TSTP Solution File: ALG419-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG419-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 17:54:48 EDT 2022
% Result : Timeout 300.07s 300.30s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG419-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 8 05:08:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.02/1.39 ============================== Prover9 ===============================
% 1.02/1.39 Prover9 (32) version 2009-11A, November 2009.
% 1.02/1.39 Process 9794 was started by sandbox2 on n026.cluster.edu,
% 1.02/1.39 Wed Jun 8 05:08:47 2022
% 1.02/1.39 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_9641_n026.cluster.edu".
% 1.02/1.39 ============================== end of head ===========================
% 1.02/1.39
% 1.02/1.39 ============================== INPUT =================================
% 1.02/1.39
% 1.02/1.39 % Reading from file /tmp/Prover9_9641_n026.cluster.edu
% 1.02/1.39
% 1.02/1.39 set(prolog_style_variables).
% 1.02/1.39 set(auto2).
% 1.02/1.39 % set(auto2) -> set(auto).
% 1.02/1.39 % set(auto) -> set(auto_inference).
% 1.02/1.39 % set(auto) -> set(auto_setup).
% 1.02/1.39 % set(auto_setup) -> set(predicate_elim).
% 1.02/1.39 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.02/1.39 % set(auto) -> set(auto_limits).
% 1.02/1.39 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.02/1.39 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.02/1.39 % set(auto) -> set(auto_denials).
% 1.02/1.39 % set(auto) -> set(auto_process).
% 1.02/1.39 % set(auto2) -> assign(new_constants, 1).
% 1.02/1.39 % set(auto2) -> assign(fold_denial_max, 3).
% 1.02/1.39 % set(auto2) -> assign(max_weight, "200.000").
% 1.02/1.39 % set(auto2) -> assign(max_hours, 1).
% 1.02/1.39 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.02/1.39 % set(auto2) -> assign(max_seconds, 0).
% 1.02/1.39 % set(auto2) -> assign(max_minutes, 5).
% 1.02/1.39 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.02/1.39 % set(auto2) -> set(sort_initial_sos).
% 1.02/1.39 % set(auto2) -> assign(sos_limit, -1).
% 1.02/1.39 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.02/1.39 % set(auto2) -> assign(max_megs, 400).
% 1.02/1.39 % set(auto2) -> assign(stats, some).
% 1.02/1.39 % set(auto2) -> clear(echo_input).
% 1.02/1.39 % set(auto2) -> set(quiet).
% 1.02/1.39 % set(auto2) -> clear(print_initial_clauses).
% 1.02/1.39 % set(auto2) -> clear(print_given).
% 1.02/1.39 assign(lrs_ticks,-1).
% 1.02/1.39 assign(sos_limit,10000).
% 1.02/1.39 assign(order,kbo).
% 1.02/1.39 set(lex_order_vars).
% 1.02/1.39 clear(print_given).
% 1.02/1.39
% 1.02/1.39 % formulas(sos). % not echoed (998 formulas)
% 1.02/1.39
% 1.02/1.39 ============================== end of input ==========================
% 1.02/1.39
% 1.02/1.39 % From the command line: assign(max_seconds, 300).
% 1.02/1.39
% 1.02/1.39 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.02/1.39
% 1.02/1.39 % Formulas that are not ordinary clauses:
% 1.02/1.39
% 1.02/1.39 ============================== end of process non-clausal formulas ===
% 1.02/1.39
% 1.02/1.39 ============================== PROCESS INITIAL CLAUSES ===============
% 1.02/1.39
% 1.02/1.39 ============================== PREDICATE ELIMINATION =================
% 1.02/1.39 1 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.02/1.39 2 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__add__self2_0) # label(axiom). [assumption].
% 1.02/1.39 3 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),B,A) = c_Divides_Odiv__class_Omod(C,B,A) # label(cls_mod__add__self1_0) # label(axiom). [assumption].
% 1.02/1.39 4 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) # label(cls_zmod__simps_I2_J_0) # label(axiom). [assumption].
% 1.02/1.39 5 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,D,A),C,A) # label(cls_zmod__simps_I1_J_0) # label(axiom). [assumption].
% 1.02/1.39 6 -class_Divides_Osemiring__div(A) | B = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A) # label(cls_mod__div__decomp_0) # label(axiom). [assumption].
% 1.02/1.39 7 -class_Divides_Osemiring__div(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A) = B # label(cls_mod__div__equality_0) # label(axiom). [assumption].
% 1.02/1.39 8 -class_Divides_Osemiring__div(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A),c_Divides_Odiv__class_Omod(C,B,A),A) = C # label(cls_mod__div__equality2_0) # label(axiom). [assumption].
% 1.02/1.39 9 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,D,A),c_Divides_Odiv__class_Odiv(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,A) # label(cls_div__dvd__div_0) # label(axiom). [assumption].
% 1.02/1.39 10 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__dvd__div_1) # label(axiom). [assumption].
% 1.02/1.39 11 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__imp__mod__0_0) # label(axiom). [assumption].
% 1.02/1.39 12 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_HOL_Ozero__class_Ozero(A) | c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__eq__mod__eq__0_1) # label(axiom). [assumption].
% 1.02/1.39 13 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mod__trivial_0) # label(axiom). [assumption].
% 1.02/1.39 14 -class_Divides_Osemiring__div(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A),D,A) = c_HOL_Oplus__class_Oplus(B,D,A) # label(cls_div__mod__equality_0) # label(axiom). [assumption].
% 1.02/1.39 15 -class_Divides_Osemiring__div(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A),c_Divides_Odiv__class_Omod(C,B,A),A),D,A) = c_HOL_Oplus__class_Oplus(C,D,A) # label(cls_div__mod__equality2_0) # label(axiom). [assumption].
% 1.02/1.39 16 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__div__trivial_0) # label(axiom). [assumption].
% 1.02/1.39 17 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(F,D,A),C,A) # label(cls_mod__add__cong_0) # label(axiom). [assumption].
% 1.02/1.39 18 -class_Divides_Osemiring__div(A) | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(B,C,A),D,A) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__power_0) # label(axiom). [assumption].
% 1.02/1.39 19 -class_Int_Onumber(A) | -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) = c_HOL_Ozero__class_Ozero(A) | -c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_dvd__eq__mod__eq__0__number__of_0) # label(axiom). [assumption].
% 1.02/1.39 20 -class_Int_Onumber(A) | -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) != c_HOL_Ozero__class_Ozero(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_dvd__eq__mod__eq__0__number__of_1) # label(axiom). [assumption].
% 1.02/1.39 21 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),D,A) = c_Divides_Odiv__class_Omod(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) # label(cls_mod__mod__cancel_0) # label(axiom). [assumption].
% 1.02/1.39 22 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,E,A),A) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(E,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_div__mult__div__if__dvd_0) # label(axiom). [assumption].
% 1.02/1.39 23 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) # label(cls_dvd__mod__imp__dvd_0) # label(axiom). [assumption].
% 1.02/1.39 24 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mod__iff_1) # label(axiom). [assumption].
% 1.02/1.39 25 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) # label(cls_dvd__mod__iff_0) # label(axiom). [assumption].
% 1.02/1.39 26 -class_Divides_Osemiring__div(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,A) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mod_0) # label(axiom). [assumption].
% 1.02/1.39 27 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,D,A),c_Divides_Odiv__class_Odiv(C,D,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,A) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,A) # label(cls_div__add_0) # label(axiom). [assumption].
% 1.02/1.39 28 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,A),c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__add__eq_0) # label(axiom). [assumption].
% 1.02/1.39 29 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__add__right__eq_0) # label(axiom). [assumption].
% 1.02/1.39 30 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A) # label(cls_mod__add__left__eq_0) # label(axiom). [assumption].
% 1.02/1.39 31 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),D,A) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),C,A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__mult_0) # label(axiom). [assumption].
% 1.02/1.39 32 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A) = C | -c_Ring__and__Field_Odvd__class_Odvd(B,C,A) # label(cls_dvd__mult__div__cancel_0) # label(axiom). [assumption].
% 1.02/1.39 33 -class_Divides_Osemiring__div(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A) = B | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__mult__self_0) # label(axiom). [assumption].
% 1.02/1.39 34 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mult__self2_0) # label(axiom). [assumption].
% 1.02/1.39 35 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),D,A) = c_Divides_Odiv__class_Omod(B,D,A) # label(cls_mod__mult__self1_0) # label(axiom). [assumption].
% 1.02/1.39 36 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__self_0) # label(axiom). [assumption].
% 1.02/1.39 37 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_mod__by__0_0) # label(axiom). [assumption].
% 1.02/1.39 38 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__by__0_0) # label(axiom). [assumption].
% 1.02/1.39 39 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__0_0) # label(axiom). [assumption].
% 1.02/1.39 40 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__0_0) # label(axiom). [assumption].
% 1.02/1.39 41 -class_Divides_Osemiring__div(A) | c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,A),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),A) = B # label(cls_semiring__div__class_Omod__div__equality_H_0) # label(axiom). [assumption].
% 1.02/1.39 42 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),B,A) = C | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1__is__id_0) # label(axiom). [assumption].
% 1.02/1.39 43 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2__is__id_0) # label(axiom). [assumption].
% 1.02/1.39 44 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1__if_0) # label(axiom). [assumption].
% 1.02/1.39 45 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_Divides_Odiv__class_Odiv(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1_0) # label(axiom). [assumption].
% 1.02/1.39 46 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) = c_Divides_Odiv__class_Odiv(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult2_0) # label(axiom). [assumption].
% 1.02/1.39 47 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self1__is__0_0) # label(axiom). [assumption].
% 1.02/1.39 48 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self2__is__0_0) # label(axiom). [assumption].
% 1.02/1.39 49 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__self_0) # label(axiom). [assumption].
% 1.02/1.39 50 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__by__1_0) # label(axiom). [assumption].
% 1.02/1.39 51 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),C,A) = c_HOL_Oplus__class_Oplus(D,c_Divides_Odiv__class_Odiv(B,C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2_0) # label(axiom). [assumption].
% 1.02/1.39 52 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),D,A) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(B,D,A),A) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1_0) # label(axiom). [assumption].
% 1.02/1.39 53 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),C,A) # label(cls_mod__mult__mult2_0) # label(axiom). [assumption].
% 1.02/1.39 54 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,A),A) # label(cls_mod__mult__mult1_0) # label(axiom). [assumption].
% 1.02/1.39 55 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(F,D,A),C,A) # label(cls_mod__mult__cong_0) # label(axiom). [assumption].
% 1.02/1.39 56 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__mult__eq_0) # label(axiom). [assumption].
% 1.02/1.39 57 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),C,A) # label(cls_zmod__simps_I4_J_0) # label(axiom). [assumption].
% 1.02/1.39 58 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__mult__right__eq_0) # label(axiom). [assumption].
% 1.02/1.39 59 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A) # label(cls_mod__mult__left__eq_0) # label(axiom). [assumption].
% 1.02/1.39 60 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,A),C,A) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,C,A),c_HOL_Oone__class_Oone(A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self2_0) # label(axiom). [assumption].
% 1.02/1.39 61 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,A),B,A) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(C,B,A),c_HOL_Oone__class_Oone(A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self1_0) # label(axiom). [assumption].
% 1.02/1.39 62 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_div__by__1_0) # label(axiom). [assumption].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(1,a,2,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat) = c_Divides_Odiv__class_Omod(B,A,tc_nat). [resolve(1,a,3,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat). [resolve(1,a,4,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). [resolve(1,a,5,a)].
% 1.02/1.39 Derived: A = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat),tc_nat). [resolve(1,a,6,a)].
% 1.02/1.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat),tc_nat) = A. [resolve(1,a,7,a)].
