321 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.34/1.64 322 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 1.34/1.64 323 class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.34/1.64 324 class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 1.34/1.66 325 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.34/1.66 326 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),C)) = C # label(cls_add__minus__cancel_0) # label(axiom). [assumption].
% 1.34/1.66 327 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom). [assumption].
% 1.34/1.66 328 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom). [assumption].
% 1.34/1.66 329 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = C # label(cls_minus__add__cancel_0) # label(axiom). [assumption].
% 1.34/1.66 330 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__equal__iff__equal_1) # label(axiom). [assumption].
% 1.34/1.66 331 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom). [assumption].
% 1.34/1.66 332 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(C,A)),c_HOL_Ouminus__class_Ouminus(B,A)) # label(cls_minus__add_0) # label(axiom). [assumption].
% 1.34/1.66 333 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Ouminus__class_Ouminus(B,A) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom). [assumption].
% 1.34/1.66 334 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__equation__iff_1) # label(axiom). [assumption].
% 1.34/1.66 335 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_1) # label(axiom). [assumption].
% 1.34/1.66 336 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_0) # label(axiom). [assumption].
% 1.34/1.66 337 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__minus_0) # label(axiom). [assumption].
% 1.34/1.66 338 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_left__minus_0) # label(axiom). [assumption].
% 1.34/1.66 339 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ouminus__class_Ouminus(B,A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus_0) # label(axiom). [assumption].
% 1.34/1.66 340 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__neg__iff__add__eq__0_0) # label(axiom). [assumption].
% 1.34/1.66 341 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ouminus__class_Ouminus(B,A) = C # label(cls_minus__unique_0) # label(axiom). [assumption].
% 1.34/1.66 342 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ouminus__class_Ouminus(C,A) # label(cls_eq__neg__iff__add__eq__0_1) # label(axiom). [assumption].
% 1.34/1.66 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),B)) = B. [resolve(325,a,326,a)].
% 1.34/1.66 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal) | A = B. [resolve(325,a,327,a)].
% 1.34/1.67 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(325,a,328,a)].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)) = B. [resolve(325,a,329,a)].
% 1.34/1.67 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(325,a,330,a)].
% 1.34/1.67 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),tc_RealDef_Oreal) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)). [resolve(325,a,332,a)].
% 1.34/1.67 Derived: c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = A. [resolve(325,a,333,a)].
% 1.34/1.67 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A. [resolve(325,a,334,a)].
% 1.34/1.67 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(325,a,335,a)].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(325,a,338,a)].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(325,a,339,a)].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) = B. [resolve(325,a,341,a)].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal). [resolve(325,a,342,a)].
% 1.34/1.67 343 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B)) = B. [resolve(343,a,326,a)].
% 1.34/1.67 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex) | A = B. [resolve(343,a,327,a)].
% 1.34/1.67 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(343,a,328,a)].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)) = B. [resolve(343,a,329,a)].
% 1.34/1.67 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(343,a,330,a)].
% 1.34/1.67 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(343,a,331,a)].
% 1.34/1.67 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)). [resolve(343,a,332,a)].
% 1.34/1.67 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(343,a,333,a)].
% 1.34/1.67 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(343,a,334,a)].
% 1.34/1.67 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(343,a,335,a)].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(343,a,338,a)].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(343,a,339,a)].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) = B. [resolve(343,a,341,a)].
% 1.34/1.67 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex). [resolve(343,a,342,a)].
% 1.34/1.67 344 class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Oab__group__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A))),C)) = C. [resolve(344,a,326,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) != c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)) | B = C. [resolve(344,a,327,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(344,a,328,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)) = C. [resolve(344,a,329,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(344,a,330,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(344,a,331,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),tc_Polynomial_Opoly(A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A))),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A))). [resolve(344,a,332,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) != c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = B. [resolve(344,a,333,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(344,a,334,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(344,a,335,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A))),B) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(344,a,338,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A))) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(344,a,339,a)].