% 1.02/1.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(B,A,tc_nat),tc_nat) = B. [resolve(1,a,8,a)].
% 1.02/1.39 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,C,tc_nat),c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat). [resolve(1,a,9,a)].
% 1.02/1.39 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_Divides_Odiv__class_Odiv(C,B,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(1,a,10,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(1,a,11,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(1,a,12,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(1,a,13,a)].
% 1.02/1.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat),tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(A,C,tc_nat). [resolve(1,a,14,a)].
% 1.02/1.39 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(B,A,tc_nat),tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(B,C,tc_nat). [resolve(1,a,15,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,16,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(D,A,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,C,tc_nat),B,tc_nat). [resolve(1,a,17,a)].
% 1.02/1.39 Derived: c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(1,a,18,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat). [resolve(1,a,21,a)].
% 1.02/1.39 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_Divides_Odiv__class_Odiv(C,D,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,D,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(1,a,22,a)].
% 1.02/1.39 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat). [resolve(1,a,23,a)].
% 1.02/1.39 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat). [resolve(1,a,24,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,C,tc_nat),c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat). [resolve(1,a,27,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat). [resolve(1,a,28,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat). [resolve(1,a,29,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_nat),B,tc_nat),C,tc_nat). [resolve(1,a,30,a)].
% 1.02/1.39 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_nat),B,tc_nat) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(1,a,31,a)].
% 1.02/1.39 Derived: c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat) = B | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat). [resolve(1,a,32,a)].
% 1.02/1.39 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat) = A | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat). [resolve(1,a,33,a)].
% 1.02/1.39 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(1,a,34,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(A,C,tc_nat). [resolve(1,a,35,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,36,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(1,a,37,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,38,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,39,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,40,a)].
% 1.02/1.40 Derived: c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_nat),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat),tc_nat) = A. [resolve(1,a,41,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat) = B | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,42,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat) = A | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,43,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,44,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(B,C,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,45,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) = c_Divides_Odiv__class_Odiv(A,C,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,46,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,47,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,48,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,49,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,50,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),B,tc_nat) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(A,B,tc_nat),tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,51,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Odiv(A,C,tc_nat),tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,52,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),B,tc_nat). [resolve(1,a,53,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat). [resolve(1,a,54,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(D,A,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,C,tc_nat),B,tc_nat). [resolve(1,a,55,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat). [resolve(1,a,56,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_nat),B,tc_nat). [resolve(1,a,57,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat). [resolve(1,a,58,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_nat),B,tc_nat),C,tc_nat). [resolve(1,a,59,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,60,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,A,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,61,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(1,a,62,a)].
% 1.02/1.40 63 class_Divides_Osemiring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(63,a,2,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),A,tc_Int_Oint) = c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint). [resolve(63,a,3,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint). [resolve(63,a,4,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),C,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(63,a,5,a)].
% 1.02/1.40 Derived: A = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(63,a,6,a)].
% 1.02/1.40 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),tc_Int_Oint) = A. [resolve(63,a,7,a)].
% 1.02/1.40 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint),tc_Int_Oint),c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint),tc_Int_Oint) = B. [resolve(63,a,8,a)].
% 1.02/1.40 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint),c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Int_Oint). [resolve(63,a,9,a)].
% 1.02/1.40 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),c_Divides_Odiv__class_Odiv(C,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(63,a,10,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(63,a,11,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(63,a,12,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(63,a,13,a)].
% 1.02/1.40 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint). [resolve(63,a,14,a)].
% 1.02/1.40 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint),tc_Int_Oint),c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint). [resolve(63,a,15,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,16,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(D,A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(63,a,17,a)].
% 1.02/1.40 Derived: c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(63,a,18,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint). [resolve(63,a,21,a)].
% 1.02/1.40 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),c_Divides_Odiv__class_Odiv(C,D,tc_Int_Oint),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(63,a,22,a)].
% 1.02/1.40 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(63,a,23,a)].
% 1.02/1.40 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Int_Oint). [resolve(63,a,24,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint),c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Int_Oint). [resolve(63,a,27,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(63,a,28,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(63,a,29,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint). [resolve(63,a,30,a)].
% 1.02/1.40 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),B,tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(63,a,31,a)].
% 1.02/1.40 Derived: c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint),tc_Int_Oint) = B | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Int_Oint). [resolve(63,a,32,a)].
% 1.02/1.40 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint) = A | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(63,a,33,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(63,a,34,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint). [resolve(63,a,35,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,36,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(63,a,37,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,38,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,39,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,40,a)].
% 1.02/1.40 Derived: c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),B,tc_Int_Oint),tc_Int_Oint) = A. [resolve(63,a,41,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),A,tc_Int_Oint) = B | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,42,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),B,tc_Int_Oint) = A | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,43,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,44,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,45,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) = c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,46,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,47,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,48,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,49,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,50,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,51,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint),tc_Int_Oint) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,52,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(63,a,53,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(63,a,54,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(D,A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(63,a,55,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(63,a,56,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),C,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(63,a,57,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(63,a,58,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint). [resolve(63,a,59,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,60,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(63,a,61,a)].
% 1.02/1.40 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(63,a,62,a)].
% 1.02/1.40 64 class_Divides_Osemiring__div(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ofield(A) # label(clsarity_Polynomial__Opoly__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(64,a,2,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,3,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,4,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(64,a,5,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | B = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(64,a,6,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(64,a,7,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = C. [resolve(64,a,8,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,tc_Polynomial_Opoly(A)). [resolve(64,a,9,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,10,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,11,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,12,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(64,a,13,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)). [resolve(64,a,14,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)). [resolve(64,a,15,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,16,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(D,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(E,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(F,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(F,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(64,a,17,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,18,a)].
% 1.02/1.40 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Polynomial_Opoly(A)). [resolve(64,a,21,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(E,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,22,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(64,a,23,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)). [resolve(64,a,24,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,tc_Polynomial_Opoly(A)). [resolve(64,a,27,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,28,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,29,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,30,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,31,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = C | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)). [resolve(64,a,32,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = B | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,33,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(64,a,34,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)). [resolve(64,a,35,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,36,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(64,a,37,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,38,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,39,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,40,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(64,a,41,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = C | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,42,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = B | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,43,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,44,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(C,D,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,45,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(B,D,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,46,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,47,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,48,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,B,tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,49,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,50,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(D,c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,51,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | D = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,52,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(64,a,53,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(64,a,54,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(D,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(E,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(F,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(F,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(64,a,55,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,56,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(64,a,57,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,58,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,59,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,60,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(C,B,tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,61,a)].
% 1.02/1.41 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(64,a,62,a)].
% 1.02/1.45 65 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.02/1.45 66 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(B,C,tc_nat),A) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 1.02/1.45 67 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 1.02/1.45 68 -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].
% 1.02/1.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(65,a,66,a)].
% 1.02/1.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(65,a,67,a)].
% 1.02/1.45 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(65,a,68,a)].
% 1.02/1.45 69 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.02/1.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint). [resolve(69,a,66,a)].
% 1.02/1.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint). [resolve(69,a,67,a)].
% 1.02/1.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(69,a,68,a)].
% 1.02/1.45 70 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.02/1.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(70,a,66,a)].
% 1.02/1.45 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(70,a,67,a)].
% 1.02/1.45 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(70,a,68,a)].
% 1.02/1.45 71 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].
% 1.02/1.45 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(71,a,66,a)].
% 1.02/1.45 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(71,a,67,a)].
% 1.02/1.45 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(71,a,68,a)].
% 1.02/1.53 72 class_Divides_Oring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 1.02/1.53 73 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(B,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__div__neg_0) # label(axiom). [assumption].
% 1.02/1.53 74 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(B,C,A),A) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,A) # label(cls_dvd__neg__div_0) # label(axiom). [assumption].
% 1.02/1.53 75 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(D,A),C,A) # label(cls_mod__minus__cong_0) # label(axiom). [assumption].
% 1.02/1.53 76 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(B,C,A),A),C,A) # label(cls_mod__minus__eq_0) # label(axiom). [assumption].
% 1.02/1.53 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(72,a,73,a)].
% 1.02/1.53 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint),tc_Int_Oint) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Int_Oint). [resolve(72,a,74,a)].
% 1.02/1.53 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(C,tc_Int_Oint),B,tc_Int_Oint). [resolve(72,a,75,a)].
% 1.02/1.53 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),tc_Int_Oint),B,tc_Int_Oint). [resolve(72,a,76,a)].
% 1.02/1.53 77 class_Divides_Oring__div(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ofield(A) # label(clsarity_Polynomial__Opoly__Divides_Oring__div) # label(axiom). [assumption].
% 1.02/1.53 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(77,a,73,a)].
% 1.02/1.53 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(77,a,74,a)].
% 1.02/1.53 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(D,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(77,a,75,a)].
% 1.02/1.53 Derived: -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(77,a,76,a)].
% 1.02/1.53 78 class_Int_Onumber__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Onumber__ring) # label(axiom). [assumption].
% 1.02/1.53 79 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 1.02/1.53 80 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom). [assumption].
% 1.02/1.53 81 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != c_HOL_Oplus__class_Oplus(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 1.02/1.53 82 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A) != c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,E,A),A) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 1.02/1.53 83 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 1.02/1.53 84 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 1.02/1.53 85 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 1.02/1.53 86 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 1.02/1.53 87 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 1.02/1.53 88 -class_Int_Onumber__ring(A) | c_HOL_Ouminus__class_Ouminus(B,A) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A),B,A) # label(cls_class__ring_Oneg__mul_0) # label(axiom). [assumption].
% 1.02/1.53 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C. [resolve(78,a,79,b)].
% 1.02/1.53 Derived: -class_Int_Oring__char__0(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(78,a,80,b)].
% 1.02/1.53 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(78,a,81,b)].
% 1.02/1.53 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,D,tc_Int_Oint),tc_Int_Oint) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(78,a,82,b)].
% 1.02/1.53 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(78,a,83,b)].
% 1.02/1.53 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | B = D | A = C. [resolve(78,a,84,b)].
% 1.02/1.54 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(78,a,86,b)].
% 1.02/1.54 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A,tc_Int_Oint). [resolve(78,a,88,a)].
% 1.02/1.54 89 class_Int_Onumber__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Onumber__ring) # label(axiom). [assumption].
% 1.02/1.54 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C. [resolve(89,a,79,b)].
% 1.02/1.54 Derived: -class_Int_Oring__char__0(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) | A = B. [resolve(89,a,80,b)].
% 1.02/1.54 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | A != c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(89,a,81,b)].
% 1.02/1.54 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(89,a,82,b)].
% 1.02/1.54 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | A = c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(89,a,83,b)].
% 1.02/1.54 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = D | A = C. [resolve(89,a,84,b)].
% 1.02/1.54 Derived: -class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(89,a,86,b)].
% 1.02/1.54 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(89,a,88,a)].
% 1.02/1.54 90 class_Int_Onumber__ring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__ring__1(A) # label(clsarity_Polynomial__Opoly__Int_Onumber__ring) # label(axiom). [assumption].
% 1.02/1.54 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)) | C = D. [resolve(90,a,79,b)].
% 1.02/1.54 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Int_Oring__char__0(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)) != c_Int_Onumber__class_Onumber__of(C,tc_Polynomial_Opoly(A)) | B = C. [resolve(90,a,80,b)].
% 1.02/1.54 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | B != c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(90,a,81,b)].
% 1.02/1.54 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | D = E | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(90,a,82,b)].
% 1.02/1.62 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | B = c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(90,a,83,b)].
% 1.02/1.62 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = E | B = D. [resolve(90,a,84,b)].
% 1.02/1.62 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | -class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(90,a,86,b)].
% 1.02/1.62 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(90,a,88,a)].
% 1.02/1.62 91 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.02/1.62 92 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 1.02/1.62 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(A,C,tc_nat) | B = C. [resolve(91,a,92,a)].
% 1.02/1.62 93 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.02/1.62 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint) | B = C. [resolve(93,a,92,a)].
% 1.02/1.62 94 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.02/1.62 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C. [resolve(94,a,92,a)].
% 1.02/1.62 95 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].
% 1.02/1.62 Derived: -class_OrderedGroup_Ocancel__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)) | C = D. [resolve(95,a,92,a)].
% 1.02/1.62 96 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.02/1.62 97 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(B,D,A) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 1.02/1.62 98 -class_OrderedGroup_Ocancel__semigroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Oplus__class_Oplus(D,C,A) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 1.02/1.62 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Oplus__class_Oplus(C,B,tc_nat) | A = C. [resolve(96,a,98,a)].
% 1.02/1.62 99 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.02/1.62 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint) | A = C. [resolve(99,a,98,a)].
% 1.02/1.62 100 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.02/1.66 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(C,B,tc_Complex_Ocomplex) | A = C. [resolve(100,a,98,a)].
% 1.02/1.66 101 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].
% 1.02/1.66 Derived: -class_OrderedGroup_Ocancel__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)) | B = D. [resolve(101,a,98,a)].
% 1.02/1.66 102 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.02/1.66 103 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.02/1.66 104 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 1.02/1.66 105 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 1.02/1.66 106 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 1.02/1.66 107 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.02/1.66 108 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 1.02/1.66 109 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 1.02/1.66 110 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 1.02/1.66 111 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 1.02/1.66 112 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 1.02/1.66 113 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 1.02/1.67 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(102,a,103,a)].
% 1.02/1.67 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(102,a,104,a)].
% 1.02/1.67 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(102,a,105,a)].
% 1.02/1.67 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(102,a,106,a)].
% 1.02/1.67 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(102,a,107,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(102,a,108,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(102,a,109,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(102,a,110,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(102,a,111,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(102,a,112,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(102,a,113,a)].
% 1.02/1.67 114 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.02/1.67 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(114,a,103,a)].
% 1.02/1.67 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(114,a,104,a)].
% 1.02/1.67 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(114,a,105,a)].
% 1.02/1.67 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(114,a,106,a)].
% 1.02/1.67 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(114,a,107,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(114,a,108,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(114,a,109,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(114,a,110,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(114,a,111,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(114,a,112,a)].
% 1.02/1.67 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(114,a,113,a)].
% 1.02/1.67 115 class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.02/1.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(115,a,103,a)].
% 1.02/1.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(115,a,104,a)].
% 1.02/1.67 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(115,a,105,a)].
% 1.02/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(115,a,106,a)].
% 1.02/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(115,a,107,a)].
% 1.02/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(115,a,108,a)].
% 1.02/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(115,a,109,a)].
% 1.02/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(115,a,110,a)].
% 1.02/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(115,a,111,a)].
% 1.02/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(115,a,112,a)].
% 1.02/1.71 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(115,a,113,a)].
% 1.02/1.71 116 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.02/1.71 117 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 1.02/1.71 118 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 1.02/1.75 119 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 1.02/1.75 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(116,a,117,a)].
% 1.02/1.75 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(116,a,118,a)].
% 1.02/1.75 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(116,a,119,a)].
% 1.02/1.75 120 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.02/1.75 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(120,a,117,a)].
% 1.02/1.75 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(120,a,118,a)].
% 1.02/1.75 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(120,a,119,a)].
% 1.02/1.75 121 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].
% 1.02/1.75 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(121,a,117,a)].
% 1.02/1.75 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(121,a,118,a)].
% 1.02/1.75 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(121,a,119,a)].
% 1.02/1.75 122 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.02/1.75 123 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 1.02/1.75 124 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 1.02/1.75 125 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 1.02/1.75 126 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 1.02/1.75 127 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(B,B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom). [assumption].
% 1.02/1.75 128 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom). [assumption].
% 1.02/1.75 129 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 1.02/1.75 130 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 1.02/1.75 131 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 1.02/1.75 132 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 1.02/1.75 133 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__eq__neg_1) # label(axiom). [assumption].
% 1.02/1.75 134 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),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].
% 1.02/1.75 135 -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].
% 1.02/1.75 136 -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].
% 1.02/1.75 137 -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].
% 1.02/1.75 138 -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].
% 1.02/1.75 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(122,a,123,a)].
% 1.02/1.75 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(122,a,125,a)].
% 1.02/1.75 Derived: c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(122,a,127,a)].
% 1.02/1.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(122,a,128,a)].
% 1.02/1.75 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(122,a,129,a)].
% 1.02/1.75 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(122,a,131,a)].
% 1.53/1.78 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(122,a,133,a)].
% 1.53/1.78 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint). [resolve(122,a,134,a)].
% 1.53/1.78 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(122,a,135,a)].
% 1.53/1.78 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(122,a,136,a)].
% 1.53/1.78 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),A,tc_Int_Oint). [resolve(122,a,137,a)].
% 1.53/1.78 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(122,a,138,a)].
% 1.53/1.78 139 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.53/1.78 140 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)) = D | -c_Polynomial_Opdivmod__rel(B,C,D,E,A) # label(cls_div__poly__eq_0) # label(axiom). [assumption].
% 1.53/1.78 141 -class_Ring__and__Field_Ofield(A) | B = C | -c_Polynomial_Opdivmod__rel(D,E,F,C,A) | -c_Polynomial_Opdivmod__rel(D,E,V6,B,A) # label(cls_pdivmod__rel__unique_1) # label(axiom). [assumption].
% 1.53/1.78 142 -class_Ring__and__Field_Ofield(A) | B = C | -c_Polynomial_Opdivmod__rel(D,E,C,F,A) | -c_Polynomial_Opdivmod__rel(D,E,B,V6,A) # label(cls_pdivmod__rel__unique_0) # label(axiom). [assumption].
% 1.53/1.78 143 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod__rel(B,C,c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),A) # label(cls_pdivmod__rel_0) # label(axiom). [assumption].
% 1.53/1.78 144 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) = D | -c_Polynomial_Opdivmod__rel(B,C,E,D,A) # label(cls_mod__poly__eq_0) # label(axiom). [assumption].
% 1.53/1.78 145 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) = B | -c_HOL_Oord__class_Oless(c_Polynomial_Odegree(B,A),c_Polynomial_Odegree(C,A),tc_nat) # label(cls_mod__poly__less_0) # label(axiom). [assumption].
% 1.53/1.78 146 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod__rel(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A) # label(cls_pdivmod__rel__by__0_0) # label(axiom). [assumption].
% 1.53/1.78 147 -class_Ring__and__Field_Ofield(A) | c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A) # label(cls_pdivmod__rel__0_0) # label(axiom). [assumption].
% 1.53/1.78 148 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Polynomial_Opdivmod__rel(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,D,A) # label(cls_pdivmod__rel__by__0__iff_0) # label(axiom). [assumption].
% 1.53/1.78 149 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,D,B,A) # label(cls_pdivmod__rel__0__iff_1) # label(axiom). [assumption].
% 1.53/1.78 150 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,B,D,A) # label(cls_pdivmod__rel__0__iff_0) # label(axiom). [assumption].
% 1.53/1.78 151 -class_Ring__and__Field_Ofield(A) | -c_Polynomial_Opdivmod__rel(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,D,A) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_pdivmod__rel__def_1) # label(axiom). [assumption].
% 1.53/1.78 152 -class_Ring__and__Field_Ofield(A) | B = C | -c_Polynomial_Opdivmod__rel(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,B,A) # label(cls_pdivmod__rel__by__0__iff_1) # label(axiom). [assumption].
% 1.53/1.79 153 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) # label(cls_poly__div__mult__right_0) # label(axiom). [assumption].
% 1.53/1.79 154 -class_Ring__and__Field_Ofield(A) | c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),A),c_Polynomial_Odegree(C,A),tc_nat) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) # label(cls_degree__mod__less_0) # label(axiom). [assumption].
% 1.53/1.79 155 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_Polynomial_Odegree(B,A),c_Polynomial_Odegree(C,A),tc_nat) # label(cls_div__poly__less_0) # label(axiom). [assumption].
% 1.53/1.79 156 -class_Ring__and__Field_Ofield(A) | c_HOL_Oord__class_Oless(c_Polynomial_Odegree(B,A),c_Polynomial_Odegree(C,A),tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Polynomial_Opdivmod__rel(D,C,E,B,A) # label(cls_pdivmod__rel__def_2) # label(axiom). [assumption].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = C | -c_Polynomial_Opdivmod__rel(A,B,C,D,tc_Complex_Ocomplex). [resolve(139,a,140,a)].
% 1.53/1.79 Derived: A = B | -c_Polynomial_Opdivmod__rel(C,D,E,B,tc_Complex_Ocomplex) | -c_Polynomial_Opdivmod__rel(C,D,F,A,tc_Complex_Ocomplex). [resolve(139,a,141,a)].
% 1.53/1.79 Derived: A = B | -c_Polynomial_Opdivmod__rel(C,D,B,E,tc_Complex_Ocomplex) | -c_Polynomial_Opdivmod__rel(C,D,A,F,tc_Complex_Ocomplex). [resolve(139,a,142,a)].
% 1.53/1.79 Derived: c_Polynomial_Opdivmod__rel(A,B,c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex). [resolve(139,a,143,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = C | -c_Polynomial_Opdivmod__rel(A,B,D,C,tc_Complex_Ocomplex). [resolve(139,a,144,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | -c_HOL_Oord__class_Oless(c_Polynomial_Odegree(A,tc_Complex_Ocomplex),c_Polynomial_Odegree(B,tc_Complex_Ocomplex),tc_nat). [resolve(139,a,145,a)].
% 1.53/1.79 Derived: c_Polynomial_Opdivmod__rel(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Complex_Ocomplex). [resolve(139,a,146,a)].
% 1.53/1.79 Derived: c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex). [resolve(139,a,147,a)].
% 1.53/1.79 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Polynomial_Opdivmod__rel(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,C,tc_Complex_Ocomplex). [resolve(139,a,148,a)].
% 1.53/1.79 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,C,A,tc_Complex_Ocomplex). [resolve(139,a,149,a)].
% 1.53/1.79 Derived: A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,A,C,tc_Complex_Ocomplex). [resolve(139,a,150,a)].
% 1.53/1.79 Derived: A = B | -c_Polynomial_Opdivmod__rel(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,A,tc_Complex_Ocomplex). [resolve(139,a,152,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(139,a,153,a)].
% 1.53/1.79 Derived: c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Polynomial_Odegree(B,tc_Complex_Ocomplex),tc_nat) | c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(139,a,154,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_HOL_Oord__class_Oless(c_Polynomial_Odegree(A,tc_Complex_Ocomplex),c_Polynomial_Odegree(B,tc_Complex_Ocomplex),tc_nat). [resolve(139,a,155,a)].
% 1.53/1.79 Derived: c_HOL_Oord__class_Oless(c_Polynomial_Odegree(A,tc_Complex_Ocomplex),c_Polynomial_Odegree(B,tc_Complex_Ocomplex),tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Polynomial_Opdivmod__rel(C,B,D,A,tc_Complex_Ocomplex). [resolve(139,a,156,a)].
% 1.53/1.79 157 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(64,a,2,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(157,a,139,a)].
% 1.53/1.79 158 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,3,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(158,a,139,a)].
% 1.53/1.79 159 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,4,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(159,a,139,a)].
% 1.53/1.79 160 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(64,a,5,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(160,a,139,a)].
% 1.53/1.79 161 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(64,a,6,a)].
% 1.53/1.79 Derived: A = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(161,a,139,a)].
% 1.53/1.79 162 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(64,a,7,a)].