% 1.34/1.67 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) = C. [resolve(344,a,341,a)].
% 1.40/1.71 Derived: -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)). [resolve(344,a,342,a)].
% 1.40/1.71 345 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 1.40/1.71 346 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 1.40/1.71 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(345,a,346,a)].
% 1.40/1.71 347 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].
% 1.40/1.71 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(347,a,346,a)].
% 1.40/1.71 348 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 1.40/1.71 Derived: -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(348,a,346,a)].
% 1.40/1.71 349 class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.40/1.71 350 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 1.40/1.71 351 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 1.40/1.71 352 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 1.40/1.71 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | B = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(349,a,350,a)].
% 1.40/1.71 353 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.40/1.71 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(353,a,350,a)].
% 1.40/1.71 354 class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.40/1.71 Derived: -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(354,a,350,a)].
% 1.40/1.71 Derived: -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(354,a,351,a)].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(354,a,352,a)].
% 1.50/1.77 355 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.50/1.77 356 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 1.50/1.77 357 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 1.50/1.77 358 class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.50/1.77 359 class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.50/1.77 360 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.50/1.77 361 -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].
% 1.50/1.77 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(360,a,361,a)].
% 1.50/1.77 362 class_Nat_Osemiring__char__0(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.50/1.77 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_RealDef_Oreal) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_RealDef_Oreal) | A = B. [resolve(362,a,361,a)].
% 1.50/1.77 363 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.50/1.77 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(363,a,361,a)].
% 1.50/1.77 364 class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.50/1.77 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)) != c_Nat_Osemiring__1__class_Oof__nat(C,tc_Polynomial_Opoly(A)) | B = C. [resolve(364,a,361,a)].
% 1.50/1.77 365 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.50/1.77 366 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),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].
% 1.50/1.77 367 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.50/1.77 368 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.50/1.77 369 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.53/1.79 370 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.53/1.79 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(365,a,366,a)].
% 1.53/1.79 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(365,a,369,a)].
% 1.53/1.79 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(365,a,370,a)].
% 1.53/1.79 371 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.53/1.79 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(371,a,366,a)].
% 1.53/1.79 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_lessequals(B,D,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal). [resolve(371,a,369,a)].
% 1.53/1.79 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),D),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(B,D,tc_RealDef_Oreal) | -c_lessequals(A,C,tc_RealDef_Oreal). [resolve(371,a,370,a)].
% 1.53/1.79 372 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.53/1.79 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),E),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(372,a,366,a)].
% 1.53/1.79 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),E),tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(372,a,369,a)].
% 1.53/1.79 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),E),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(372,a,370,a)].
% 1.53/1.79 373 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.53/1.79 374 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C)),E) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 1.56/1.83 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B)),D). [resolve(373,a,374,a)].
% 1.56/1.83 375 class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.56/1.83 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C)),B)),D). [resolve(375,a,374,a)].
% 1.56/1.83 376 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.56/1.83 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B)),D). [resolve(376,a,374,a)].
% 1.56/1.83 377 class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__0(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.56/1.83 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D)),C)),E). [resolve(377,a,374,a)].
% 1.56/1.83 378 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.56/1.83 379 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 1.56/1.83 380 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.56/1.83 381 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.56/1.83 382 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.56/1.83 383 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 1.56/1.83 384 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 1.56/1.83 385 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) # label(cls_foldl__absorb0_0) # label(axiom). [assumption].
% 1.56/1.86 386 -class_OrderedGroup_Omonoid__add(A) | c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A) # label(cls_monoid__add__class_Oaxioms_0) # label(axiom). [assumption].
% 1.56/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(382,a,383,a)].
% 1.56/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(382,a,384,a)].
% 1.56/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,tc_nat)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat). [resolve(382,a,385,a)].
% 1.56/1.86 Derived: c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat). [resolve(382,a,386,a)].
% 1.56/1.86 387 class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.56/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),A) = A. [resolve(387,a,383,a)].
% 1.56/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = A. [resolve(387,a,384,a)].
% 1.56/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal,tc_RealDef_Oreal)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A,B,tc_RealDef_Oreal,tc_RealDef_Oreal). [resolve(387,a,385,a)].
% 1.56/1.86 Derived: c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),tc_RealDef_Oreal). [resolve(387,a,386,a)].
% 1.56/1.86 388 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.56/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(388,a,383,a)].
% 1.56/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(388,a,384,a)].
% 1.56/1.86 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,B,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(388,a,385,a)].
% 1.56/1.86 Derived: c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(388,a,386,a)].
% 1.56/1.86 389 class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.56/1.86 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B) = B. [resolve(389,a,383,a)].
% 1.56/1.86 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))) = B. [resolve(389,a,384,a)].
% 1.56/1.86 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B,C,tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)). [resolve(389,a,385,a)].
% 1.56/1.86 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(389,a,386,a)].
% 1.56/1.86 390 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.56/1.90 391 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 1.56/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(390,a,391,a)].
% 1.56/1.90 392 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.56/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),B),C)). [resolve(392,a,391,a)].
% 1.56/1.90 393 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.56/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)). [resolve(393,a,391,a)].
% 1.56/1.90 394 class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.56/1.90 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D)). [resolve(394,a,391,a)].
% 1.56/1.90 395 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.56/1.90 396 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 1.56/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(395,a,396,a)].
% 1.56/1.90 397 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.56/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),C) | B = C. [resolve(397,a,396,a)].
% 1.56/1.90 398 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.56/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(398,a,396,a)].
% 1.56/1.90 399 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocancel__comm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.56/1.90 Derived: -class_OrderedGroup_Ocancel__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),D) | C = D. [resolve(399,a,396,a)].
% 1.56/1.90 400 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.56/1.90 401 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 1.56/1.90 402 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 1.70/1.99 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(400,a,402,a)].
% 1.70/1.99 403 class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.70/1.99 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_RealDef_Oreal),C),B) | A = C. [resolve(403,a,402,a)].
% 1.70/1.99 404 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.70/1.99 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B) | A = C. [resolve(404,a,402,a)].
% 1.70/1.99 405 class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocancel__comm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.70/1.99 Derived: -class_OrderedGroup_Ocancel__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),D),C) | B = D. [resolve(405,a,402,a)].
% 1.70/1.99 406 class_Int_Oring__char__0(tc_RealDef_Oreal) # label(clsarity_RealDef__Oreal__Int_Oring__char__0) # label(axiom). [assumption].
% 1.70/1.99 407 -class_Ring__and__Field_Oidom(A) | -class_Int_Oring__char__0(A) | c_Polynomial_Opoly(B,A) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_poly__zero_0) # label(axiom). [assumption].
% 1.70/1.99 408 -class_Ring__and__Field_Oidom(A) | -class_Int_Oring__char__0(A) | c_Polynomial_Opoly(B,A) != c_Polynomial_Opoly(C,A) | B = C # label(cls_poly__eq__iff_0) # label(axiom). [assumption].
% 1.70/1.99 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_Polynomial_Opoly(A,tc_RealDef_Oreal) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)). [resolve(406,a,407,b)].
% 1.70/1.99 Derived: -class_Ring__and__Field_Oidom(tc_RealDef_Oreal) | c_Polynomial_Opoly(A,tc_RealDef_Oreal) != c_Polynomial_Opoly(B,tc_RealDef_Oreal) | A = B. [resolve(406,a,408,b)].
% 1.70/1.99 409 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption].
% 1.70/1.99 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_Polynomial_Opoly(A,tc_Complex_Ocomplex) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(409,a,407,b)].
% 1.70/1.99 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_Polynomial_Opoly(A,tc_Complex_Ocomplex) != c_Polynomial_Opoly(B,tc_Complex_Ocomplex) | A = B. [resolve(409,a,408,b)].
% 1.70/1.99 410 class_Int_Oring__char__0(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Int_Oring__char__0) # label(axiom). [assumption].