% 1.53/1.79 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A. [resolve(162,a,139,a)].
% 1.53/1.79 163 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = C. [resolve(64,a,8,a)].
% 1.53/1.79 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B. [resolve(163,a,139,a)].
% 1.53/1.79 164 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,tc_Polynomial_Opoly(A)). [resolve(64,a,9,a)].
% 1.53/1.79 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(164,a,139,a)].
% 1.53/1.79 165 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,10,a)].
% 1.53/1.79 Derived: c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(165,a,139,a)].
% 1.53/1.79 166 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,11,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(166,a,139,a)].
% 1.53/1.79 167 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,12,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(167,a,139,a)].
% 1.53/1.79 168 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(64,a,13,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(168,a,139,a)].
% 1.53/1.79 169 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)). [resolve(64,a,14,a)].
% 1.53/1.79 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(169,a,139,a)].
% 1.53/1.79 170 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)). [resolve(64,a,15,a)].
% 1.53/1.79 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(170,a,139,a)].
% 1.53/1.79 171 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,16,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(171,a,139,a)].
% 1.53/1.79 172 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(D,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(E,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(F,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(F,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(64,a,17,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(D,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(E,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(D,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(172,a,139,a)].
% 1.53/1.79 173 -class_Ring__and__Field_Ofield(A) | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,18,a)].
% 1.53/1.79 Derived: c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(173,a,139,a)].
% 1.53/1.79 174 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Polynomial_Opoly(A)). [resolve(64,a,21,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(174,a,139,a)].
% 1.53/1.79 175 -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(E,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,22,a)].
% 1.53/1.79 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(C,D,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(175,a,139,a)].
% 1.53/1.79 176 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(64,a,23,a)].
% 1.53/1.79 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(176,a,139,a)].
% 1.53/1.79 177 -class_Ring__and__Field_Ofield(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A)). [resolve(64,a,24,a)].
% 1.53/1.79 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(177,a,139,a)].
% 1.53/1.79 178 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Odiv(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(D,B,tc_Polynomial_Opoly(A)). [resolve(64,a,27,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(178,a,139,a)].
% 1.53/1.79 179 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,28,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(179,a,139,a)].
% 1.53/1.79 180 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,29,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(180,a,139,a)].
% 1.53/1.79 181 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,30,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(181,a,139,a)].
% 1.53/1.79 182 -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,31,a)].
% 1.53/1.79 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(182,a,139,a)].
% 1.53/1.79 183 -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = C | -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A)). [resolve(64,a,32,a)].
% 1.53/1.79 Derived: c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(183,a,139,a)].
% 1.53/1.79 184 -class_Ring__and__Field_Ofield(A) | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = B | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(64,a,33,a)].
% 1.53/1.79 Derived: c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(184,a,139,a)].
% 1.53/1.79 185 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)). [resolve(64,a,34,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(185,a,139,a)].
% 1.53/1.79 186 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)). [resolve(64,a,35,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(186,a,139,a)].
% 1.53/1.79 187 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,36,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(187,a,139,a)].
% 1.53/1.79 188 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(64,a,37,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A. [resolve(188,a,139,a)].
% 1.53/1.79 189 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,38,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(189,a,139,a)].
% 1.53/1.79 190 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,39,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(190,a,139,a)].
% 1.53/1.79 191 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,40,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(191,a,139,a)].
% 1.53/1.79 192 -class_Ring__and__Field_Ofield(A) | c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(64,a,41,a)].
% 1.53/1.79 Derived: c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A. [resolve(192,a,139,a)].
% 1.53/1.79 193 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = C | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,42,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = B | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(193,a,139,a)].
% 1.53/1.79 194 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = B | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,43,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(194,a,139,a)].
% 1.53/1.79 195 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,44,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(195,a,139,a)].
% 1.53/1.79 196 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(C,D,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,45,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(196,a,139,a)].
% 1.53/1.79 197 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Odiv(B,D,tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,46,a)].
% 1.53/1.79 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Odiv(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(197,a,139,a)].
% 1.53/1.79 198 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,47,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(198,a,139,a)].
% 1.53/1.80 199 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,48,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(199,a,139,a)].
% 1.53/1.80 200 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,B,tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,49,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(200,a,139,a)].
% 1.53/1.80 201 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,50,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(201,a,139,a)].
% 1.53/1.80 202 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(D,c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,51,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(202,a,139,a)].
% 1.53/1.80 203 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | D = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,52,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Odiv(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(203,a,139,a)].
% 1.53/1.80 204 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(64,a,53,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(204,a,139,a)].
% 1.53/1.80 205 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(64,a,54,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(205,a,139,a)].
% 1.53/1.80 206 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(D,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(E,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(F,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(F,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(64,a,55,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(D,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(E,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(D,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(206,a,139,a)].
% 1.53/1.80 207 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,56,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(207,a,139,a)].
% 1.53/1.80 208 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(64,a,57,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(208,a,139,a)].
% 1.53/1.80 209 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,58,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(209,a,139,a)].
% 1.53/1.80 210 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(64,a,59,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(210,a,139,a)].
% 1.53/1.80 211 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,60,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(211,a,139,a)].
% 1.53/1.80 212 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(C,B,tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(64,a,61,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(212,a,139,a)].
% 1.53/1.80 213 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(64,a,62,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A. [resolve(213,a,139,a)].
% 1.53/1.80 214 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(77,a,73,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(214,a,139,a)].
% 1.53/1.80 215 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_Polynomial_Opoly(A)). [resolve(77,a,74,a)].
% 1.53/1.80 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(215,a,139,a)].
% 1.58/1.82 216 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)) != c_Divides_Odiv__class_Omod(D,C,tc_Polynomial_Opoly(A)) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(77,a,75,a)].
% 1.58/1.82 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Divides_Odiv__class_Omod(C,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(216,a,139,a)].
% 1.58/1.82 217 -class_Ring__and__Field_Ofield(A) | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(77,a,76,a)].
% 1.58/1.82 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)). [resolve(217,a,139,a)].
% 1.58/1.82 218 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.58/1.82 219 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,A),A),A) # label(cls_left__distrib__number__of_0) # label(axiom). [assumption].
% 1.58/1.82 220 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A) # label(cls_right__distrib__number__of_0) # label(axiom). [assumption].
% 1.58/1.82 221 -class_Ring__and__Field_Osemiring(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,A),C,A),E,A) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 1.58/1.82 Derived: -class_Int_Onumber(tc_nat) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat),tc_nat). [resolve(218,a,219,a)].
% 1.58/1.82 Derived: -class_Int_Onumber(tc_nat) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_nat),B,tc_nat),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_nat),C,tc_nat),tc_nat). [resolve(218,a,220,a)].
% 1.58/1.82 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_nat),D,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat),D,tc_nat). [resolve(218,a,221,a)].
% 1.58/1.83 222 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.58/1.83 Derived: -class_Int_Onumber(tc_Int_Oint) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(222,a,219,a)].
% 1.58/1.83 Derived: -class_Int_Onumber(tc_Int_Oint) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),C,tc_Int_Oint),tc_Int_Oint). [resolve(222,a,220,a)].
% 1.58/1.83 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),D,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),B,tc_Int_Oint),D,tc_Int_Oint). [resolve(222,a,221,a)].
% 1.58/1.83 223 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.58/1.83 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(223,a,219,a)].
% 1.58/1.83 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(223,a,220,a)].
% 1.58/1.83 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),D,tc_Complex_Ocomplex). [resolve(223,a,221,a)].
% 1.58/1.83 224 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].
% 1.58/1.83 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Int_Onumber(tc_Polynomial_Opoly(A)) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(224,a,219,a)].
% 1.58/1.83 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Int_Onumber(tc_Polynomial_Opoly(A)) | c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(224,a,220,a)].
% 1.60/1.86 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),E,tc_Polynomial_Opoly(A)). [resolve(224,a,221,a)].
% 1.60/1.86 225 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.60/1.86 226 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | -c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 1.60/1.86 227 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 1.60/1.86 228 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.60/1.86 229 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.60/1.86 230 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.60/1.86 231 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.60/1.86 232 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.60/1.86 233 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.60/1.86 234 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.60/1.86 235 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.60/1.86 236 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.60/1.86 237 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.60/1.86 238 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.60/1.86 239 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.60/1.86 240 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.60/1.86 241 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.60/1.86 242 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.60/1.86 243 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.60/1.86 Derived: -class_Int_Onumber(tc_nat) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -c_lessequals(c_Int_Onumber__class_Onumber__of(B,tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat). [resolve(225,a,226,a)].
% 1.60/1.86 Derived: -class_Int_Onumber(tc_nat) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat). [resolve(225,a,227,a)].
% 1.60/1.86 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(225,a,228,a)].
% 1.60/1.86 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(225,a,229,a)].
% 1.60/1.86 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(225,a,231,a)].
% 1.60/1.86 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(225,a,232,a)].
% 1.60/1.86 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(225,a,234,a)].
% 1.60/1.86 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(225,a,238,a)].
% 1.60/1.86 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(225,a,239,a)].
% 1.60/1.86 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(225,a,240,a)].
% 1.60/1.86 244 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 1.60/1.86 Derived: -class_Int_Onumber(tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint). [resolve(244,a,226,a)].
% 1.60/1.86 Derived: -class_Int_Onumber(tc_Int_Oint) | c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint). [resolve(244,a,227,a)].
% 1.60/1.86 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(244,a,228,a)].
% 1.60/1.86 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(244,a,229,a)].
% 1.60/1.86 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(244,a,231,a)].
% 1.60/1.86 Derived: -c_lessequals(A,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(244,a,232,a)].
% 1.60/1.86 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(244,a,234,a)].
% 1.60/1.86 Derived: -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(244,a,238,a)].
% 1.60/1.86 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(244,a,239,a)].
% 1.60/1.86 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(244,a,240,a)].
% 1.60/1.86 245 class_Orderings_Olinorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Olinorder) # label(axiom). [assumption].
% 1.60/1.86 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber(tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_Int_Onumber__class_Onumber__of(C,tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(245,a,226,a)].
% 1.60/1.86 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber(tc_Polynomial_Opoly(A)) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(245,a,227,a)].
% 1.60/1.86 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(245,a,228,a)].
% 1.60/1.90 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(245,a,229,a)].
% 1.60/1.90 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(245,a,231,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(B,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,B,tc_Polynomial_Opoly(A)). [resolve(245,a,232,a)].
% 1.60/1.90 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(245,a,234,a)].
% 1.60/1.90 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(B,B,tc_Polynomial_Opoly(A)). [resolve(245,a,238,a)].
% 1.60/1.90 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(245,a,239,a)].
% 1.60/1.90 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(245,a,240,a)].
% 1.60/1.90 246 class_Orderings_Opreorder(tc_nat) # label(clsarity_nat__Orderings_Opreorder) # label(axiom). [assumption].
% 1.60/1.90 247 -class_Orderings_Opreorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__refl_0) # label(axiom). [assumption].
% 1.60/1.90 248 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_lessequals(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__trans_0) # label(axiom). [assumption].
% 1.60/1.90 249 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_order__less__le__trans_0) # label(axiom). [assumption].
% 1.60/1.90 250 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_lessequals(B,D,A) # label(cls_order__le__less__trans_0) # label(axiom). [assumption].
% 1.60/1.90 251 -class_Orderings_Opreorder(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_order__less__imp__le_0) # label(axiom). [assumption].
% 1.60/1.90 252 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_less__le__not__le_2) # label(axiom). [assumption].
% 1.60/1.90 253 -class_Orderings_Opreorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_less__le__not__le_1) # label(axiom). [assumption].
% 1.60/1.90 254 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__irrefl_0) # label(axiom). [assumption].
% 1.60/1.90 255 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_H_0) # label(axiom). [assumption].
% 1.60/1.90 256 -class_Orderings_Opreorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_order__less__asym_0) # label(axiom). [assumption].
% 1.60/1.90 257 -class_Orderings_Opreorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_order__less__trans_0) # label(axiom). [assumption].
% 1.60/1.90 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(246,a,248,a)].
% 1.60/1.90 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(C,B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(246,a,249,a)].
% 1.60/1.90 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(246,a,250,a)].
% 1.60/1.90 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(246,a,251,a)].
% 1.60/1.90 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(246,a,257,a)].
% 1.60/1.90 258 class_Orderings_Opreorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Opreorder) # label(axiom). [assumption].
% 1.60/1.90 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(258,a,248,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(258,a,249,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(258,a,250,a)].
% 1.67/1.93 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(258,a,251,a)].
% 1.67/1.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(258,a,257,a)].
% 1.67/1.93 259 class_Orderings_Opreorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Opreorder) # label(axiom). [assumption].
% 1.67/1.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(259,a,248,a)].
% 1.67/1.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(259,a,249,a)].
% 1.67/1.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(259,a,250,a)].
% 1.67/1.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)). [resolve(259,a,251,a)].
% 1.67/1.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(259,a,257,a)].
% 1.67/1.93 260 class_Orderings_Oorder(tc_nat) # label(clsarity_nat__Orderings_Oorder) # label(axiom). [assumption].
% 1.67/1.93 261 -class_Orderings_Oorder(A) | c_lessequals(B,B,A) # label(cls_order__eq__iff_0) # label(axiom). [assumption].
% 1.67/1.93 262 -class_Orderings_Oorder(A) | B = C | -c_lessequals(B,C,A) | -c_lessequals(C,B,A) # label(cls_order__antisym__conv_0) # label(axiom). [assumption].
% 1.67/1.93 263 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__eq__iff_2) # label(axiom). [assumption].
% 1.67/1.93 264 -class_Orderings_Oorder(A) | B = C | -c_lessequals(C,B,A) | -c_lessequals(B,C,A) # label(cls_order__antisym_0) # label(axiom). [assumption].
% 1.67/1.93 265 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_lessequals(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I6_J_0) # label(axiom). [assumption].
% 1.67/1.93 266 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_xt1_I7_J_0) # label(axiom). [assumption].
% 1.67/1.93 267 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(D,C,A) # label(cls_xt1_I8_J_0) # label(axiom). [assumption].
% 1.67/1.93 268 -class_Orderings_Oorder(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_order__le__less_1) # label(axiom). [assumption].
% 1.67/1.93 269 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | -c_lessequals(B,C,A) # label(cls_xt1_I11_J_0) # label(axiom). [assumption].
% 1.67/1.93 270 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) | C = B # label(cls_xt1_I12_J_0) # label(axiom). [assumption].
% 1.67/1.93 271 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) | B = C # label(cls_order__neq__le__trans_0) # label(axiom). [assumption].
% 1.67/1.93 272 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | B = C | -c_lessequals(B,C,A) # label(cls_order__le__neq__trans_0) # label(axiom). [assumption].
% 1.67/1.93 273 -class_Orderings_Oorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_order__le__less_0) # label(axiom). [assumption].
% 1.67/1.93 274 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | B = C | -c_lessequals(B,C,A) # label(cls_order__less__le_2) # label(axiom). [assumption].
% 1.67/1.96 275 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_order__less__le_1) # label(axiom). [assumption].
% 1.67/1.96 276 -class_Orderings_Oorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_xt1_I9_J_0) # label(axiom). [assumption].
% 1.67/1.96 277 -class_Orderings_Oorder(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_xt1_I10_J_0) # label(axiom). [assumption].
% 1.67/1.96 Derived: A = B | -c_lessequals(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(260,a,262,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | B = A | -c_lessequals(A,B,tc_nat). [resolve(260,a,269,a)].
% 1.67/1.96 278 class_Orderings_Oorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Oorder) # label(axiom). [assumption].
% 1.67/1.96 Derived: A = B | -c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(278,a,262,a)].
% 1.67/1.96 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | B = A | -c_lessequals(A,B,tc_Int_Oint). [resolve(278,a,269,a)].
% 1.67/1.96 279 class_Orderings_Oorder(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Orderings_Oorder) # label(axiom). [assumption].
% 1.67/1.96 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = C | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(C,B,tc_Polynomial_Opoly(A)). [resolve(279,a,262,a)].
% 1.67/1.96 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | C = B | -c_lessequals(B,C,tc_Polynomial_Opoly(A)). [resolve(279,a,269,a)].
% 1.67/1.96 280 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.67/1.96 281 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 1.67/1.96 282 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 1.67/1.96 283 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 1.67/1.96 284 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 1.67/1.96 285 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.67/1.96 286 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.67/1.96 287 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.67/1.96 288 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.67/1.96 289 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.67/1.97 290 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.67/1.97 291 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.67/1.97 292 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.67/1.97 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(280,a,282,a)].
% 1.67/1.97 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat). [resolve(280,a,284,a)].
% 1.67/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(280,a,285,a)].
% 1.67/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(280,a,286,a)].
% 1.67/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(280,a,287,a)].
% 1.67/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(280,a,288,a)].
% 1.67/1.97 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(280,a,289,a)].
% 1.67/1.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_nat),c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(280,a,290,a)].
% 1.67/1.97 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(280,a,291,a)].
% 1.67/1.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat). [resolve(280,a,292,a)].
% 1.67/1.97 293 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.67/1.97 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(293,a,282,a)].
% 1.67/1.97 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(293,a,284,a)].
% 1.67/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(293,a,285,a)].
% 1.67/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(293,a,286,a)].
% 1.67/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(293,a,287,a)].
% 1.67/1.97 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(293,a,288,a)].
% 1.67/1.97 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(293,a,289,a)].
% 1.67/1.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(293,a,290,a)].
% 1.67/1.97 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(293,a,291,a)].
% 1.67/1.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(293,a,292,a)].
% 1.67/1.97 294 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].
% 1.67/1.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(294,a,282,a)].
% 1.67/1.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(D,B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(294,a,284,a)].
% 1.67/1.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(294,a,285,a)].
% 1.67/1.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(294,a,286,a)].
% 1.67/1.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(294,a,287,a)].
% 1.67/1.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(294,a,288,a)].
% 1.67/1.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(294,a,289,a)].
% 1.67/1.97 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(294,a,290,a)].
% 1.73/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)). [resolve(294,a,291,a)].
% 1.73/2.03 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(294,a,292,a)].
% 1.73/2.03 295 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.73/2.03 296 -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].
% 1.73/2.03 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(295,a,296,a)].
% 1.73/2.03 297 class_Nat_Osemiring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.73/2.03 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint) | A = B. [resolve(297,a,296,a)].
% 1.73/2.03 298 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.73/2.03 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(298,a,296,a)].
% 1.73/2.03 299 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].
% 1.73/2.03 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(299,a,296,a)].
% 1.73/2.03 300 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.73/2.03 301 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_lessequals(B,C,tc_nat) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 1.73/2.03 302 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 1.73/2.03 303 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.73/2.03 304 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.73/2.03 305 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(D,C,tc_nat) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 1.73/2.03 306 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 1.73/2.03 307 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 1.73/2.03 308 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 1.73/2.03 309 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.73/2.03 310 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.73/2.03 311 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.73/2.03 312 -class_Ring__and__Field_Oordered__semidom(A) | -c_lessequals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.73/2.03 313 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(A),A),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.73/2.03 314 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(B,D,A) # label(cls_power__mono_0) # label(axiom). [assumption].
% 1.73/2.03 315 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 1.73/2.03 316 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_Power_Opower__class_Opower(B,c_Suc(D),A),c_Power_Opower__class_Opower(C,c_Suc(D),A),A) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 1.73/2.03 317 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,c_Suc(C),A) != c_Power_Opower__class_Opower(D,c_Suc(C),A) | B = D | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 1.73/2.03 318 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.73/2.03 319 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_nat) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.73/2.03 320 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 1.73/2.03 321 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(A),c_HOL_Oone__class_Oone(A),A),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 1.73/2.03 322 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 1.73/2.03 323 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,c_Suc(C),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.73/2.03 324 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) | -c_lessequals(C,D,tc_nat) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 1.73/2.03 325 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),A),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.73/2.03 326 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.73/2.03 327 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.73/2.03 328 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(D,C,A) | B = D | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 1.73/2.03 329 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 1.73/2.03 330 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 1.73/2.03 331 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.73/2.03 332 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.73/2.03 333 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.73/2.03 334 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.73/2.03 335 -class_Ring__and__Field_Oordered__semidom(A) | c_Power_Opower__class_Opower(B,C,A) != c_Power_Opower__class_Opower(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.73/2.03 336 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.73/2.03 337 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.73/2.03 338 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.73/2.03 339 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.73/2.03 340 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 1.73/2.03 341 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 1.73/2.03 342 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 1.73/2.03 343 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 1.73/2.03 Derived: c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(300,a,301,a)].
% 1.73/2.03 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(300,a,302,a)].
% 1.73/2.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(300,a,303,a)].
% 1.73/2.03 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(C,B,tc_nat). [resolve(300,a,305,a)].
% 1.73/2.03 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(C,A,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(300,a,306,a)].
% 1.73/2.03 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_lessequals(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(300,a,308,a)].
% 1.73/2.03 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(300,a,309,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(300,a,310,a)].
% 1.73/2.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(300,a,311,a)].
% 1.73/2.03 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(300,a,312,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat). [resolve(300,a,313,a)].
% 1.73/2.03 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(300,a,314,a)].
% 1.73/2.03 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(300,a,315,a)].
% 1.73/2.03 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_nat),c_Power_Opower__class_Opower(B,c_Suc(C),tc_nat),tc_nat). [resolve(300,a,316,a)].
% 1.73/2.03 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_nat) | A = C | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(300,a,317,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(300,a,318,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(300,a,319,a)].
% 1.73/2.03 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(300,a,320,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat). [resolve(300,a,321,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat). [resolve(300,a,322,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(300,a,323,a)].
% 1.73/2.03 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(300,a,324,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(300,a,325,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(300,a,326,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(300,a,327,a)].
% 1.73/2.03 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(C,B,tc_nat) | A = C | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(300,a,328,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(300,a,329,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(300,a,330,a)].
% 1.73/2.03 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(300,a,331,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(300,a,332,a)].
% 1.73/2.04 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(300,a,333,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(300,a,334,a)].
% 1.73/2.04 Derived: c_Power_Opower__class_Opower(A,B,tc_nat) != c_Power_Opower__class_Opower(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | B = C. [resolve(300,a,335,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(300,a,336,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_Power_Opower__class_Opower(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(300,a,337,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(300,a,340,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(300,a,341,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(300,a,342,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(300,a,343,a)].
% 1.73/2.04 344 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.73/2.04 Derived: c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_nat). [resolve(344,a,301,a)].
% 1.73/2.04 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint). [resolve(344,a,302,a)].
% 1.73/2.04 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint). [resolve(344,a,303,a)].
% 1.73/2.04 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(C,B,tc_nat). [resolve(344,a,305,a)].
% 1.73/2.04 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(C,A,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),C,tc_Int_Oint). [resolve(344,a,306,a)].
% 1.73/2.04 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,308,a)].
% 1.73/2.04 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(344,a,309,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(344,a,310,a)].
% 1.73/2.04 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(344,a,311,a)].
% 1.73/2.04 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(344,a,312,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(344,a,313,a)].
% 1.73/2.04 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(344,a,314,a)].
% 1.73/2.04 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,315,a)].