% 1.70/1.99 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_Polynomial_Opoly(B,tc_Polynomial_Opoly(A)) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(A))),tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(A))). [resolve(410,a,407,b)].
% 1.70/1.99 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_Polynomial_Opoly(B,tc_Polynomial_Opoly(A)) != c_Polynomial_Opoly(C,tc_Polynomial_Opoly(A)) | B = C. [resolve(410,a,408,b)].
% 1.70/1.99
% 1.70/1.99 ============================== end predicate elimination =============
% 1.70/1.99
% 1.70/1.99 Auto_denials: (non-Horn, no changes).
% 1.70/1.99
% 1.70/1.99 Term ordering decisions:
% 1.70/1.99 Function symbol KB weights: tc_RealDef_Oreal=1. tc_nat=1. tc_Complex_Ocomplex=1. t_a=1. v_pa____=1. v_c____=1. v_p=1. v_q____=1. t_b=1. v_n____=1. hAPP=1. c_HOL_Ouminus__class_Ouminus=1. c_Polynomial_Opoly=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Polynomial_Ocoeff=1. c_Polynomial_Odegree=1. c_Fundamental__Theorem__Algebra__Mirabelle_Opsize=1. c_RealVector_Onorm__class_Onorm=1. tc_fun=1. v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1=1. tc_Polynomial_Opoly=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Otimes__class_Otimes=1. c_Power_Opower__class_Opower=1. c_HOL_Oone__class_Oone=1. c_Suc=1. v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1=1. v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2=1. v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3=1. v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2=1. v_sko__unknown__thm__rrS__1=1. c_Polynomial_OpCons=1. c_Polynomial_Osmult=1. c_Power_Opower_Opower=1. c_Polynomial_Omonom=1. c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly=1. c_fequal=1. c_Polynomial_Oorder=1. c_Polynomial_Opcompose=1. c_HOL_OIf=1. c_List_Ofoldl=1. c_Polynomial_Opoly__rec=1.
% 1.70/1.99
% 1.70/1.99 ============================== PROOF =================================
% 1.70/1.99 % SZS status Unsatisfiable
% 1.70/1.99 % SZS output start Refutation
% 1.70/1.99
% 1.70/1.99 % Proof 1 at 1.03 (+ 0.00) seconds.
% 1.70/1.99 % Length of proof is 3.
% 1.70/1.99 % Level of proof is 1.
% 1.70/1.99 % Maximum clause weight is 6.000.
% 1.70/1.99 % Given clauses 0.
% 1.70/1.99
% 1.70/1.99 707 -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex) # label(cls_CHAINED_0) # label(axiom). [assumption].
% 1.70/1.99 708 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 1.70/1.99 709 $F. [copy(708),unit_del(a,707)].
% 1.70/1.99
% 1.70/1.99 % SZS output end Refutation
% 1.70/1.99 ============================== end of proof ==========================
% 1.70/1.99
% 1.70/1.99 ============================== STATISTICS ============================
% 1.70/1.99
% 1.70/1.99 Given=0. Generated=243. Kept=206. proofs=1.
% 1.70/1.99 Usable=0. Sos=0. Demods=18. Limbo=206, Disabled=660. Hints=0.
% 1.70/1.99 Megabytes=1.16.
% 1.70/1.99 User_CPU=1.03, System_CPU=0.00, Wall_clock=1.
% 1.70/1.99
% 1.70/1.99 ============================== end of statistics =====================
% 1.70/1.99
% 1.70/1.99 ============================== end of search =========================
% 1.70/1.99
% 1.70/1.99 THEOREM PROVED
% 1.70/1.99 % SZS status Unsatisfiable
% 1.70/1.99
% 1.70/1.99 Exiting with 1 proof.
% 1.70/1.99
% 1.70/1.99 Process 2249 exit (max_proofs) Thu Jun 9 05:23:54 2022
% 1.70/1.99 Prover9 interrupted
%------------------------------------------------------------------------------