% 1.73/2.04 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_Power_Opower__class_Opower(A,c_Suc(C),tc_Int_Oint),c_Power_Opower__class_Opower(B,c_Suc(C),tc_Int_Oint),tc_Int_Oint). [resolve(344,a,316,a)].
% 1.73/2.04 Derived: c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint) != c_Power_Opower__class_Opower(C,c_Suc(B),tc_Int_Oint) | A = C | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,317,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint). [resolve(344,a,318,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(344,a,319,a)].
% 1.73/2.04 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,320,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(344,a,321,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(344,a,322,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,323,a)].
% 1.73/2.04 Derived: c_lessequals(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,C,tc_nat). [resolve(344,a,324,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,c_Suc(B),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,325,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint). [resolve(344,a,326,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(344,a,327,a)].
% 1.73/2.04 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_Power_Opower__class_Opower(C,B,tc_Int_Oint) | A = C | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,328,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(344,a,329,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,330,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(344,a,331,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,332,a)].
% 1.73/2.04 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(344,a,333,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(344,a,334,a)].
% 1.73/2.04 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_Power_Opower__class_Opower(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | B = C. [resolve(344,a,335,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_Int_Oint),c_Power_Opower__class_Opower(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),C,tc_Int_Oint). [resolve(344,a,336,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_Power_Opower__class_Opower(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(344,a,337,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,340,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,341,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,342,a)].
% 1.73/2.04 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(344,a,343,a)].
% 1.73/2.04 345 class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,C,tc_nat). [resolve(345,a,301,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(345,a,302,a)].
% 1.73/2.04 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(345,a,303,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Oone__class_Oone(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(D,C,tc_nat). [resolve(345,a,305,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Power_Opower__class_Opower(D,B,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(345,a,306,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(345,a,308,a)].
% 1.73/2.04 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(345,a,309,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(345,a,310,a)].
% 1.73/2.04 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(345,a,311,a)].
% 1.73/2.04 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(345,a,312,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(345,a,313,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(D,C,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(B,D,tc_Polynomial_Opoly(A)). [resolve(345,a,314,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,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(345,a,315,a)].
% 1.73/2.04 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(c_Power_Opower__class_Opower(B,c_Suc(D),tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(C,c_Suc(D),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(345,a,316,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Power_Opower__class_Opower(B,c_Suc(C),tc_Polynomial_Opoly(A)) != c_Power_Opower__class_Opower(D,c_Suc(C),tc_Polynomial_Opoly(A)) | 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(345,a,317,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(345,a,318,a)].
% 1.73/2.04 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_Nat_Osemiring__1__class_Oof__nat(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(345,a,319,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(345,a,320,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(345,a,321,a)].
% 1.73/2.04 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(c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(345,a,322,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,c_Suc(C),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(345,a,323,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_nat). [resolve(345,a,324,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),tc_Polynomial_Opoly(A)),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(345,a,325,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(345,a,326,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(345,a,327,a)].
% 1.73/2.04 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)) != c_Power_Opower__class_Opower(D,C,tc_Polynomial_Opoly(A)) | B = D | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(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(345,a,328,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(345,a,329,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,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(345,a,330,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,D,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)) | -c_HOL_Oord__class_Oless(D,C,tc_nat). [resolve(345,a,331,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,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(345,a,332,a)].
% 1.73/2.05 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(345,a,333,a)].
% 1.73/2.05 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(345,a,334,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)) != c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | C = D. [resolve(345,a,335,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(345,a,336,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_nat). [resolve(345,a,337,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(345,a,340,a)].
% 1.73/2.05 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(345,a,341,a)].
% 1.87/2.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(345,a,342,a)].
% 1.87/2.12 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(345,a,343,a)].
% 1.87/2.12 346 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.87/2.12 347 -class_OrderedGroup_Oab__semigroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 1.87/2.12 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). [resolve(346,a,347,a)].
% 1.87/2.12 348 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.87/2.12 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(348,a,347,a)].
% 1.87/2.12 349 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.87/2.12 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(349,a,347,a)].
% 1.87/2.12 350 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].
% 1.87/2.12 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(350,a,347,a)].
% 1.87/2.12 351 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.87/2.12 352 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.87/2.12 353 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.87/2.12 354 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.87/2.12 355 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.87/2.12 356 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 1.90/2.16 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(351,a,352,a)].
% 1.90/2.16 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(351,a,353,a)].
% 1.90/2.16 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(351,a,356,a)].
% 1.90/2.16 357 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.90/2.16 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(357,a,352,a)].
% 1.90/2.16 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(357,a,353,a)].
% 1.90/2.16 Derived: c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),c_HOL_Oplus__class_Oplus(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(357,a,356,a)].
% 1.90/2.16 358 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].
% 1.90/2.16 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(358,a,352,a)].
% 1.90/2.16 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(358,a,353,a)].
% 1.90/2.16 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(358,a,356,a)].
% 1.90/2.16 359 class_Ring__and__Field_Osgn__if(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osgn__if) # label(axiom). [assumption].
% 1.90/2.16 360 -class_Ring__and__Field_Osgn__if(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn0_0) # label(axiom). [assumption].
% 1.90/2.16 361 -class_Ring__and__Field_Osgn__if(A) | c_HOL_Osgn__class_Osgn(B,A) = c_HOL_Oone__class_Oone(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__if_1) # label(axiom). [assumption].
% 1.90/2.16 362 -class_Ring__and__Field_Osgn__if(A) | c_HOL_Osgn__class_Osgn(B,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__if_2) # label(axiom). [assumption].
% 1.90/2.16 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(359,a,360,a)].
% 1.90/2.16 Derived: c_HOL_Osgn__class_Osgn(A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(359,a,361,a)].
% 1.98/2.23 Derived: c_HOL_Osgn__class_Osgn(A,tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(359,a,362,a)].
% 1.98/2.23 363 class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if) # label(axiom). [assumption].
% 1.98/2.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(363,a,360,a)].
% 1.98/2.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(B,tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(363,a,361,a)].
% 1.98/2.23 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Osgn__class_Osgn(B,tc_Polynomial_Opoly(A)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(363,a,362,a)].
% 1.98/2.23 364 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 1.98/2.23 365 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__zero_0) # label(axiom). [assumption].
% 1.98/2.23 366 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sgn__zero__iff_0) # label(axiom). [assumption].
% 1.98/2.23 367 -class_RealVector_Oreal__normed__vector(A) | c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(B,A),A) # label(cls_sgn__minus_0) # label(axiom). [assumption].
% 1.98/2.23 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(364,a,365,a)].
% 1.98/2.23 Derived: c_HOL_Osgn__class_Osgn(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(364,a,366,a)].
% 1.98/2.23 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(364,a,367,a)].
% 1.98/2.23 368 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.98/2.23 369 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,A),A) | -c_lessequals(E,D,A) | -c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,A),A) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 1.98/2.23 370 -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].
% 1.98/2.23 371 -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].
% 1.98/2.23 372 -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].
% 1.98/2.23 373 -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].
% 1.98/2.23 374 -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].
% 1.98/2.23 375 -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].
% 1.98/2.23 376 -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].
% 1.98/2.23 377 -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].
% 1.98/2.23 378 -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].
% 1.98/2.23 379 -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].
% 1.98/2.23 380 -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].
% 1.98/2.23 381 -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].
% 1.98/2.23 382 -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].
% 1.98/2.23 383 -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].
% 1.98/2.23 384 -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].
% 1.98/2.23 385 -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].
% 1.98/2.23 386 -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].
% 1.98/2.23 387 -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].
% 1.98/2.23 388 -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].
% 1.98/2.23 389 -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].
% 1.98/2.23 Derived: c_lessequals(A,c_HOL_Oplus__class_Oplus(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(A,c_HOL_Oplus__class_Oplus(B,D,tc_Int_Oint),tc_Int_Oint). [resolve(368,a,369,a)].
% 1.98/2.24 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(368,a,370,a)].
% 1.98/2.24 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(368,a,371,a)].
% 1.98/2.24 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(368,a,372,a)].
% 1.98/2.24 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(368,a,373,a)].
% 1.98/2.24 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(368,a,374,a)].
% 1.98/2.24 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(368,a,375,a)].
% 1.98/2.24 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),A,tc_Int_Oint). [resolve(368,a,376,a)].
% 1.98/2.24 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(368,a,378,a)].
% 1.98/2.24 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(368,a,380,a)].
% 1.98/2.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(368,a,381,a)].
% 1.98/2.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(368,a,382,a)].
% 1.98/2.24 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(368,a,383,a)].
% 1.98/2.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(368,a,384,a)].
% 1.98/2.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(368,a,385,a)].
% 1.98/2.24 Derived: c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),A,tc_Int_Oint). [resolve(368,a,386,a)].
% 1.98/2.24 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(368,a,388,a)].
% 1.98/2.24 390 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].
% 1.98/2.24 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(E,D,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Oplus__class_Oplus(C,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(390,a,369,a)].
% 1.98/2.24 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(390,a,370,a)].
% 1.98/2.24 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(390,a,371,a)].
% 1.98/2.24 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(390,a,372,a)].
% 1.98/2.24 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(390,a,373,a)].
% 1.98/2.24 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(390,a,374,a)].
% 1.98/2.24 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(390,a,375,a)].
% 1.98/2.24 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(390,a,376,a)].
% 1.98/2.24 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(390,a,378,a)].
% 1.98/2.24 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(390,a,380,a)].
% 1.98/2.24 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(390,a,381,a)].
% 1.98/2.24 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(390,a,382,a)].
% 1.98/2.24 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(390,a,383,a)].
% 1.98/2.24 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(390,a,384,a)].
% 1.98/2.24 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(390,a,385,a)].
% 1.98/2.27 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(390,a,386,a)].
% 1.98/2.27 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(390,a,388,a)].
% 1.98/2.27 391 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 1.98/2.27 392 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 1.98/2.27 393 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 1.98/2.27 394 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 1.98/2.27 395 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 1.98/2.27 396 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_0) # label(axiom). [assumption].
% 1.98/2.27 397 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_1) # label(axiom). [assumption].
% 1.98/2.27 398 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,B,A),A) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 1.98/2.27 399 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 1.98/2.27 400 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 1.98/2.27 401 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 1.98/2.27 402 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 1.98/2.27 403 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 1.98/2.27 404 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 1.98/2.27 405 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 1.98/2.27 406 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 1.98/2.27 407 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom). [assumption].
% 1.98/2.27 408 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 1.98/2.27 409 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 1.98/2.27 410 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,C,A),c_HOL_Otimes__class_Otimes(B,B,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 1.98/2.27 411 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 1.98/2.27 412 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Omonoid__mult(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__even__power_0) # label(axiom). [assumption].
% 1.98/2.27 413 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 1.98/2.27 414 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 1.98/2.27 415 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 1.98/2.27 416 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 1.98/2.27 417 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 1.98/2.27 418 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 1.98/2.27 419 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 1.98/2.27 420 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),A) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 1.98/2.27 421 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 1.98/2.27 422 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 1.98/2.27 423 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 1.98/2.27 424 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 1.98/2.27 425 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 1.98/2.27 426 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 1.98/2.27 427 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 1.98/2.27 428 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 1.98/2.27 429 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 1.98/2.27 430 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 1.98/2.27 431 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(D,B,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 1.98/2.27 432 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 1.98/2.27 433 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 1.98/2.27 434 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 1.98/2.27 435 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 1.98/2.27 436 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 1.98/2.27 437 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 1.98/2.27 438 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 1.98/2.27 439 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 1.98/2.27 440 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 1.98/2.27 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,393,a)].
% 1.98/2.27 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,394,a)].
% 1.98/2.28 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,396,a)].
% 1.98/2.28 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,397,a)].
% 1.98/2.28 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,398,a)].
% 1.98/2.28 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(391,a,399,a)].
% 1.98/2.28 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,400,a)].
% 1.98/2.28 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,402,a)].
% 1.98/2.28 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,403,a)].
% 1.98/2.28 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(391,a,405,a)].
% 1.98/2.28 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,406,a)].
% 1.98/2.28 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,407,a)].
% 1.98/2.28 Derived: c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,408,a)].
% 1.98/2.28 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(391,a,409,a)].
% 1.98/2.28 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,410,a)].
% 1.98/2.28 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,411,a)].
% 1.98/2.28 Derived: -class_OrderedGroup_Omonoid__mult(tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(391,a,412,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,413,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(391,a,414,a)].
% 1.98/2.28 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,415,a)].
% 1.98/2.28 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,416,a)].
% 1.98/2.28 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(391,a,417,a)].
% 1.98/2.28 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(391,a,418,a)].
% 1.98/2.28 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,419,a)].
% 1.98/2.28 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(391,a,420,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,421,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,422,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,423,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,424,a)].
% 1.98/2.28 Derived: -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,425,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,426,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,427,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,428,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint). [resolve(391,a,429,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,430,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,431,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(391,a,432,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,434,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(391,a,435,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(391,a,438,a)].
% 1.98/2.28 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(391,a,440,a)].
% 1.98/2.28 441 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].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,393,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,394,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(441,a,396,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(441,a,397,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,398,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(441,a,399,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,400,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,402,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,403,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(441,a,405,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,406,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(441,a,407,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,408,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,409,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,410,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,411,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | -class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(A)) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat). [resolve(441,a,412,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(441,a,413,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(441,a,414,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,415,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,416,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(441,a,417,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(441,a,418,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,419,a)].
% 1.98/2.28 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,420,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,421,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,422,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,423,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,424,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,425,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,426,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,427,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,428,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,429,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,430,a)].
% 1.98/2.29 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,431,a)].
% 2.06/2.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(441,a,432,a)].
% 2.06/2.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,434,a)].
% 2.06/2.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(441,a,435,a)].
% 2.06/2.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)). [resolve(441,a,438,a)].
% 2.06/2.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(441,a,440,a)].
% 2.06/2.37 442 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.06/2.37 443 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 2.06/2.37 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(442,a,443,a)].
% 2.06/2.37 444 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.06/2.37 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(444,a,443,a)].
% 2.06/2.37 445 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].
% 2.06/2.37 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,D,tc_Polynomial_Opoly(A)). [resolve(445,a,443,a)].
% 2.06/2.37 446 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.06/2.37 447 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 2.16/2.41 448 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 2.16/2.41 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(446,a,448,a)].
% 2.16/2.41 449 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.16/2.41 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(449,a,448,a)].
% 2.16/2.41 450 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].
% 2.16/2.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(450,a,448,a)].
% 2.16/2.41 451 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 2.16/2.41 452 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,C,A) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 2.16/2.41 453 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 2.16/2.41 454 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 2.16/2.41 455 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 2.16/2.41 456 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 2.16/2.41 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,B,tc_Int_Oint). [resolve(451,a,452,a)].
% 2.16/2.41 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(C,A,tc_Int_Oint). [resolve(451,a,453,a)].
% 2.16/2.41 457 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].
% 2.16/2.41 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,C,tc_Polynomial_Opoly(A)). [resolve(457,a,452,a)].
% 2.19/2.49 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(D,B,tc_Polynomial_Opoly(A)). [resolve(457,a,453,a)].
% 2.19/2.49 458 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.19/2.49 459 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.19/2.49 460 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 2.19/2.49 461 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 2.19/2.49 462 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 2.19/2.49 463 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 2.19/2.49 464 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 2.19/2.49 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(458,a,459,a)].
% 2.19/2.49 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(458,a,460,a)].
% 2.19/2.49 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(458,a,461,a)].
% 2.19/2.49 465 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.19/2.49 466 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].
% 2.19/2.49 467 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.19/2.49 468 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 2.19/2.49 469 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 2.27/2.53 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(467,a,468,a)].
% 2.27/2.53 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(467,a,469,a)].
% 2.27/2.53 470 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.27/2.53 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(470,a,468,a)].
% 2.27/2.53 Derived: c_lessequals(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(470,a,469,a)].
% 2.27/2.53 471 class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.27/2.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(471,a,468,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(471,a,469,a)].
% 2.27/2.53 472 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.27/2.53 473 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_0) # label(axiom). [assumption].
% 2.27/2.53 474 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_1) # label(axiom). [assumption].
% 2.27/2.53 475 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff__number__of_2) # label(axiom). [assumption].
% 2.27/2.53 476 -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].
% 2.27/2.53 477 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 2.27/2.53 478 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 2.27/2.53 479 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 2.27/2.53 480 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(472,a,473,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(472,a,474,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(472,a,475,a)].
% 2.27/2.53 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(472,a,476,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(472,a,477,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(472,a,478,a)].
% 2.27/2.53 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(472,a,479,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(472,a,480,a)].
% 2.27/2.53 481 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(481,a,473,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(481,a,474,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(481,a,475,a)].
% 2.27/2.53 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(481,a,476,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(481,a,477,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(481,a,478,a)].
% 2.27/2.53 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(481,a,479,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(481,a,480,a)].
% 2.27/2.53 482 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(482,a,473,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(482,a,474,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(482,a,475,a)].
% 2.27/2.53 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(482,a,476,a)].
% 2.27/2.53 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(482,a,477,a)].
% 2.27/2.54 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(482,a,478,a)].
% 2.27/2.54 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(482,a,479,a)].
% 2.27/2.54 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(482,a,480,a)].
% 2.27/2.54 483 class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.27/2.54 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)) | c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(483,a,473,a)].
% 2.27/2.54 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)) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(483,a,474,a)].
% 2.27/2.54 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)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(483,a,475,a)].
% 2.27/2.54 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(483,a,476,a)].
% 2.27/2.54 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)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(483,a,477,a)].
% 2.27/2.54 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)) | c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(483,a,478,a)].
% 2.27/2.54 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(483,a,479,a)].
% 2.27/2.54 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)) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(483,a,480,a)].
% 2.34/2.58 484 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.34/2.58 485 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 2.34/2.58 486 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left__number__of_1) # label(axiom). [assumption].
% 2.34/2.58 487 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left__number__of_0) # label(axiom). [assumption].
% 2.34/2.58 488 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 2.34/2.58 489 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 2.34/2.58 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(484,a,485,a)].
% 2.34/2.58 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(484,a,486,a)].
% 2.34/2.58 Derived: -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(484,a,487,a)].
% 2.34/2.58 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(484,a,488,a)].
% 2.34/2.58 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(484,a,489,a)].
% 2.34/2.58 490 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.34/2.58 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Suc(A),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(490,a,485,a)].
% 2.34/2.58 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(490,a,486,a)].
% 2.34/2.58 Derived: -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(490,a,487,a)].
% 2.34/2.58 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(490,a,488,a)].
% 2.34/2.62 Derived: -class_Power_Opower(tc_Int_Oint) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(490,a,489,a)].
% 2.34/2.62 491 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.34/2.62 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Suc(A),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(491,a,485,a)].
% 2.34/2.62 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(491,a,486,a)].
% 2.34/2.62 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(491,a,487,a)].
% 2.34/2.62 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(491,a,488,a)].
% 2.34/2.62 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(491,a,489,a)].
% 2.34/2.62 492 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].
% 2.34/2.62 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Suc(B),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(492,a,485,a)].
% 2.34/2.62 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(492,a,486,a)].
% 2.34/2.62 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(492,a,487,a)].
% 2.34/2.62 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(A)) = c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)). [resolve(492,a,488,a)].
% 2.34/2.62 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_Power_Opower(tc_Polynomial_Opoly(A)) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(492,a,489,a)].
% 2.34/2.62 493 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.34/2.62 494 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_left__minus_0) # label(axiom). [assumption].
% 2.34/2.62 495 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus_0) # label(axiom). [assumption].
% 2.34/2.62 496 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__neg__iff__add__eq__0_0) # label(axiom). [assumption].
% 2.34/2.62 497 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ouminus__class_Ouminus(B,A) = C # label(cls_minus__unique_0) # label(axiom). [assumption].
% 2.34/2.62 498 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ouminus__class_Ouminus(C,A) # label(cls_eq__neg__iff__add__eq__0_1) # label(axiom). [assumption].
% 2.34/2.62 499 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(B,C,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_minus__add_0) # label(axiom). [assumption].
% 2.34/2.62 500 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Oplus__class_Oplus(B,C,A),A) = C # label(cls_minus__add__cancel_0) # label(axiom). [assumption].
% 2.34/2.62 501 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),C,A),A) = C # label(cls_add__minus__cancel_0) # label(axiom). [assumption].
% 2.34/2.62 502 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__equal__iff__equal_1) # label(axiom). [assumption].
% 2.34/2.62 503 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom). [assumption].
% 2.34/2.62 504 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom). [assumption].
% 2.34/2.62 505 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom). [assumption].
% 2.34/2.62 506 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Ouminus__class_Ouminus(B,A) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom). [assumption].
% 2.34/2.62 507 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__equation__iff_1) # label(axiom). [assumption].
% 2.34/2.62 508 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_1) # label(axiom). [assumption].
% 2.34/2.62 509 -class_OrderedGroup_Ogroup__add(A) | B = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_equation__minus__iff_0) # label(axiom). [assumption].
% 2.34/2.62 510 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B # label(cls_minus__minus_0) # label(axiom). [assumption].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(493,a,494,a)].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(493,a,495,a)].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) = B. [resolve(493,a,497,a)].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint). [resolve(493,a,498,a)].
% 2.34/2.62 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(493,a,499,a)].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),tc_Int_Oint) = B. [resolve(493,a,500,a)].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint),tc_Int_Oint) = B. [resolve(493,a,501,a)].
% 2.34/2.62 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(493,a,502,a)].
% 2.34/2.62 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(493,a,503,a)].
% 2.34/2.62 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) != c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint) | A = B. [resolve(493,a,504,a)].
% 2.34/2.62 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(493,a,505,a)].
% 2.34/2.62 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) | c_HOL_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(493,a,506,a)].
% 2.34/2.62 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) = A. [resolve(493,a,507,a)].
% 2.34/2.62 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(493,a,508,a)].
% 2.34/2.62 511 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(511,a,494,a)].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(511,a,495,a)].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) = B. [resolve(511,a,497,a)].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex). [resolve(511,a,498,a)].
% 2.34/2.62 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(511,a,499,a)].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = B. [resolve(511,a,500,a)].
% 2.34/2.62 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = B. [resolve(511,a,501,a)].
% 2.34/2.62 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(511,a,502,a)].
% 2.34/2.62 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(511,a,503,a)].
% 2.34/2.62 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex) | A = B. [resolve(511,a,504,a)].
% 2.34/2.62 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(511,a,505,a)].
% 2.34/2.62 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(511,a,506,a)].
% 2.34/2.62 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(511,a,507,a)].
% 2.34/2.62 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(511,a,508,a)].
% 2.34/2.67 512 class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Oab__group__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.34/2.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(512,a,494,a)].
% 2.34/2.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(512,a,495,a)].
% 2.34/2.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)) = C. [resolve(512,a,497,a)].
% 2.34/2.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)). [resolve(512,a,498,a)].
% 2.34/2.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(512,a,499,a)].
% 2.34/2.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = C. [resolve(512,a,500,a)].
% 2.34/2.67 Derived: -class_OrderedGroup_Oab__group__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = C. [resolve(512,a,501,a)].
% 2.34/2.67 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(512,a,502,a)].
% 2.34/2.67 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(512,a,503,a)].
% 2.34/2.67 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(512,a,504,a)].
% 2.34/2.67 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(512,a,505,a)].
% 2.34/2.67 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(512,a,506,a)].
% 2.34/2.67 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(512,a,507,a)].
% 2.34/2.67 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(512,a,508,a)].
% 2.34/2.67 513 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.34/2.67 514 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 2.34/2.67 515 -class_OrderedGroup_Omonoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 2.34/2.67 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(513,a,514,a)].
% 2.34/2.67 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = A. [resolve(513,a,515,a)].
% 2.49/2.75 516 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.49/2.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(516,a,514,a)].
% 2.49/2.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = A. [resolve(516,a,515,a)].
% 2.49/2.75 517 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.49/2.75 Derived: c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(517,a,514,a)].
% 2.49/2.75 Derived: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A. [resolve(517,a,515,a)].
% 2.49/2.75 518 class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(A)) | -class_OrderedGroup_Ocomm__monoid__add(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 2.49/2.75 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = B. [resolve(518,a,514,a)].
% 2.49/2.75 Derived: -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = B. [resolve(518,a,515,a)].
% 2.49/2.75 519 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption].
% 2.49/2.75 520 -class_RealVector_Oreal__normed__div__algebra(A) | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Osgn__class_Osgn(C,A),A) # label(cls_sgn__mult_0) # label(axiom). [assumption].
% 2.49/2.75 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(A,tc_Complex_Ocomplex),c_HOL_Osgn__class_Osgn(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(519,a,520,a)].
% 2.49/2.75 521 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.49/2.75 522 -class_Ring__and__Field_Ocomm__semiring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 2.49/2.75 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(521,a,522,a)].
% 2.49/2.75 523 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.49/2.75 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(523,a,522,a)].
% 2.49/2.75 524 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.49/2.75 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(524,a,522,a)].
% 2.49/2.75 525 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].
% 2.49/2.75 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(525,a,522,a)].
% 2.49/2.80 526 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 2.49/2.80 527 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult_Oadd__left_0) # label(axiom). [assumption].
% 2.49/2.80 528 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__left_Oadd_0) # label(axiom). [assumption].
% 2.49/2.80 529 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult_Oadd__right_0) # label(axiom). [assumption].
% 2.49/2.80 530 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) # label(cls_mult__right_Oadd_0) # label(axiom). [assumption].
% 2.49/2.80 531 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 2.49/2.80 532 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 2.49/2.80 533 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 2.49/2.80 534 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 2.49/2.80 535 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 2.49/2.80 536 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 2.49/2.80 537 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 2.49/2.80 538 -class_RealVector_Oreal__normed__algebra(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 2.49/2.80 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(A,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(526,a,529,a)].
% 2.49/2.80 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(526,a,531,a)].
% 2.49/2.80 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(526,a,533,a)].
% 2.49/2.80 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(526,a,535,a)].
% 2.49/2.80 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(526,a,537,a)].
% 2.58/2.88 539 class_Ring__and__Field_Odvd(tc_nat) # label(clsarity_nat__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.58/2.88 540 -class_Ring__and__Field_Odvd(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_dvdI_0) # label(axiom). [assumption].
% 2.58/2.88 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). [resolve(539,a,540,a)].
% 2.58/2.88 541 class_Ring__and__Field_Odvd(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.58/2.88 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(541,a,540,a)].
% 2.58/2.88 542 class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.58/2.88 Derived: c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(542,a,540,a)].
% 2.58/2.88 543 class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Ocomm__semiring__1(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) # label(axiom). [assumption].
% 2.58/2.88 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(543,a,540,a)].
% 2.58/2.88 544 class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 2.58/2.88 545 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__eq__neg__nonpos_0) # label(axiom). [assumption].
% 2.58/2.88 546 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__eq__neg__nonpos_1) # label(axiom). [assumption].
% 2.58/2.88 547 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) # label(cls_neg__less__eq__nonneg_0) # label(axiom). [assumption].
% 2.58/2.88 548 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__eq__nonneg_1) # label(axiom). [assumption].
% 2.58/2.88 549 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 2.58/2.88 550 -class_OrderedGroup_Oordered__ab__group__add(A) | c_HOL_Ouminus__class_Ouminus(B,A) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 2.58/2.88 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) != A | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(544,a,550,a)].
% 2.58/2.88 551 class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 2.58/2.88 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(551,a,545,a)].
% 2.58/2.88 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(551,a,546,a)].
% 2.58/2.88 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(551,a,547,a)].
% 2.66/2.93 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(551,a,548,a)].
% 2.66/2.93 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(551,a,549,a)].
% 2.66/2.93 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(551,a,550,a)].
% 2.66/2.93 552 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.66/2.93 553 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 2.66/2.93 554 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 2.66/2.93 555 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 2.66/2.93 556 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 2.66/2.93 557 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 2.66/2.93 558 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 2.66/2.93 559 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 2.66/2.93 560 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 2.66/2.93 561 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 2.66/2.93 562 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 2.66/2.93 563 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 2.66/2.93 564 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 2.66/2.93 565 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 2.66/2.93 566 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 2.66/2.93 567 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 2.66/2.93 568 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 2.66/2.93 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat). [resolve(552,a,553,a)].
% 2.66/2.93 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(552,a,554,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(552,a,555,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat). [resolve(552,a,556,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(552,a,557,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(552,a,558,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(552,a,559,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(552,a,560,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(552,a,561,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(552,a,562,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). [resolve(552,a,564,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat). [resolve(552,a,565,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(552,a,566,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(552,a,567,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(552,a,568,a)].
% 2.66/2.93 569 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.66/2.93 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(569,a,554,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(569,a,555,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(569,a,556,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(569,a,557,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(569,a,558,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(569,a,559,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Otimes__class_Otimes(C,D,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(569,a,560,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(569,a,561,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(569,a,562,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(569,a,564,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(569,a,565,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(569,a,566,a)].
% 2.66/2.93 570 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].
% 2.66/2.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(B,C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(570,a,554,a)].
% 2.66/2.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(570,a,555,a)].
% 2.66/2.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(570,a,556,a)].
% 2.66/2.93 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(570,a,557,a)].
% 2.66/2.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(570,a,558,a)].
% 2.66/2.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,E,tc_Polynomial_Opoly(A)) | -c_lessequals(B,D,tc_Polynomial_Opoly(A)). [resolve(570,a,559,a)].
% 2.66/2.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(D,E,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_lessequals(C,E,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,D,tc_Polynomial_Opoly(A)). [resolve(570,a,560,a)].
% 2.66/2.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(570,a,561,a)].
% 2.66/2.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(570,a,562,a)].
% 2.66/2.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(570,a,564,a)].
% 2.66/2.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,B,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(570,a,565,a)].
% 2.66/2.98 Derived: -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)). [resolve(570,a,566,a)].
% 2.66/2.98 571 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.66/2.98 572 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 2.87/3.10 573 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 2.87/3.10 574 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.87/3.10 575 class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oordered__idom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.87/3.10 576 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 2.87/3.10 577 -class_RealVector_Oreal__normed__algebra__1(A) | c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_sgn__one_0) # label(axiom). [assumption].
% 2.87/3.10 Derived: c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(576,a,577,a)].
% 2.87/3.10 578 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.87/3.10 579 -class_Ring__and__Field_Oring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Otimes__class_Otimes(B,C,A) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 2.87/3.10 580 -class_Ring__and__Field_Oring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 2.87/3.10 581 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 2.87/3.10 582 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 2.87/3.10 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint). [resolve(578,a,579,a)].
% 2.87/3.10 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint). [resolve(578,a,580,a)].
% 2.87/3.10 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint). [resolve(578,a,581,a)].
% 2.87/3.10 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(578,a,582,a)].
% 2.87/3.10 583 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.87/3.10 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex). [resolve(583,a,579,a)].
% 2.87/3.10 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(583,a,580,a)].
% 2.87/3.10 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(583,a,581,a)].
% 2.87/3.19 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(583,a,582,a)].
% 2.87/3.19 584 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].
% 2.87/3.19 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)). [resolve(584,a,579,a)].
% 2.87/3.19 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(584,a,580,a)].
% 2.96/3.19 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(584,a,581,a)].
% 2.96/3.19 Derived: -class_Ring__and__Field_Ocomm__ring(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)). [resolve(584,a,582,a)].
% 2.96/3.19 585 class_Ring__and__Field_Oring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 2.96/3.19 586 -class_Ring__and__Field_Oring__1(A) | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A),C,A),c_Power_Opower__class_Opower(B,C,A),A) # label(cls_power__minus_0) # label(axiom). [assumption].
% 2.96/3.19 Derived: c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),B,tc_Int_Oint),c_Power_Opower__class_Opower(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(585,a,586,a)].
% 2.96/3.19 587 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 2.96/3.19 Derived: c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(587,a,586,a)].
% 2.96/3.19 588 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].
% 2.96/3.19 Derived: -class_Ring__and__Field_Ocomm__ring__1(A) | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(B,tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),C,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(588,a,586,a)].
% 2.96/3.19 589 class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.96/3.19 590 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 2.96/3.23 591 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 2.96/3.23 592 -class_Ring__and__Field_Oring__no__zero__divisors(A) | c_HOL_Otimes__class_Otimes(B,C,A) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 2.96/3.23 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(589,a,590,a)].
% 2.96/3.23 Derived: c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(589,a,591,a)].
% 2.96/3.23 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(589,a,592,a)].
% 2.96/3.23 593 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.96/3.23 Derived: c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(593,a,592,a)].
% 2.96/3.23 594 class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # label(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 2.96/3.23 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(594,a,590,a)].
% 2.96/3.23 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(594,a,591,a)].
% 2.96/3.23 Derived: -class_Ring__and__Field_Oidom(A) | c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) | B = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)). [resolve(594,a,592,a)].
% 2.96/3.23 595 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.96/3.23 596 -class_OrderedGroup_Oab__semigroup__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 2.96/3.23 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). [resolve(595,a,596,a)].
% 2.96/3.23 597 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.96/3.23 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(597,a,596,a)].
% 2.96/3.23 598 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.96/3.23 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(598,a,596,a)].
% 2.96/3.23 599 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].
% 2.96/3.23 Derived: -class_Ring__and__Field_Ocomm__semiring__0(A) | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(599,a,596,a)].
% 3.09/3.36 600 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.09/3.36 601 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 3.09/3.36 602 -class_OrderedGroup_Ocomm__monoid__mult(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A) = B # label(cls_mult__1_0) # label(axiom). [assumption].
% 3.09/3.36 Derived: c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,C,tc_nat),c_Power_Opower__class_Opower(B,C,tc_nat),tc_nat). [resolve(600,a,601,a)].
% 3.09/3.36 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = A. [resolve(600,a,602,a)].
% 3.09/3.36 603 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.09/3.36 Derived: c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,C,tc_Int_Oint),c_Power_Opower__class_Opower(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(603,a,601,a)].
% 3.09/3.36 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) = A. [resolve(603,a,602,a)].
% 3.09/3.36 604 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.09/3.36 Derived: c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(604,a,601,a)].
% 3.09/3.36 Derived: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = A. [resolve(604,a,602,a)].
% 3.09/3.36 605 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].
% 3.09/3.36 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A)) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,tc_Polynomial_Opoly(A)),c_Power_Opower__class_Opower(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)). [resolve(605,a,601,a)].
% 3.09/3.36 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A)) = B. [resolve(605,a,602,a)].
% 3.09/3.36 606 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 3.09/3.36 607 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 3.09/3.36 Derived: c_Power_Opower__class_Opower(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(606,a,607,a)].
% 3.09/3.36 608 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].
% 3.09/3.36 Derived: c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(608,a,607,a)].
% 3.09/3.36 609 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(A)) | -class_Ring__and__Field_Oidom(A) # labelCputime limit exceeded (core dumped)
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